edi t editor christos h. skiadas - cmsim.net · 2010-09-26 · conference (chaos2010) on chaotic...

Edi t

Editor

Editor

Christos H. Skiadas

June 1 - 4, 2010

Chania Crete Greece

ii

MAICh

Prefecture of Chania

Swets

iii

Introduction

Chaotic Modeling and Simulation International Conference

Chania, Crete (Greece) June 1 - 4, 2010

It is our pleasure to welcome the guests, participants and contributors to the 3nd International Conference (CHAOS2010) on Chaotic Modeling, Simulation and Applications. The study of nonlinear systems and dynamics has emerged as a major area of interdisciplinary research and found very interesting applications. This conference is intended to provide a widely selected forum among Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and in Engineering Sciences.

The principal aim of CHAOS2010 International Conference is to expand the development of the theories of the applied nonlinear field, the methods and the empirical data and computer techniques, and the best theoretical achievements of chaotic theory as well. CHAOS2010 Conference provides a forum for bringing the various groups working in the area of Nonlinear Systems and Dynamics, Chaotic theory and Application for exchanging views and reporting research findings.

We thank all the contributors to the success of this conference and especially the authors of this Book of Abstracts of CHAOS 2010.

Chania, May 2010

Christos H. SkiadasConference Chair

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Honorary Committee

David Ruelle Academie des Sciences de ParisHonorary Professor at the Institut des Hautes Etudes Scientifiques of Bures-sur-Yvette, FranceLeon O. ChuaEECS Department, University of California, Berkeley, USAEditor of the International Journal of Bifurcation and ChaosJi-Huan HeDonghua University, Shanghai, ChinaEditor of Int. Journal of Nonlinear Sciences and Numerical SimulationGannady A. LeonovDean of Mathematics and Mechanics Faculty, Saint-Petersburg State University, RussiaMember (corresponding) of Russian Academy of ScienceFerdinand VerhulstMathematics Faculty, Utrecht, The Netherlands

International Scientific CommitteeC. H. Skiadas (Technical University of Crete, Chania, Greece),

Chair

H. Adeli (The Ohio State University, USA)

J.-O. Aidanpaa (Division of Solid Mechanics, Lulea University of Technology, Sweden)

N. Akhmediev ( Australian National University, Australia )

M. Amabili (McGill University, Montreal, Canada)

J. Awrejcewicz (Technical University of Lodz, Poland)

J. M. Balthazar (UNESP-Rio Claro, State University of Sao Paulo, Brasil)

S. Bishop (University College London, UK)

T. Bountis (University of Patras, Greece)

Y. S. Boutalis (Democritus University of Thrace, Greece)

C. Chandre (Centre de Physique Theorique, Marseille, France)

M. Christodoulou (Technical University of Crete, Chania, Crete, Greece)

P. Commendatore (Universit? di Napoli 'Federico II', Italy)

D. Dhar (Tata Institute of Fundamental Research, India)

J. Dimotikalis (Technological Educational Institute, Crete, Greece)

B. Epureanu (University of Michigan, Ann Arbor, MI, USA)

G. Fagiolo (Sant'Anna School of Advanced Studies, Pisa, Italy)

V. Grigoras (University of Iasi, Romania)

K. Hagan, University of Limerick, Ireland

L. Hong (Xi'an Jiaotong University, Xi'an, Shaanxi, China)

G. Hunt (Centre for Nonlinear Mechanics, University of Bath, Bath, UK)

T. Kapitaniak (Technical University of Lodz, Lodz, Poland)

G. P. Kapoor (Indian Institute of Technology Kanpur, Kanpur, India)

A. Katsirikou, (University of Piraeus, Library) Conference Secretary

A. Kolesnikov (Southern Federal University, Russia)

J. Kretz (University of Music and Performing Arts, Vienna, Austria)

V. Krysko (Dept. of Math. and Modeling, Saratov State Technical University, Russia)

W. Li (Northwestern Polytechnical University, China)

B. L. Lan (School of Engineering, Monash University, Selangor, Malaysia)

V J Law (Dublin City University, Glasnevin, Dublin, Ireland)

V. Lucarini (University of Bologna, Italy)

J. A. T. Machado (ISEP-Institute of Engineering of Porto, Porto, Portugal)

W. M. Macek (Cardinal Stefan Wyszynski University, Warsaw, Poland)

P. Mahanti (University of New Brunswick, Saint John, Canada)

G. M. Mahmoud (Assiut University, Assiut, Egypt)

P. Manneville (Laboratoire d'Hydrodynamique, Ecole Polytechnique, France)

A. S. Mikhailov (Fritz Haber Institute of Max Planck Society, Berlin, Germany)

E. R. Miranda (University of Plymouth, UK)

M. S. M. Noorani (University Kebangsaan Malaysia)

G. V. Orman (Transilvania University of Brasov, Romania)

S. Panchev (Bulgarian Academy of Sciences, Bulgaria)

G. Pedrizzetti (University of Trieste, Trieste, Italy)

F. Pellicano (Universita di Modena e Reggio Emilia, Italy)

S. V. Prants (Pacific Oceanological Institute of RAS, Vladivostok, Russia)

A.G. Ramm (Kansas State University, Kansas, USA)

G. Rega (University of Rome "La Sapienza", Italy)

H. Skiadas (Hanover College, Hanover, USA)

V. Snasel (VSB-Technical University of Ostrava, Czech)

D. Sotiropoulos (Technical University of Crete, Chania, Crete, Greece)

B. Spagnolo (University of Palermo, Italy)

P. D. Spanos (Rice University, Houston, TX, USA)

J. C. Sprott (University of Wisconsin, Madison, WI, USA)

S. Thurner (Medical University of Vienna, Austria)

D. Trigiante (Universit? di Firenze, Firenze, Italy)

G. Unal (Yeditepe University, Istanbul, Turkey)

A. Valyaev (Nuclear Safety Institute of RAS, Russia)

A. Vakakis (National Technical University of Athens, Greece)

J. P. van der Weele (University of Patras, Greece)

M. Wiercigroch (University of Aberdeen, Aberdeen, Scotland, UK)

M. V. Zakrzhevsky (Institute of Mechanics, Riga Technical University, Latvia)

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Keynote Talks

Gennady LeonovMember (corresponding) of Russian Academy of ScienceDean of Mathematics and Mechanics FacultySaint-Petersburg State University, RussiaAttractors, limit cycles and homoclinic orbits of low dimensional quadratic systems

Sergey V. PrantsLaboratory of Nonlinear Dynamical SystemsPacific Oceanological Institute of the Russian Academy of SciencesVladivostok, RussiaDe Broglie-wave chaos

Alexander G. RammMathematics Department, Kansas State UniversityManhattan, KS 66506-2602, USAhttp://www.math.ksu.edu/~rammScattering by many small inhomogeneities

Valentin V. SokolovBudker Institute of Nuclear Physics and Novosibirsk Technical UniversityNovosibirsk, RussiaClassical Versus Quantum Dynamical Chaos: Sensitivity to External Perturbations, Stability and Reversibility

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Contents

Authors Title Page

Mina B. Abd-el-Malek,Hossam S. Hassan

Solution of Burgers’ equation via Lie-group analysis 1

Jan-Olov Aidanpää and Göran Lindkvist

Dynamics of a Rubbing Jeffcott Rotor with Three Blades

1

M. Amabili, K. Karagiozis, S. Farhadi, K. Khorshidi

Nonlinear vibration of plates with different boundary conditions using higher order theory

1

Ivan L.Andronov Chaos, Quasi-Periodicity and Multi-Periodicity in Stars: Mathematical Modeling, Physical Theory vs Astronomical Observations

2

Dorota Aniszewska, Marek Rybaczuk

Exploring process of fibre breaking in NOL samples of composite during quasi-static process of fracture

2

Raina Arora, Nita Parekh Controlling Dynamical Networks 3

Artemyev A.V., Neishtadt A.I., Zelenyi L.M

The peculiarities of the motion of charged particle in space plasma configuration

4

George Atsalakis and Christos H. Skiadas

Forecasting the diffusion of technology 4

Minos Axenides and Emmanouel Floratos

Strange Attractors in Dissipative Nambu Mechanics 4

L.N. Bagautdinova, F.M. Gaisin, E.E. Son

The turbulent phase of the multichannel discharge burning with the electrolytic cathode

5

Zygmunt Bak Modulated fractals as the projections of the (+)-D

fractals

5

Jayanta K. Bhattacharjee, Sagar Chakraborty and Amartya Sarkar

A Methodology for Classifying Periodic Orbits 6

Barbashin M. U. Ethnicity and Ethnic Processes: The Chaos Theory 6

R.Sh.Basyrov, Al.F.Gaysin Turbulent mixing in Gas Vapor Discharge Plasma with jet electrolyte cathode

7

Biri Venceslas, GiroudAnthony

Using chaotic maps for heterogeneous fog rendering in computer graphics

7

Katarzyna Bizon, Gaetano Continillo and Marek Berezowski

Model reduction by empirical spectral methods via sampling of chaotic orbits

7

A. Bogomolov, S. Pavluchenko, A. Toporensky

Escaping rate statistics for two chaotic systems in astrophysics

8

Yu.L.Bolotin, V.A.Cherkaskiy, G.I.Ivashkevich

Over-barrier decay of the mixed state in multi-well potentials

8

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Volodymyr Bondarenko and Iryna Kovalevska

Record keeping of systems of random engineering characteristics of support during calculation of under border stresses of the rocks

9

D. Borgogno, D. Grasso, F. Pegoraro, T.J. Schep

Lagrangian coherent structures in three-dimensional collisionless magnetic reconnection events

9

Wojciech Borkowski & Andrzej Nowak

Can artificial neural networks mimic arbitrary dynamics?

9

Vitalii V. Breus Chaos in Cataclysmic Variables: Spin Pulses in Intermediate Polars

10

O. Cakar, O. O. Aybar, A. S. Hacinliyan, I. Kusbeyzi

Chaoticity in the Time Evolution of Foreign Currency Exchange Rates in Turkey

10

Acilina Caneco, Clara Grácio and J. Leonel Rocha

Symbolic dynamics and chaotic synchronization 12

Alberto Carrassi and Stephane Vannitsem

Accounting for model error in data assimilation 12

N. D. Chavda, V. Potbhare Transition form Poisson to GOE in Finite Interacting Boson System (using one- plus two-body random matrix ensembles with spin)

13

N. D. Chavda, V. Potbhare Average-fluctuation separation in Finite Interacting Boson System (using one- plus two-body random matrix ensembles with spin)

13

N.I. Chernobrovkina Legal chaos as the result of interaction of the institutional order poles

13

Chernous V.V. Social chaos in the process of regional institutional reforms in the South of Russia and the Caucasus

14

Lidia L.Chinarova, IvanL.Andronov

Chaos in Cataclysmic Variables: Outbursts in the UGSS Dwarf Nova Stars

14

Octaviana Datcu, Jean-Pierre Barbot, Adriana Vlad

New Enciphering Algorithm Based on Chaotic Generalized Hé non Map

14

Ezequiel Del Rio, Sergio Elaskar, Jose M Donoso and Luis Conde

Characteristic Relations and Reinjection Probability Densities of Type-II and II Intermittencies

15

Vijay Dhadke Comparative thermal Analysis of disc and drum brake Performance

15

Dick O.E. Multifractal and wavelet analysis of epileptic seizures 16

Yiannis Dimotikalis Application of Local Forecasting Methods to Greek Stock Exchange Data

17

D. Domanska Fuzzy weather forecast in forecasting pollution concentrations

17

N.N. Efimov, A.S. Oshchepkov, А.В. Ryzhkov

Dynamics of burning out of particles of the fuel dust in volume of the fire chamber of the copper

18

P. Oseloka Ezepue, O. Anwar Bé g & Alireza Heidari

Chaos, complexity theory, global financial crisis and the prospects for financial engineering research in (pre-emerging) financial markets: a work -in- progress

18

V.I. Filippenko Resolvents of linear operators, generated by 19

ix

generalized quasi-differential expression

Ruben Fossion, Emmanuel Landa, Victor Velazquez, Alfred U’Ren, Alejandro Frank

The dripping laser: quantum chaos in a phase transition in light

19

Mădălin Frunzete, Adrian Luca, Adriana Vlad

On the Statistical Independence in the Context of the Rössler Map

20

Kenta Fukushima, Vladimir Ryabov

Analysis of homoclinic bifurcation in Duffing oscillator under two-frequency excitation: Peculiarity of usingMelnikov method in combination with averaging technique

21

Gennady G. Galustov Creativity of information systems from the standpoints of synergetics

21

Al.F.Gaysin, Az.F.Gaysin, F.M.Gaysin

Gas-vapour discharge between jet electrolyte cathode and solid anode at low pressures

22

Y. А. Gelozhe, A. V. Semenov

Processes ordering in nonlinear automatic phase control system

22

Αnastasia Georgaki and Cristos Tsolakis

Pre-fractal patterns in Iannis Xenakis’ algorithmic composition: a critical approach

22

G.I. Gerasimov Synergetic potential of developmental education concepts

23

Evgeniya Gerasimova, Oleg Naimark

Structural-scaling transitions and nonlinear chaotic dynamics of DNA ensembles

23

R. Gheisari Forced Chemical Confinement Fusion in Two Layers of Hydrogen Isotopes: Using A Difference Equations Approach

24

Gheisari R., Mohamadsalehi F.

Solution of Time-space Dependent Equations As Balance Transport Equations and Stability of The Numerical Method in Two Layers Reactor Design of Muon Catalyzed Fusion

24

N.M. Glazunov Arithmetic Modelling of Stochastic Dynamics 25

Victor Grigoras, Carmen Grigoras

Time Variant Chaos Encryption 25

Sergey G. Grishchenko, Nataliya N. Kisel

The Computer simulation for electromagnetic properties control of the metamaterial structures

26

Sergey G. Grishchenko, Nataliya N. Kisel’

Quasy-optic simulation of multilayer objects in the problems of the electromagnetism

26

Valerii I. Grytsay Investigation Chaotic Dynamic of Biochemical Process using Lyapunov indices

26

A.R. Guzhova, V.I. Kozlov, V.P. Statsenko, G.S. Firsova, Yu.V. Yanilkin

Comparison of different approaches to shock capturing turbulent flow simulations

27

Kerry L. Hagan Aesthetic Considerations in Algorithmic and Generative Composition

27

Alireza Heidari , O. Anwar Bé g & P. Oseloka Ezepue

AN ANALYTICAL AND NUMERICAL INVESTIGATION OF THE DISSIPATIVE CHAOS IN SEMICONDUCTOR SUPERLATTICES

28

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Alexander E. Hramov, Alexey A. Koronovskii

Unstable periodic spatio-temporal states of spatial extended chaotic systems

28

A.E. Hramov, A.A. Koronovskii, M.K. Kurovskaya, O.I. Moskalenko

Comparison of the Characteristics of Eyelet Intermittency and Type-I intermittency with Noise

29

Mikhail B. Ignatyev The linguo-combinatorial simulation of complex chaotic systems

29

Gabriele Inglese Recovering a vector field with the aid of controlled noise

30

Adela Ionescu Computational standpoint of mixing flows- from turbulence to chaos

30

Mihai Iordache, Lucia Dumitriu, Jean-Marie Paillot, Iulia Dumitrescu

Analysis of Coupled Oscillators Applied to 1-D Antenna Arrays

31

Sajid Iqbal, Kashif Ali Khan, Shahid Iqbal

Understanding Chaos using Discrete-Time Map for Buck Converter

31

V. Jasaitis, F. Ivanauskas and R. Bakanas

Self-ordered front under aperiodically oscillating zero-mean ac force: front dynamics with time delays

31

N. Jevtic, P. Stine, J.S. Schweitzer

Identifying Time-Series Candidates for Efficient Nonlinear Projective Noise Reduction II

32

Audrius Jutas Basic deformation principles based on transformations of atomic systems of crystalline materials

32

Vladimir L. Kalashnikov Dissipative Solitons: Perturbations and Chaos Formation

33

Svetlana Karitskaya Luminescence of structures formed in aqueous alcohol solutions of anthraquinone

33

Marcin Karwinski Nature inspired language modelling for text analysis solutions

34

Rupak Kharel, Krishna Busawon, Z. Ghassemlooy

Modified Chaotic Shift Keying using Indirect Coupled Chaotic Synchronization for Secure Digital Communication

34

O.B. Khavroshkin, V.V. Tsyplakov

Nonlinearity of earth: astonishing diversity and prospects

34

O.B. Khavroshkin, V.V. Tsyplakov

Reducint of seismic vulnerability and short time earthquake prediction: Methods and instruments of nonlinear seismology

35

Khavroshkin O.B., Tsyplakov V. V.

Seismic lunar nonlinearity: peculiarities and Moon as astrophysic and cosmogonic detector

36

Boris Khots and Dmitriy Khots

Chaos problems in Observer’s Mathematics 37

Cha-kyum Kim and Jong Tae Lee

Hindcast of Storm Surge in the South Sea of Korea 37

Ivan Klevchuk Bifurcation of countable number of periodic solutions in singularly perturbed differential-difference equations

37

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R. Kobayashi and V.B. Ryabov

Statistical complexity of low-and high-dimensional dynamical systems II

38

Alexander A. Kolesnikov Space flying vehicles orbital motion control system synthesis: power invariants

38

Alexander A. Kolesnikov Synthesis method for new class of oscillators with inertial nonlinearity

39

Anatoly A. Kolesnikov Synergetics and scientific cognition 39

Alnatoly A. Kolesnikov Problem of synthesis of new natural laws: introduction in the system physics. Synergetics approach (plenary report)

39

Anatoly A. Kolesnikov, Victor A. Kobzev, Phuong Nguyen

The method of adaptive control for amphibian aircraft motion under conditions of external environment extreme action

40

Tatiana A. Kolesnikova Crisis control of risk society: synergetics conception 40

Anatoly Korets, Alexandr Krylov, Evgeny Mironov

Structural Heterogeneity of Detonation Diamond –Containing Material

41

Mustafa Kosem and N. Serap Sengor

An Energy Based Investigation of Chua's Circuit 41

Korniy Kostkin Movement of the linear configuration of the five vortices

41

V.I.Kozlov, A.R.Guzhova, Yu.V.Yanilkin

2D version of modified Nikiforov model 42

Svetlana A. Krasnova, Victor A. Utkin and Anton V. Utkin

Method of State Space Expansion in Non-interacting control

42

Olga D. Kreerenko Adaptive control of the nonlinear dynamic object at the stage of breaking under indefinite contact surface conditions

43

Johannes Kretz Freedom and Necessity in Computer Aided Composition: A Thinking Framework and its Application

43

Alexander M. Krot A nonlinear Schrödinger equation in the statistical theory of spheroidal bodies

44

V.L. Kulinskii, O.O. Chepizhko

On the relation between Vicsek and Kuramoto models of spontaneous synchronization

45

Victor M. Kureychik Electronic computing equipment blocks placement based on synergetics principles

45

Victor M. Kureychik, Veronika I. Pisarenko

Synergetic ideas in innovative education 45

Semen A. Kurkin, Alexander E. Hramov, Alexey A. Koronovskii, Igor I. Magda

Chaotic Oscillations Control in Microwave Virtual Cathode Oscillators

46

I. Kusbeyzi, O. O. Aybar, A. S. Hacinliyan

A Predator - Prey Model with the Nonlinear Self Interaction Coupling xky

47

Andrew A. Kuzmenko Problem of electrical power system nonlinear control synthesis: synergetics approach

48

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Andrew A. Kuzmenko, Vitaly V. Ozerov

Synergetics approach to turbine nonlinear adaptive regulator design

49

A. P. Kuznetsov, N. V. Stankevich

The stabilization of chaos in the Rössler system by pulsed and harmonic signals

49

Kuznetsova D., Sibgatullin I. About transitional processes in penetrative convection 49

Yurij Kyzyurov Dissipation Rate of Kinetic Energy of Turbulence Inferred for the Upper Atmosphere from Sporadic-E Parameters

50

George I. Lambrou, Aristotelis Chatziioannou, Spiros Vlahopoulos, Maria Moschovi and George P. Chrousos

Evidence for Deterministic Chaos in Aperiodic Oscillations of Acute Lymphoblastic Leukemia Cells in Long-Term Culture

51

Boon Leong Lan Testing the different chaotic trajectories predicted by special-relativistic and Newtonian mechanics for a slow-moving dynamical system

51

E. Landa, R. Fossion,1 P. Stransky, I. Morales, V. Velazquez, J.C. Lopez Vieyra and A. Frank

Scale Invariance in Chaotic Time Series: Classical and Quantum Examples

52

Rosário Laureano, Clara Grácio, Diana A. Mendes

Research of chaotic synchronization phenomena on the field of visual processes in ophthalmology

52

Rosário Laureano, Diana A. Mendes and Manuel A. Martins Ferreira

Asymptotic and practical synchronization of one-dimensional chaotic quadratic maps using a non-symmetric coupling

52

V J Law, C E Nwankire, D P Dowling and S Daniels

Acoustic Emission within an Atmospheric Helium Corona Discharge Jet

53

Michał Ławniczak, SzymonBauch, Oleh Hul, and LeszekSirko

Experimental investigation of the cross-correlation function and the enhancement factor for graphs with and without time reversal symmetry

54

I.G. Lebo, A.I. Lebo The model of energy transport in turbulent under critical laser plasma of porous target

54

Gennady A. Leonov Attractors, limit cycles and homoclinic orbits of low dimensional quadratic systems

55

G. Litak, R. Rusinek Dynamics of Steel Turning by Recurrence Plots 55

N.A.Loginov, Az.F.Gaysin, F.M.Gaysin, E.E.Son , Al.F.Gaysin

Multichannel discharges between turbulence current and porous material

56

Anatoliy V. Lubskiy Non-classical model of historical research and synergetic ideas

56

Valerio Lucarini, Klaus Fraedrich

Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

56

Wieslaw M. Macek Multifractal Turbulence in the Solar System Plasma 57

Vlad Maftei, Victor Grigoras Sensitivity Analysis of Chaos Synchronization in 58

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Colpitts Oscillators

Rakesh Mahla, Manish Shrimali, Anup Poonia, Chirag Jain

Random network of coupled chaotic maps for economic dynamics

58

Andrew A. Kuzmenko, Vitaly V. Ozerov


59

M.B. Marinov The constructive potential of social chaos in modern society: regional peculiarity

59

Amirhossein Davaie Markazi, Ali Abbasi

Dynamical Analysis of AFM Micro-Cantilever and Control of Its Chaotic Behaviour via AFSMC Algorithm

59

George Matalliotakis,Christos H. Skiadas , Vardoulaki Maria

Dynamic Modelling and Comparative Analysis for Life Table Data of non-European Countries

60

Radu Matei, Carmen Grigoras

Nonlinear Dynamics in CNN’s with Second Order Cells

60

Massimo Materassi Mutual Information and Dynamics 61

Oleg Yu. Mayorov, Vladmir N. Fenchenko

Reliability of bioelectric activity (EEG, ECG and HRV) researches of the deterministic chaos by the nonlinear analysis methods

61

E.E. Meshkov Shock tube investigations of the instability of a two-gas interface accelerated by a shock wave

62

Larisa A. Minasyan Concept of “self organization” in the light of cosmological problems

62

Eduardo Miranda and Jaime Serquera

Algorithmic Sound Composition using Coupled Cellular Automata

63

Olga I. Moskalenko, Alexey A. Koronovskii, Alexander E. Hramov, Svetlana A. Shurygina

Analysis of generalized synchronization in mutually coupled dynamical systems

63

Banibrata Mukhopadhyay Search for chaos in black holes and neutron stars 65

Iryna V. Musatenko Investigation Chaotic Dynamics of Nonlinear System 65

Alexey S. Mushenko Nonlinear adaptive control for aircraft flight under chaotic wind disturbances

65

T.B.Mustafin, Al.F.Gaysin, F.M.Gaysin

Turbulent mixing in gas-vapor discharge plasma with jet electrolyte anode

66

Anis Naanaa, Zouhair BenJemaa and Safya Belghith

Chaotic vs Classical Codes for Synchronous TH-UWB Multiple-Access System in IEEE 802.15.4a Multi-path Channel

66

Vera I. Nemchina The crisis communication in the space of social chaos 66

Umberto Neri and Beatrice Venturi

ON BIFURCATIONS TO LEADING TO CHAOS IN IS-LM MODEL

67

N.Mohammad Nouri, Alireza Mofidi, Seyyed Mohammad

Large Eddy Simulation of Turbulent Drag Reduction over Hydrophobic Surfaces

67

xiv

Amin Kariminia

N. Mohammad Nouri, Seyyed Mohammad Amin Kariminia, Alireza Mofidi

Investigation of Performance of Different Sub-grid Scale Models in Improvement of 3D Large Eddy Simulation of Turbulent Near Wall Boundary Layer

67

Tomasz Nowicki Asymptotic behavior and limit sets of piecewise izometric transformations derived from an Error Diffusion algorithm

68

Ryo Onishi, Yuya Baba and Keiko Takahashi

Efficient Large-Scale Forcing in Finite-Difference Simulations of Steady Isotropic Turbulence

68

Gabriel V. Orman On a Problem of Approximation of Markov Chains by a Solution of a Stochastic Differential Equation

69

Jiaqing Pan An ill-posed problem of determining nonlinearity in diffusion process

69

U. Paniveni, V.Krishan, Jagdev Singh , R.Srikanth

Supergranular Activity Dependence 69

Leonidas Pantelidis The complete solution for the classical four-spin Heisenberg ring

70

Supriyo Paul, Sandeep Reddy, Pankaj Wahi and Mahendra K. Verma

A bifurcation scenario for large-P Rayleigh-Benard Convection

70

Ivan M. Pershin Data processing distributed systems 70

Andrey N. Popov Synergetic Synthesis of Energy Saving Control Systems for Electromechanical Processes

71

Eleri A. Pound Chaos as Compositional Order 71

G.P. Pavlos, A.C. Iliopoulos, L.P. Karakatsanis, V.G. Tsoutsouras, E.G. Pavlos

Complexity Theory: from Microscopic to Macroscopic level, Concepts and Applications

72

Vinicio Pelino, Filippo Maimone

Energy cycle for the Lorenz-63 attractor 72

Dinis D. Pestana, J. Leonel Rocha and Sandra M. Aleixo

Regular variation, Paretian distributions, and the interplay of light and heavy tails in the fractality of asymptotic models

73

R. Petritsch, S.A. Pietsch Assessing ergodic properties of ecological time series 74

S.A. Pietsch, R. Petritsch The Ergodic View of Ecosystem Behaviour 74

Dmitry Pikulin Tools for Investigation of Dynamics of DC-DC Converters within Matlab/Simulink

74

S.V. Prants De Broglie-wave chaos 75

E.P. Prokopev Synergetic approaches to problems of evolution of properties of materials and nanomaterials of the basis of silicon

75

M.V. Ragulskaya , V.V. Pipin The chaos and order in human ECG under the influence of space weather and other external factors

76

Alexander G. Ramm Scattering by many small inhomogeneities and applications

77

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J. Leonel Rocha, Sandra M. Aleixo and Dinis D. Pestana

Beta(p,q)-Cantor Sets — Determinism and Randomness

77

Paola Rodriguez Imazio and Pablo Mininni

Cancellation exponents in helical and non-helical flows

78

Vladimir B. Ryabov Predicting chaos with second method of Lyapunov 78

Zaynab Salloum Existence results for flows of slightly compressible viscoelastic fluid in a singular bounded domain

79

H.Samadzadeh, B. Abdi Simulation and FEM Analysis of Batch Sugar Centrifuge Shaft

79

A.M.Selvam Universal Inverse Power law distribution for Fractal Fluctuations in Dynamical Systems: Applications for Predictability of Inter - annual Variability of Indian Region Rainfall

80

Babak Shokri, Leila Rajaei,Sedighe Mirabotalebi

Transition of electromagnetic wave through a warm overdense plasma layer

80

A.Yu. Shvets, V.A. Sirenko Variety of chaotic behaviour of the deterministic nonideal hydrodynamic systems

81

Christos H. Skiadas A Model of Conflicting Populations for the study of Stock Markets

81

Christos H. Skiadas and Charilaos Skiadas

Chaotic Modeling: Lessons and developments during the last decades

82

Sunantha Sodsee, Maytiyanin Komkhao, Zhong Li

Leader-Following Discrete-Time Consensus Protocol on a Buyer-Seller Network

82

Valentin V. Sokolov, Oleg V. Zhirov and Yaroslav A. Kharkov

Classical Versus Quantum Dynamical Chaos: Sensitivity to External Perturbations, Stability and Reversibility

82

Anastasios D. Sotiropoulos Composing Chaotic Music from the Letter m 83

Dimitrios A. Sotiropoulos On Logistic-Like Iterative Maps 84

Dimitrios A. Sotiropoulos On the Timbre of Algorithmic Chaotic Sounds 85

Vaggelis D. Sotiropoulos The Rainbow Effect on Composing Chaotic Algorithmic Music

85

Banlue Srisuchinwong and Buncha Munmuangsaen

A Highly Chaotic Attractor for a Dual-Channel Single-Attractor, Private Communication System

86

Banlue Srisuchinwong, Teerachot Siriburanon, and Teera Nontapradit

Compound Structures of Six New Chaotic Attractors in a Modified Only-Single-Coefficient Jerk Model Based on Sinh-1 Nonlinearity

86

K. Stasiewicz, M. Strumik, B. Thidè

Observations and modeling of chaos and solitons in quasi-parallel bow shocks

86

Pavel Stránský, Michal Macek, Pavel Cejnar, Alejandro Frank, Ruben Fossion, Emmanuel Landa

Manifestation of chaos in collective models of nuclei 87

Tadeusz (Ted) Szuba Importance of the Chaos for computational processes of Collective Intelligence in social structures

87

xvi

Reza Taghavi Zenouz and Farzin Ghanadi

Experimental and Numerical Investigations of Flow Incidence Effects on Surface Pressure Distributions of Axial Compressor Blades

88

Yuri V. Talagaev and Andrey F. Tarakanov

Superstability and Optimal Matrix Correction of the Class of Chaotic Systems

88

Sedat Tardu Imperfect phase syncronization of the wall turbulence: Experiments and direct numerical sumulations

89

Siavash Tayefi and Abdolreza Ohadi

Investigating the effect of structural properties on bifurcation and chaotic behavior of passive walking biped with an upper body

89

Horia-Nicolai Teodorescu and Victor Cojocaru

Complex Signal Generators based on Capacitors and on Piezoelectric Loads

90

S.F. Timashev, Yu.S. Polyakov, S.G. Lakeev

Anomal diffusion” in the dynamics of complex processes

90

V.A. Timofeeva, A.B. Solovieva, Misurkin P.I., S.F. Timashev

Parameterization of atomic force microscopy chaotic images

91

Dmitry V. Timoshenko Problem of search of the first integrals in nonlinear dynamics tasks

91

Polina P. Tkachova From chaos to self-organization: structure and system of the poetic literary text

92

Pichitra Uangpairoj and Kontorn Chamniprasart

Numerical Simulation and Wall Shear Stress Analysis of Pulsating Flow in the Channel of Plate Heat Exchanger

92

David Urminsky Shadowing unstable orbits of the 3-body problem 93

Maksim A. Vaskov Chaos in corporate governance systems: typology, characteristics and overcoming ways

93

Venger, E. F., Lokshyn, B. and Maslov V.P.

Glue composition containing micro- and nanosized fillers

93

Anna Vereshchagina The crisis of traditional family and the alternatives of the family institution development in different regions of Russia: theoretical analysis in the network of synergetic paradigm

93

Gennady E. Veselov Nonlinear complex system’s hierarchical control strategies synthesis tasks

94

Gennady E. Veselov Nonlinear complex system’s hierarchical control strategies synthesis tasks

94

Natalia A. Virnina Chaos in Cataclysmic Variables: Superhumps in the UGSU Dwarf Nova Stars

94

Yuri G. Volkov The ideas of synergy and Russian identity 95

Vyklyuk Yaroslav Mathematical simulation of urbanization processes based on analogies with physical fractals

95

Pankaj Wahi, Pankaj K. Mishra, Pinaki Pal, Supriyo Paul, Mahendra K. Verma.

Patterns and Chaos in low- and zero-Prandtl number convection

95

xvii

C. L. Xaplanteris and E. Filippaki

Drift waves’ synchronization by using an externalsignal. The stabilization of a chaotic plasma turbulence

96

Vilor L. Zakovorotny The Interrelation Between Irreversibility and Evolution in the Dynamics of Electrical-Mechanical Systems in the Process of Friction and Cutting-Processing

96

G. Žibret & T. Verbovšek Chaos game technique as a tool for the analysis of natural geomorphological features

96

Author Index 97-

3rd Chaotic Modeling and Simulation International Conference, 1-4 June 2010, Chania Crete Greece

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Solution of Burgers’ equation via Lie-group analysis

Mina B. Abd-el-Malek a, Hossam S. Hassan ba Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria

University, Alexandria 21544, Egypt, [email protected] Department of Basic and Applied Science, Arab Academy for Science, Technology and

Maritime Transport, P.O.BOX 1029 Alexandria, Egypt, [email protected]

An analysis for Burgers’ equation is performed via symmetry analysis. We study the Burgers’ equation with two cases for the kinematic viscosity. Firstly, with unity kinematic viscosity. Secondly, with time-dependent kinematic viscosity. By employing Lie-group method to the Burgers’ equation, the symmetries of the equation are determined. Using these symmetries, an exact solution, in case of unity kinematic viscosity, is found analytically. For the time-dependent kinematic viscosity, the resulting differential equation is solved numerically using shooting method coupled with Runge-Kutta scheme and the results are plotted. Keywords: Burgers’ equation; Lie-group; Symmetries MSC: 35Q53; 76M60; 37L20

Dynamics of a Rubbing Jeffcott Rotor with Three Blades

Jan-Olov Aidanpää and Göran LindkvistLuleå University of Technology, Luleå, Sweden

Email: [email protected] ,[email protected]

The non-linear behaviour of rubbing cylindrical rotors have been studied in several papers. In such systems rich dynamics have been found for frequencies above the natural frequency. Below natural frequency the solution was found to be stationary. In this paper the influence of blades is studied. A Jeffcott rotor with three blades is used and the contacts are described by large displacement beam theory. The model shows that no stationary point will exist and complex behaviour will occur below the natural frequency. For the studied rotor, failure due to high stresses will occur at driving frequencies below 50% of the natural frequency and instability at 80% of the natural frequency. The paper shows that the dynamics of bladed rotors differs from the dynamics of rubbing circular rotors. If a bladed rotor is used it is essential to study a model with blades. Otherwise the general conclusions on the dynamics can be wrong.Keywords: rotor, dynamic, impact, rubbing, beam, blade.

NONLINEAR VIBRATION OF PLATES WITH DIFFERENT BOUNDARY CONDITIONS USING HIGHER ORDER THEORY

M. Amabili1, K. Karagiozis1, S. Farhadi2, K. Khorshidi31Department of Mechanical Engineering, McGill University,

817 Sherbrooke Street West, Montreal, Qué bec, H3A 2K6, Canada2Department of Mechanical Engineering, Kurdistan University, Tehran, Iran

3Department of Mechanical Engineering, Iran University of Science and Technology,Narmak, Tehran 16846-13114, Iran

Numerous applications of plate structures may be found in aerospace and marine engineering. The present study is a continuation of the work by Amabili and Sirwan [1] extending their investigation to laminate composite rectangular plates with different boundary conditions subjected to an external point force. The excitation frequency lies within the neighbourhood of the fundamental mode of the plate. The analysis is performed using three

CHAOS 2010, Book of Abstracts

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different nonlinear plate theories, namely: i) the classical Von Kárman theory, ii) first-order shear deformation theory, and iii) third-order shear deformation theory. The plates are tested using three sets of boundary conditions: a) classical clamped boundary conditions, b) simply-supported ends with immovable edges, and c) simply-supported ends with movable boundaries. The results discuss the limitations associated with using lower order theory to describe the large-amplitude oscillations of plates, investigate the effect of boundary conditions highlighting the different responses obtained from using isotropic or laminate composite rectangular plates and indicate chaotic oscillations observed for specific values of the excitation force. 1. Amabili, M., Farhadi, S., Shear deformation versus classical theories for nonlinear vibrations of rectangular isotropic and laminated composite plates, Journal of Sound and Vibration 320 (2009) 649-667.

Chaos, Quasi-Periodicity and Multi-Periodicity in Stars: Mathematical Modeling, Physical Theory vs Astronomical Observations

Ivan L.AndronovAstronomical Observatory, Odessa National University, Odessa, Ukraine

We review processes, which take place in variable stars of different types - cataclysmic, eruptive, pulsating, eclipsing, elliptic, spotted etc (totally 70+ types). Many variable stars exhibit features characteristic for different classes. The situation becomes much more complicated in different types of interacting binary stars which may be characterized by a variety of combinations of types of intrinsic variability of one or both stellar components, superimposed onto their rotation and presence of the accreting structures - stream, disk, column. The main types of variability may be classified as "mono-periodic" (often "multi-harmonic"), "multi-periodic" (simultaneously acting or alternatively switching modes), "quasi-periodic", "irregular", "random" ("shot noise"). A high impact to the variability is from the chaotic processes. Theoretical models are reviewed. From the observational point of view, the separation of contributions of chaotic and non-chaotic contributions is complicated due to an irregular distribution of arguments of the astronomical signals, which are either relatively short discrete runs (of space or ground-based observations) separated by large gaps, or irregularly spaced "Sky Patrol" observations from point-source or wide-field photometric monitoring.For this purpose, we have elaborated a series of algorithms and programs, which are parts of our expert system of advanced methods for the time series analysis of mono-channel and multi-channel signals. This expert system was applied to 1300+ variable stars of different types according to the international campaign "Inter-Longitude Astronomy" (ILA). The highlights of theoretical and observational results are presented.

Exploring process of fibre breaking in NOL samples of composite during quasi-static process of fracture

Dorota Aniszewska(1), Marek Rybaczuk(2)

Institute of Materials Science and Applied MechanicsWroclaw University of Technology, Wroclaw, Poland

Email: (1) [email protected](2) [email protected]

This paper presents numerical methods of modelling composites, which allow observation of composite fibre breaking during static loads without using invasive experimental methods. Our simulations are based on cellular automata, which is an alternative method to study behaviour of dynamical systems. We assume defects evolution in composite as a dynamical system depending on external and internal forces and properties of fibres.

We examine fibre breaking in nol samples of fibre reinforced composite with constant


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matrix-fibres interaction. Each long fibre is build with hundreds of cellular automata. Under force F fibre can break if force exceed minimal value. Probability of breaking randomized for every cellular automata is compared with function of fatigue properties of single fibre described with Weibull distribution. Fibres can interact with each other in neighbourhood with certain (correlation) radius. Any broken parts of other fibre entails additional stress concentration. Broken fibre is weakened along and force is higher in the adjoining fibres. The simulations were performed for the same size of specimen with various correlation radius and various velocity of force growth.

Our final goal is exploring of defects evolution and formulating them in terms of fractals. Fractal geometry is able to describe the complexity of defects in composite, as in any other material, using fractal dimension and their size with fractal measure. This paper presents partially results of our continuous work of examination defects evolution with dynamical systems methods. This approach lets us answer the question if defects growth can be chaotic.Keywords: Cellular Automata, Fractal measure, Fractal dimension, Chaos.

Controlling Dynamical Networks

Raina Arora and Nita ParekhCenter for Computational Natural Sciences and Bioinformatics

International Institute of Information Technology, [email protected]

Two classes of networks that have been extensively studied in the analysis of physical systems are: (i) regular networks, wherein each node interacts with a specified number of neighboring nodes on geometrical lattices, and (ii) random networks, wherein every pair of nodes have a fixed probability of interacting with each other. Recently much attention is being focused on a class of network models that are neither strictly regular nor completely random, but are somewhere in-between and exhibit properties of both, called small world networks. These networks are shown to exhibit high clustering (i.e., nodes sharing a common neighbor have a higher probability of being connected to each other than to other nodes) and a low average path length (the average of the shortest distance/path between every pair of nodes in the network). Examples for small-world networks are found to occur widely across the biological (e.g., neural connection patterns), social (e.g., friendship network, co-authorship) and technological (e.g., the world wide web) domains. Also it has been observed that a large number of real complex systems exhibit power-law behaviour in their degree distribution, i.e., a few nodes have a very high degree. Such networks are referred to as scale-free networks. Thus, non-standard topologies with long-range connections (i.e., non-local diffusion) and uneven degree distributions are not uncommon in real-life systems and may provide different kinds of spatiotemporal dynamics depending on the extent of non-local diffusion. Here we discuss the characterization and control of spatiotemporal dynamics on four different network topologies, viz., (i) regular, (ii) random, (iii) small-world, and (iv) scale-free by external perturbation or pinning a few nodes in the network. This would provide us insight into the role of the network topology (the underlying connectivity structure) on the dynamics of the systems defined on such networks and the efficacy with which the dynamics can be the controlled or manipulated.An extensively studied example of a nonlinear system exhibiting a wide variety of complex dynamics ranging from simple periodic behavior to chaos is the logistic map. Here we define coupled logistic maps on the four different topologies and systematically investigate the control by external perturbation/pinning for two chaotic regimes: (i) r = 3.6 (weak-chaos), and (ii) r = 3.9 (strong chaos). Our preliminary results show that pinning nodes at regularly spaced intervals, 2nd, 4th, etc., the pinning strength required on a small-world network is similar to that in case of regular networks. For 25% of the nodes pinned, the dynamics on the scale-free topology is controllable but on random networks, it is not. However, on pinning nodes having high centrality measures, viz., degree, betweenness and closeness, we observe that control of the spatiotemporal dynamics is achieved, by pinning only 10% of high degree/ betweenness nodes in low chaotic regime on both small-world and scale-free networks. Complete control of the network is not observed on pinning nodes with high closeness values.


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For strongly chaotic dynamics, control is achievable only on scale-free networks on pinning 20% of nodes having either high degree, betweenness, or closeness values.

Key Words: Dynamics, Control, Topologies, Coupled Logistic Maps, Chaos, Regular, Smallworld, Random, Scale-free networks, Centrality

The peculiarities of the motion of charged particle in space plasma configuration

Artemyev A.V. (Space Research Institute, RAS), Neishtadt A.I. (Space Research Institute, RAS and Loughborough Univ., UK), Zelenyi L.M. (Space Research Institute, RAS)

Space Research Institute, RAS, Moscow, [email protected]

Earth’s magnetotail has complicated magnetic structure with a sharp magnetic field reversal.We consider charge particle motion in this strongly inhomogeneous magnetic field which is important for the understanding both of the global dynamic of solar- terrestrial system and microphysical effects of particle acceleration. There is a small parameter in the system: ratio between curvature radius of magnetic field lines and particle gyroradius and particle motion can be separated into fast and slow parts. In the course of fast motion the corresponding adiabatic invariant is approximately conserved. The case of classical field reversals where magnetic field has linear dependence on coordinates in the vicinity of a neutral plane has been thoroughly studied earlier. However recent spacecraft measurements indicated that space current sheets might have more complicated bifurcated structure where magnetic field has cubic dependence on coordinates. In our work we have derived the analytical expressions both for values of adiabatic invariant and its jumps and analyse the peculiarities of particle motion in this new more “exotic“ configuration.This work was supported in part by the RF Presidential Program for State Support of Leading Scientific Schools (project no. NSh-472.2008.2) and the Russian Foundation for Basic Research (project nos. 09-01-00333). Key Words: plasma, particle nonlinear motion, chaos, separatrix crossing

Forecasting the diffusion of technology

George Atsalakis and Christos H. SkiadasData analysis and Forecasting Laboratory

Technical University of [email protected]

In this paper we give several aspects of the innovation diffusion modeling applied to some cases of technology diffusion. Especially the varying saturation level is explored and a method is proposed to improve the fitting and forecasting performance of the related diffusion models. Illustrative examples are given along with characteristic graphs.

Strange Attractors in Dissipative Nambu Mechanics

Minos Axenides and Emmanouel FloratosInstitute of Nuclear Physics NCSR Demokritos, Agia Paraskevi, Attiki, Greece

[email protected]

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in R3 phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and Rössler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting


5

surfaces, the so called Nambu Hamiltonians. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors.Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantizationof the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian N x N matrices in R3. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the 3N2 dimensional phase space. Key Words: Strange Chaotic Attractors, Dissipative Nambu Mechanics

The turbulent phase of the multichannel discharge burning with the electrolytic cathode

L.N. Bagautdinova, F.M. Gaisin, E.E. SonKazan State Technical University nam.A.N.Tupolev, Kazan, Russia

[email protected]

With the passage of electrical current through the electrolytic cell that contains two metal electrodes, one of which (active electrode) has a much smaller surface than the second, at a gradual increase in the voltage across the electrodes causes the different phases of the process. The first phase of the process in the range of voltage U = 10-40V, which is observed on the active electrode is a conventional electrolysis, when is occur gas emission and transference of the metal ions depending on the composition of the electrolyte and electrode material. The increase the voltage of discharge up to U = 60-70B leads to the formation of the stable stationary vapor-gas shell. In the third phase of the process at voltages above U> 80V observed a transition in turbulent regime, characterized by disruption of the vapor-gas shell and there is an intensive mixing of electrolytic-plasma environment. Based on the experiment! al data was describe the mechanism of interruption of current at the turbulent phase of theprocess of the plasma burning. Key Words: the multichannal discharge, Rayleigh-Taylor instability, turbulent mixing

Modulated fractals as the projections of the (+)-D fractals.

Zygmunt BakInstitute of Physics, Jan Dlugosz University, Czestochowa Poland.

Email: [email protected]

Although physical systems modeled by fractals are non-translation-invariant it is well-known fact that the self-similar fractals as well as the physical quantities on fractal substrates show log-periodicities. This opens a possibility to describe the symmetries of some self-affine fractals in the way that is reminiscent of conventional formalism developed for crystalline systems. Motivated by this fact we present the study of fractal scaling symmetry, which is similar in spirit to the solid state theory. We limit our considerations to the systems which show multi-scale self-similarity [1]. The effective space can be obtained as a projection or expectation value of a higher-dimensional space. Independently, there exist inverse approaches, when from the image of a projection we want to draw some conclusions concerning properties of the original, higher-dimensional, fractal system. The need to asses the higher-dimensional fractal dimension of fractal systems basing on their 2-D projections is very frequent in many areas of physics. This


6

necessity is generated by many experimental techniques, when we obtain images of e.g., X-ray or optic projections of fractal systems. In some cases lower dimensional and/or fractal solutions of the system evolution can be used to construct exact solutions of higher-dimensional integrable model [2]. The fact that some physical phenomena uncover the full fractal symmetry in the (+)-D space, which is invisible in the lower dimensional D space, has been noticed earlier e.g., in high-energy physics [1]. In our study, by considering some non-orthogonal projections of conventional fractals onto the plane we define a new family of hierarchical structures which we call as the modulated fractals. We show one to one correspondence between a set of linear scaling transformations inherent to 3D fractals and some 3D crystals, a problem discussed earlier in [3]. With the use of derived isomorphism we introduce the idea of a new class of geometrical objects -modulated fractals, which exactly match (in the log scale) some modulated crystal (supercrystal) lattices. Basing on the analogies with the supercrystals we prove that nD modulated fractals with k-modulations can be treated as the conventional fractals within the (n+k)-dimensional space projected onto the nD space. Further, we show that modulated fractals provide a natural link between ordinary fractals and multifractals. Finally we show how the concept of fractional analysis is applied in the description of the (modified) dynamics of physical phenomena in fractal systems.

[1] W. Yuanfang, Z. Yang, L. Lianshou, Phys. Rev. B 51 (1995) 6576.

[2] X. Tang, S. Lou, Y. Zhang, Phys. Rev.B 66 (2002) 046601.

[3] Z. Bak, R. Jaroszewicz, Eur. J. Phys. B 64 (2008) 231

A Methodology for Classifying Periodic Orbits

Jayanta K. Bhattacharjee1,a, Sagar Chakraborty2,b and Amartya Sarkar1,c

1 S. .N. B. N. C. B. S., JD-Block, Sector-III, Salt Lake, Kolkata-982 NBIA, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.

a Email: [email protected] Email: [email protected]

c Email: [email protected]

We propose a unified methodology, based on renormalization group theory, for finding out existence of periodic solutions in a plethora of nonlinear dynamical systems appearing across disciplines. The technique will be shown to have the non-trivial ability of classifying the solutions into limit cycles and periodic orbits surrounding a center.Key Words: Limit cycle, Center, Renormalization group, Two-dimensional dynamical systems.

Ethnicity and Ethnic Processes: The Chaos Theory

Barbashin M. U.Southern Federal University,

105/42, Bolshaya Sadovaya str., Rostov-on-Don, 344006, Russia; [email protected]

To implement new reforms in ethno-social and ethno-political sphere one needs as to understand the social role and instrumental meaning of ethnicity as to study ethnic processes from the chaos theory. Social researchers, experts and politicians are interested in the understanding of the chaos processes of regional and ethnic communities formation. The Chaos Theory is a new methodological direction in Social Sciences, but inadequate sociological analysis of ethnic processes from the point of key methodological positions of the chaos theory is not allowed to implement preventive social measures against the ethno-separatism and ethno-religious extremism.


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TURBULENT MIXING IN GAS-VAPOR DISCHARGE PLASMA WITH JET ELECTROLYTE CATHODE

R.Sh.Basyrov, Al.F.GaysinKazan State Technical University, Kazan, Russian Federation

[email protected]

Mixing of electrolyte and discharge plasma is studied. The discharge burning between jet electrolyte cathode and metal anode at pressures p = 7.6 – 608 Torr, jet lengths d = 3.0 – 5.0 mm, is considered. Saturated solutions of NaCl in water were used as electrolyte. The flow rate of the jet was in the range G = 2.0 – 4.5 g/s. The experiments show that a cone shaped glow discharge engulfing the jet is formed. A diffuse glow discharge is observed at the tip of the jet. The electrolyte jet gets curling motion with pressure increase from 7.6 to 304 Torr. A glow discharge burns also on the metal anode surface. The burning character of the discharge changes with time. A multichannel discharge is observed at the end of the jet. The glow discharge burns higher along the jet which transforms to multichannel discharge at p = 304 Torr. Further increase of pressure from 304 to 608 Torr leads to a complete transition fro! m glow to multichannel discharge with turbulent mixing in electrolyte jet. Key Words: plasma; discharge; turbulent mixing; electrolyte

Using chaotic maps for heterogeneous fog rendering in computer graphics

BIRI Venceslas, GIROUD AnthonyUniversite Paris Est LIGM, Champs / Marne, France

[email protected]

Computer graphics aim at representing realistic virtual universe. And chaotic and fractal behaviours are current in nature, so researches in computer graphic use frequently chaos theory to represent natural phenomena. The advantage being that chaotic equations are often quite simple to compute and offer continuous evolution that, we believe, can be seen as natural. We follow this idea in an exploratory research to represent heterogeneous fog in large virtual outdoor scene. Our method generates, using any chaotic map, a “fog map” representing the different density of fog in the scene. After blurring this image, we reconstruct a density field function using wavelet base functions. Finally, we render the fog using the fogmap into the virtual world. Thanks to chaotic map, we can animate continuously the fog in changing initial parameters (like changing the constant c in the complex quadratic maps (Julia Set)). We will also look for iterated functions related to fluids dynamic representing more closely fog phenomenon. Key Words: computer graphics, chaotic maps, fog

Model reduction by empirical spectral methods via sampling of chaotic orbits

Katarzyna Bizon1, Gaetano Continillo2 and Marek Berezowski3

1Instituto di Ricerche sulla Combustione CNR, Naples, Italy, [email protected]à del Sannio, Department of Engineering, Piazza Roma 21, 82100 Benevento, Italy

3Silesian University of Technology, Faculty of Mathematics and Physics, ul. Kaszubska 23, 44-100 Gliwice, Poland

In this work, Proper Orthogonal Decomposition (POD) coupled with spectral Galerkin is applied to the one-dimensional transient distributed model of a tubular reactor with an external heat recycle for energy recovery, which generates complex oscillatory – periodic and chaotic – profiles of temperature and conversion degree. In particular, the effect of the cooling medium temperature onto system dynamics is considered.


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The model described by partial differential equations is first approximated with a cascade of a Continuous Stirred Tank Reactors (CSTR), to deliver a reference solution and samples for the determination of the POD basis. This leads to a relatively high order of the ordinary differential equations system, which is then reduced by employing the spectral Galerkin method. The issue of the optimal construction of the POD basis is addressed by sampling of the chaotic orbits with the aim of constructing a reduced order model (ROM) able to capture the global attractor of the system. In order to demonstrate that such orbits are the most appropriate for the determination of the POD basis, because they incorporate the maximum amount ofinformation about the system behavior, the information entropy of the orbit is defined and calculated for varying cooling temperature.It is shown that sampling of the chaotic solutions allows for the determination of the POD basis that, when employed in the POD/Galerkin method, delivers accurate solutions, even for values of the parameter for which the model behavior is far from chaotic, i.e. periodic orbits or fixed points. The reverse does not apply – sampling of the periodic orbits or fixed points doesnot allow for the approximation of the chaotic dynamics. Key Words: chemical reactor modeling, proper orthogonal decomposition, reduced order modeling, bifurcation analysis

Escaping rate statistics for two chaotic systems in astrophysics

A. Bogomolov, S. Pavluchenko, A. ToporenskySternberg Astronomical Institute, Moscow, Russia

[email protected]

We consider escaping rate statistics for two famous Hamiltonian chaotic systems in astrophysics -- three-body problem and cosmological dynamics in the presence of a scalar field. The phase space of these systems are known to contain islands of regular dynamics surrounded by a chaotic "sea". Presence of such islands usually leads to power-law tails in N(t) distributions, where N is the number of trajectories which did not escape the system after time t. We describe the transitions from exponential to power-law decay of the function N(t) for systems under investigations and show how indexes of these power-law tails depend on parameters of the system. Key Words: Hamiltonian dynamics, three-body problem, cosmology

Over-barrier decay of the mixed state in multi-well potentials

Yu.L.Bolotin, V.A.Cherkaskiy, G.I.IvashkevichNational Scientific Center "Kharkov Institute of Physics and Technology"

1 Akademicheskaya Str., Kharkov, 61108 [email protected]

Classical escape in 2D Hamiltonian systems with the mixed state has been studied numerically and analytically. The wide class of potentials with the mixed state is presented by polinomial potentials. In potentials, where the mixed state could be realized, i.e. the configuration space contains regions of both regular and chaotic motion, escape problem has a number of new features. In particular, some local minima become a trap with number of particles depending on energy and other values that characterize the ensemble of particles. Choosing the form of initial ensemble one chooses the set of parameters that determine the number of trapped particles.Numerical simulations involved in the research are heavily based on usage of GPU's technology. This allows to dramatically reducing computation time and increase the size of the ensembles. Key Words Hamiltonian chaos, escape, GPGPU


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Record keeping of systems of random engineering characteristics of support during calculation of under border stresses of the rocks

Volodymyr Bondarenko and Iryna KovalevskaNational Mining University of Ukraine, Dnipropetrovsk, Ukraine

Coal extraction is the strategic component of energy security for Ukraine and it guarantees stable development of Ukraine’s metallurgical sector. But most of the mines of Ukraine have been functioning under extremely hard mining-geological conditions and that needs complex support schemes to be used. In order to find an optimal support for openings, some calculating experiments are being conducted in National Mining University of Ukraine, and the method of finite elements implementation is in the basis of these experiments.

Lagrangian coherent structures in three-dimensional collisionless magnetic reconnection events

D. Borgogno, D. Grasso, F. Pegoraro, T.J. SchepBurning Plasma Research Group, Politecnico di Torino, Torino, Italy

[email protected]

We apply the Finite Time Lyapunov Exponents (FTLE) technique as an effective tool for investigating the development of a chaotic magnetic field in the presence of magnetic reconnection. Searching for the ridges of the FTLE field, we identify when local chaos develops the Lagrangian coherent structures as the barriers to the magnetic field line transport. It is shown that these barriers cease to exist when the transition to global chaos occurs.Key Words: Plasma physics, magnetic reconnection, Lagrangian coherent structures, finite time Lyapunov exponents

Can artificial neural networks mimic arbitrary dynamics?

Wojciech Borkowski & Andrzej NowakUniversity of Warsaw, Institute for Social Studies, Warszawa, Poland

[email protected]

How to represent in connectionist models dynamical aspects of processes and changes that take place in the environment is one of the main challenges facing connectionist modeling.Traditionally temporal sequences are modeled by recurrent network models. We discuss how a self-organizing dynamical network of potentially chaotic elements may be evolved to model temporal trajectories of external events. We analyze the effectiveness of the evolution paradigm, and the relation between the complexity of the emergent network and features of the trajectories the network is trying to learn. Key Words: neural networks, genetic algorithms, cluster computing, logistic iteration


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Chaos in Cataclysmic Variables: Spin Pulses in Intermediate Polars

Vitalii V. BreusDepartment "High and Applied Mathematics", Odessa National Maritime University

Odessa, Ukraine, [email protected]

Photometric pulses at the light curves of the "intermediate polars" subclass of interacting binary stars are caused by the periodic change of the view angle between the line of sight and the accretion column above the surface of the magnetic white dwarf. Despite a nearly periodic nature of this process, the light curves are not strictly periodic, and they correspond to a limit cycle, as the accretion streamdisk+columns undergo chaotic variations perturbed by a periodic gravimagnetic rotator. We study this process based on own photometric two-channel observations of a group of intermediate polars. Chaotic behaviour has a strong contribution into total brightness variations in these systems. Key Words: time series analysis, photometric data, intermediate polars, interacting binary stars, astronomy

Chaoticity in the Time Evolution of Foreign Currency Exchange Rates in Turkey

O. Cakar†, O. O. Aybar†*, A. S. Hacinliyan†‡*, I. Kusbeyzi†*

‡Yeditepe University, Istanbul, TurkeyDepartment of Physics, [email protected]

†Yeditepe University, Istanbul, TurkeyDepartment of Information Systems and Technologies, [email protected]

*Gebze Institute of Technology, Kocaeli, TurkeyDepartment of Mathematics, [email protected]

Tools from chaos theory that have found recent use in analysing financial markets have been applied to the US Dollar and Euro buying and selling rates against the Turkish currency. The reason for choosing the foreign exchange rate in this analysis is the fact that foreign currency is an indicator of not only the globalization of economy but also savings and investment.Fractal Geometry is the geometry of real nature and intimately related to chaos. Fractal structures are suitable for applying to social sciences because of their self similarity and dynamic dimensions. Time series analysis have been extensively used in market analysis. Financial time series are best analysed by using nonlinear time series analysis tools such as rescaled range (R/S) analysis, detrended fluctuation analysis (DFA) if heteroscedastity is dominant and nonlinear time series analysis including mutual information combined with False Nearset Neighbours (FNN). These techniques reveal possible fractal structures. The Fractal Market Hypothesis of Edgar Peters lies at the root of the analysis of financial markets with the help of chaotic structures. This hypothesis states that; 1. A market consists of many investors with different investment horizons.2. The information set that is important to each investment horizon is different. As long as

the market maintains this fractal structure, with no characteristic time scale, the market remains stable. When the market's investment horizon becomes uniform, the market becomes unstable because everyone is trading based upon the same information set.

The results of the analyses show that fractal structures can explain the analysed data more closely than classical linear time series analyses. Moreover, in most cases, the behavior of the combined data is nearly the same as the behavior observed when the data is split into yearly bins. This indicates that relatively long term trade and investment trends have been uniform during the period under study. More specifically, if one looks at the analysis types one by one:


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R/S analysis indicates the presence of two regimes in the data and is therefore incompatible with the results from the other analysis methods which do not give sufficient evidence for two regimes. Since the data contains fluctuations and noise by R/S analysis involves the effect of extreme values, we may be seeing two regimes. R/S analysis has been extensively used for financial data and the two different regimes that it suggests can come from short and long term trends in the yearly data and overall data involving the exchange rates, however one of the regimes can alternatively come from day to day random fluctuations.The DFA analysis seems to be affected from short term fluctuations. Only one regime seems to be indicated by the analysis; this can be used to indicate the characteristic of the market as relatively consistent and stable if fluctuations are ignored.Nonlinear time series analyses reveals that the embedding dimension to be nearly 3. This would indicate a one dimensional trend according to Takens’s theorem. On the other hand, if we look at the Hurst results, the dimension is nearly 1.7. We can say that FNN can better eliminate the fluctuations and noise in this case and give us more clear cut results. On the other hand, this can also be interpreted as a sign of fractal behavior.

Keywords: Financial markets, Time Series Analysis, Detrended Fluctuation Analysis, R/S Analysis on noisy data

References

[1] Abhyankar, A., L. Copeland, and W. Wong. Uncovering Nonlinear Structure in Real-Time Stock-Market Indexes. Jounal of Business & Economic Statistics, 15N1: 1-14, 1997.

[2] Hacınlıyan, A., Sahin, G., Erenturk, M., Detrended fluctuation analysis in natural languages using non-corpus parametrization, Chaos, Solitons and Fractal, 41, 1, 198-205, 2009.

[3] Barkoulas, John, and Nickolaos Travolos. Chaos in an emerging capital market? The case of the Athens Stock Exchange. Applied Financial Economics, 8: 231-243, 1998.

[4] Hacınlıyan A., Y. Skarlatos, H. A. Yıldırım and G. Sahin. Characterization of Chaocity in The Transient Current Through PMMA Thin Films, Physical Review B. 73, 13, 2006.

[5] Crilly , A., R. Earnshaw, and H. Jones. Applications of Fractals and Chaos. 1. Berlin, Germany: Springer-Verlag, 1993.

[6] Hallegatte, Stephane, Michael Ghil, and Patrice Dumas. Business Cycles, Bifurcations and Chaos in a Neo-Classical Model with Investment Dynamics. Elsevier Science, 1-40, 2006.

[7] Atak K., O. Ö. Aybar, G. Şahin, A. Hacınlıyan and Y. Skarlatos. Chaoticity analysis of the current through pure, hydrogenated and hydrophobically modified PEG-Si thin films under varying relative humidity. Central European Journal of Physics. 7, 3, 568-574, 2009.

[8] Hacınlıyan A., Y. Skarlatos, G. Şahin, K. Atak and O. Ö. Aybar. Possible Stretched Exponential Parametrization for Humidity Absorption in Polymers. The European Physical Journal E. 28, 4, 369-376, 2009.

[9] Hacınlıyan A., Y. Skarlatos, H.A. Yildirim and G. Şahin. Characterization of chaoticity in the transient current through PMMA thin films. Fractals. 14, 125-131, 2006.

[10] Liebovitch, Larry, and Daniela Scheurle. Two Lessons from Fractals and Chaos.Complexity, 5N4: 34-43, 2000.

[11] Richards, Gordon. A Fractal Forecasting Model for Financial Time Series. Journal of Forecasting, 23: 587-602, 2004.

[12] Peters E. E. Fractal Market Analysis: Applying Chaos Theory to Investment and Economics. New York: John Wiley & Sons, Inc., 1994.


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Symbolic dynamics and chaotic synchronization

Acilina Caneco(1), Clara Grácio(2) and J. Leonel Rocha(3)

(1) Mathematics Unit, Instituto Superior de Engenharia de Lisboa,Lisboa and CIMA-UE É vora, Portugal. Email: [email protected].

(2) Department of Mathematics, Universidade de É vora and CIMA-UE, É vora, Portugal. Email: [email protected]

(3) Mathematics Unit, Instituto Superior de Engenharia de Lisboa and CEAUL, Lisboa, Portugal. Email: [email protected]

This paper explores some aspects of the relationship between the phenomenon of synchronization of two coupled oscillators and the symbolic dynamics of the associated maps. Numerical simulations with coupled Duffing oscillators will be given. The phenomenon of synchronization in dynamical systems has been known for a long time. Many different types of synchronization have been detected in nonlinear systems starting from the simplest complete chaotic synchronization which takes place when the identical coupled systems exhibit identical, but still chaotic motion. Chaotic motion can be detected and studied with symbolic dynamics theory. Synchronization is also evident in the sequences of symbols associated to an appropriate Markov partition.Keywords: Chaotic synchronization, Symbolic dynamics, Symbolic synchronization, Kneading theory.

Accounting for model error in data assimilation

Alberto Carrassi and Stephane VannitsemInstitut Royal Mé té orologique de Belgique – IRM, Bruxelles, Belgium

[email protected]

Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. Due to the lack of a unique framework for the model error treatment and to the difficulty to accumulate reliable statistics, these errors are usually either ignored or modeled on the basis of simple assumptions such as white noise or first order Markov process.By using a deterministic formulation, an approach to account for the model error in data assimilation is proposed. This deterministic perspective has been the guideline for model error treatment in sequential and variational schemes. The approach is based on a formal expression for the deterministic evolution of the model error and on the use of an approximation suitable for practical nonlinear filtering problems. The accuracy of this approximation is inherently connected to the stability property of the dynamics such as the spectrum of Lyapunov exponents.First, the deterministic description of the model error evolution, incorporated into the classical extended Kalman filter equations, is used to estimate the contribution to the forecast error covariance due to model imperfections. Results reveal that substantial improvements of the filter accuracy can be gained as compared with the classical white noise assumption.A natural step ahead implies the online estimation of the model parameters in conjunction with the system's state. The EKF in the state augmentation formulation is implemented. The dynamical evolution law for the model error is used here also to estimate the cross covariance between errors in the state estimate and parameters, and provide an efficient online estimate of both in a wide range of initial parametric error amplitude.The extension to variational schemes is presented in the sequel. The state estimation problem requires here the model error time correlations. A straightforward way to estimate these correlations using the deterministic approach is proposed, and it is incorporated in the weak-constraint variational assimilation. Results with two simple dynamics of increased complexity suggest the potential for the successful application to more realistic situations. Key Words Data assimilation, Numerical Weather Prediction.


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Transition from Poisson to GOE in Finite Interacting Boson System(using (1+2)-body random matrix ensembles with spin)

N. D. Chavda, V. PotbhareDepartment of Applied Physics, Faculty of Technology & Engineering

The M S University of Baroda, Vadodara, Gujarat, [email protected]

Following the work on one-body plus two-body random matrix ensembles with spin for fermions; EGOE(1+2)-s, Boson ensemble with good spin s=1/2 (so called two fluid boson systems with ms= 1/2 distinguishing the two fluids ), BEGOE(1+2)-s, is defined. Density of states is obtained numerically for m=10 bosons in Ω=4 doubly degenerate single particle states with good total spin S. The fixed-S density is found close to a Gaussian. Nearest Neighbor Spacing Distribution (NNSD) has been studied for BEGOE(1+2)-s as a function of two-body interaction strength for lowest three values of total spin S. The NNSD for these so called two-fluid boson ensembles is found to be Poisson like for small 2-body interaction strength, and moves steadily to Wigner form as the 2-body interaction strength is increased.Key Words: One plus two-body random matrix ensembles with spin; Boson EGOE(1+2)-s; Interacting Bosons; Two-fluid bosons; spacing distribution

Average-fluctuation separation in Finite Interacting Boson System(using two-body random matrix ensembles with spin)

N. D. Chavda, V. PotbhareDepartment of Applied Physics, Faculty of Technology & Engineering

The M S University of Baroda, Vadodara, Gujarat, [email protected]

Drawing an analogy form the work on embedded Gaussian orthogonal two-body random matrix ensemble with spin for fermions, EGOE(2)-s, embedded Gaussian orthogonal two-body random matrix ensemble with good spin s =1/2) for Bosons (so called two-fluid boson systems with ms= 1/2 distinguishing the two fluids ), BEGOE(2)-s , is defined. BEGOE(2)- sis constructed in good spin basis and density of states is computed numerically for 10 bosons in 4 doubly degenerate single particle states for each good total spin S. The fixed-S density of states is found close to a Gaussian. Moreover, for each total spin S, it is demonstrated that BEGOE(2)-s ensembles exhibit average-fluctuations separation with the smoothed state density being a corrected Gaussian and the fluctuations are of GOE type. Using the unfolded spectra of fixed-(m,S), the Nearest Neighbour Spacing Distribution (NNSD) is calculated for each S and compared with the GOE results.Key Words: Average-fluctuations separation; Embedded Gaussian Orthogonal two-body random matrix Ensemble with spin for Boson; BEGOE(2)-s; Interacting Bosons; Two-fluid Bosons

Legal chaos as the result of interaction of the institutional order poles

N.I. ChernobrovkinaSouthern Federal University,

105/42, Bolshaya Sadovaya str., Rostov-on-Don, 344006, Russia

Legal chaos is a reaction of actors (individuals) vested with freedom of choice to reasons of state fixed by legislature. In consequence of disparity between formal and real sides of applicable legislation individuals are in confrontation with legislation and law activity of the state. The cause of this confrontation is availability of formal and informal practices in the sphere of law and order.


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Social chaos in the process of regional institutional reforms in the South of Russia and the Caucasus

Chernous V.V.Southern Federal University,


By the instrumentality of comparative analysis the pendulum nature of social processes in the states of the South Caucasus and constituent territories of Russian Federation in the North Caucasus were explored, the radical institutional reforms’ influence on deconstruction of regional social order and the role of ethno-societal system in regional stabilization were detected.

Chaos in Cataclysmic Variables: Outbursts in the UGSS Dwarf Nova Stars

Lidia L.Chinarova, Ivan L.AndronovAstronomical Observatory, Odessa National University, Odessa, Ukraine

[email protected]

Outbursts in the SS CYg - type dwarf nova stars arize due to the instability of the accretion disk its limit cycle behavior. Thus the occurrence of the outbursts is chaotic, rather than periodic. We study time series of photometric observations of a group of dwarf novae spanning time intervals from few decades to a century, based on all complied published "monitoring" - type observations. For the analysis, we use the extension of the Auto-Correlation Analysis adopted for irregularly spaced data. From the auto-correlation function analysis, we determine characteristic width of the outburst pulse, as well as recurrence time. In some stars, we detected supercycles of few-year length, which may be interpreted as luminosity changes due to the variations of the accretion rate (mass flux) from a red secondary star onto the white dwarf. Key Words: Time series analysis, autocorrelation, dwarf nova stars, outbursts, chaos in stars

New Enciphering Algorithm Based on Chaotic Generalized Hé non Map

Octaviana Datcu1, Jean-Pierre Barbot2 , Adriana Vlad1,3

1 Faculty of Electronics, Telecommunications and Information Technology,POLITEHNICA University of Bucharest, Romania

2 Equipe Commande des Systèmes, Ecole Nationale Supé rieure de l'Electronique et de ses Applications, Cergy-Pontoise, France

3 Research Institute for Artificial Intelligence, Romanian [email protected], [email protected], [email protected]

The paper belongs to the field of chaotic based cryptography. It relies on some suggestions from classical fundamentals as mixing functions (C.E. Shannon) and on the known publication of M.S.Baptista (“Cryptography with chaos”, Physics Letters A 240, 1998) -a paper essentially implying the ergodicity assumption of the chaotic signal. This latter publication is considered by cryptanalysts (Alvarez et al., “Some Hints for the Design of Digital Chaos-Based Cryptosystems: Lessons Learned from Cryptanalysis”, International Federation of Automatic Control, 2nd IFAC conference on analysis and control of chaotic systems, London, 2009) "a milestone" of chaotic cryptography.

The first step was to choose a chaotic system of a higher dimension than Baptista used, aiming to obtain a more complex system having a hyperchaotic behaviour. The


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proposed algorithm is based on Generalized Hé non Map (3D), stated in literature (G.Grassi, D.A.Miller, “Theory and Experimental Realization of Observer-Based Discrete-Time Hyperchaos Synchronization”, IEEE Trans. on Circuits and Systems —I: Fundamental Theory and applications, vol. 49, No. 3, March 2002) as hyperchaotic for a number of bifurcation parameters.

The paper advances a new mixing function based on the Generalized Hé non Map, which may be used as an inner element in a cipher, providing a good practical diffusion and confusion. A random variable transform is applied on the state of the chaotic system at k iteration in order to obtain a new random variable of a quasiuniform law. This new random variable is further transformed, through a series of other functions containing elements of the secret key, into a discret random variable having q values. The q discret values – which are ASCII numbers - are combined by a simple relation with the plain-message, also in ASCII format. It is obtained a first mask of the original message, involving the Generalized Hé non Map. On this result (in its binary representation form) other simple transformations that depend on the state of the Generalized Hé non Map are applied. That finally allows getting a transformed version of the message that can be included in one of the states of the Generalized Hé non Map without disturbing its chaotic behavior.

The results, including a perception of the diffusion and the confusion involved, are illustrated on natural text and jpeg image.

Keywords: Generalized Hé non Map, chaos based enciphering algorithm, mixing functions, random variable transform

Noise Influence on the Characteristic Relations and Reinjection Probability Densities of Type-II and III Intermittencies

Ezequiel Del Rio1, Sergio Elaskar

2, J.M. Donoso

1 and L. Conde

1

1 Dept. Física Aplicada. ETS Ingenieros AeronáuticosUniv. Polité cnica de Madrid. 28040 Madrid. Spain

Email: mailto:[email protected]

Dept. Aeronáutica. Facultad de Ciencias Exactas, Físicas y Naturales.Univ. Nacional de Córdoba. Avda. Vé lez Sarfield 1611.

Córdoba 5000. Argentina.Email: [email protected]

This paper explores the effect of the noise in the reinjection probability densities (RPD) for type-II and type-III intermittencies by using the temporal series of iterative maps. The RPD are calculated by means of a new method proposed in Refs. [1] and [2]. The results are compared with both, numerical simulations and analytical calculations. We provide an explanation for the gap observed in early experiments around the unstable point in the Poincaré map. The external noise produces a non-linear characteristic relation. We show that and added white noise approaches the RPD to the uniform reinjection for small values of the distance from the critical point whereas the it does not affect for larger values of . The main classical results can be deduced from our RPD as particular cases.

Keywords: Intermittency. Characteristic relations. Reinjection probability density.

References

[1] E. Del Rio and S. Elaskar. New charactristic relations in type-II intermittency. Int. J. Bif. Chaos, 20. (4). pp. 1–7 (2010)

[2] E. Del Río, M.G. Velarde and A. Rodríguez-Lozano. Long time data series and difficulties with the characterization of chaotic attractors: a case study with intermittency III. Chaos. Sol. Frac., 4. (12). pp. 2169–2179 (1994)


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Comparative thermal Analysis of disc and drum brake Performance

Vijay DhadkeM.Tech Mechanical, New Panvel, Maharashtra, India

[email protected]

During vehicle deceleration due to braking there is friction between the lining surface and the brake drum or disc. In this process the kinetic energy of vehicle is turned into thermal energy that raises temperature of components. The heating of brake system in the course of braking is a great problem, because besides damaging the system, it may also affect the wheel and tire, which can cause accidents.A transient analysis for the thermo elastic contact problem of the drum and disc brake with heat generation is performed using the finite element analysis. To analyze the thermo elastic phenomenon occurring in drum and disc brake, the occupied heat conduction and elastic equations are solved with contact problems.The numerical simulation for the thermo elastic behavior of drum and disc brake are obtained in the repeated brake condition. The computational results are presented for the distribution of heat flux and temperature on each friction surface between the contacting bodies. Also, thermo elastic instability (TIE) phenomenon, the unstable growth of contact pressure temperature and the influence of the material properties on the thermo elastic behaviors. The maximum temperature on the friction surfaces is investigated in present study to facilitate the conceptual design of the drum and disc brake system. Based on thermal analytic results the thermo elastic behaviors of drum and disc brake are compared.Key Words Keywords: Brake, Temperature, Thermal Analysis, Transient analysis, Thermo Elastic Instability.

Multifractal and wavelet analysis of epileptic seizures

Dick O.E.Pavlov Institute of Physiology, RAS, St. -Petersburg, Russia

[email protected]

The aim of the study is to develop quantitative parameters of human electroencephalographic (EEG) recordings with epileptic seizures. We used long-lasting recordings from 10 subjects with temporal lobe epilepsy obtained as part of their clinical investigation. The continuous wavelet transform of the EEG segments with the Gaussian wavelet and the wavelet-transform modulus maxima method enable us to evaluate the energy spectra of the segments, to find lines of local maximums, to gain the scaling exponents and to construct the singularity spectra.We have shown that the significant increase of the energy with respect to background and the redistribution of the energy over the frequency range are observed in the patterns involving the epileptic activity. The singularity spectra expand so that the degree of irregularity and multifractality of the segments enhances. Comparing the results gained for the patterns obtained during different functional probes such as open and closed eyes or hyperventilation we demonstrate the high selectivity of the analyzed parameters (the redistribution of the energy over the frequency, the position and width of the singularity spectrum) for detecting the epileptic patterns. Thus, the employed tools give a good ability to estimate changes in the brain activity.Keywords: ultifractal, wavelet, EEG, epileptic


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Application of Local Forecasting Methods to Greek Stock Exchange Data

Yiannis DimotikalisDepartment of Finance and Insurance

Technological Educational Institute of CreteAghios Nikolaos, Crete, Greece

[email protected]

Local forecasting methods, both univariate and multivariate applied to Greek Stock Exchange data and their forecasting ability is examined. The application to real stock data is compared with application to artificially created data by simulation. The capability of local forecasting to detect the deterministic or stochastic nature of data is discussed and analyzed.

Fuzzy weather forecast in forecasting pollution concentrations

D. DomanskaDepartment of Modelling and Computer Graphics, Institute of Informatics, University of

Silesia, Bedzinska 39, Sosnowiec, 41-200, [email protected]

M. WojtylakInstitute of Meteorology and Water Management (IMGW), Bratkow 10

Katowice, 40-045, Poland, [email protected]

In this paper we want to present dependences between weather forecasts data from Institute of Meteorology and Water Management and received data in our program using to forecast pollution concentrations. Calculations are kept on set of actual and historical meteorological data.Our model using to forecast pollution concentrations is important in todays because pollutions have very big influnece on our life in particular polllutions PM10 (particulate matter less than 10 μm in diameter). The effects of inhaling particulate matter have been widely studied in humans and animals and include asthma, lung cancer, cardiovascular issues, and premature death. Because of the size of the particle, they can penetrate the deepest part of the lungs.In APFM for the weather forecast chosen we find similar weather forecasts. Next, we find real meteorological situations from the historical data which correspond to them and we create fuzzy numbers, that is, the fuzzy weather forecasts. Then we estimate the validity of the weather forecast on the basis of the historical data and its checkability. We investigate it with the help of an indicators’ set, which corresponds to the parameters of the weather forecast, using the similarities rule of the weather forecast to the meteorological situation, a proper distance and data analysis.This comprehensive analysis allows us to investigate the effectiveness of forecasting pollution concentrations, putting the dependence between particular attributes describing the weather forecast in order and proving the legitimacy of the applicable fuzzy numbers in air pollution forecasting. Models are created for data, which are measured and forecasting in Poland. By reason of this data our model are testing in real sets of data and effects are received in active system.

Keywords: Fuzzy system models, Fuzzy numbers, Fuzzy matrix, Fuzzy weather forecast, Airpollution forecasting


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Dynamics of burning out of particles of the fuel dust in volume of the fire chamber of the copper

N.N. Efimov, A.S. Oshchepkov, А.В. Ryzhkov South Russia State Technical University (Novocherkassk polytechnical institute),

Novocherkassk, [email protected]

The fuel particle in volume of a fire chamber of a copper passes in chaotic movement stage by stage processes of heating, ignition and burning. Thus the particle is exposed to various external influences: dynamics of process of burning of a particle occurs in a changing external temperature field; the particle in process of burning out decreases on weight; the chemical compound of a particle and at the same time physical and chemical characteristics changes. In work management possibility is investigated by such multifactorial process.

Chaos, complexity theory, global financial crisis and the prospects for financial engineering research in (pre-emerging) financial markets: a work -in- progress

P. Oseloka Ezepuea, O. Anwar Bé gb & Alireza HeidaricaResearch Leader: Business Intelligence & Quantitative Modelling, Department of Computing,

Room 2211 Harmer Building, Sheffield Hallam University, Sheffield, S1 1WB, England, UK. Email: [email protected]

b Research Leader: Biomechanics, Biotechnology and Computational Magnetohydrodynamics, Mechanical Engineering Program, Department of Engineering and Mathematics, Room 4112, Sheaf Building, Sheffield Hallam University, Sheffield, S1 1WB,

England, UK. Email:[email protected] Physics, Department of Chemistry, Ferdowsi University of Mashhad,

Mashhad 91775-1436, Iran. Email: [email protected]

Though the impact of the 2007-09 global financial crisis is regionally differentiated among the triad of financial markets - developed markets of Europe and USA (in which it is most severe), emerging markets of Asia and the BRIC countries (Brazil, Russia, India and China), and pre-emerging markets of Sub-Sahara Africa and the Middle East (in which it is less severe) -global communities of academics, practitioners, national and international economic development and financial regulatory bodies are intensely debating approaches to prevent such events happening in the future. This paper reflects up on and collates some of the key ideas emerging from this debate into an agenda for mathematical modelling of financial markets. The main focus of the paper is on the combined roles of chaos, complexity theory, simulation and economic methodologies in this agenda, and the lessons to be learned from the crisis for effective management of investments and financial risks in the markets, especially pre-emerging African markets. The paper is empirically illuminated with snapshots of data modelling from the Nigerian financial system.Key words: Chaos, complexity theory, stochastic modelling, investments, financial risk management


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Resolvents of linear operators, generated by generalized quasi-differential expression

V.I. Filippenko108/4 Shevshenko Str., Shakhty, Rostov Region, Russia, 346500

[email protected]

Let 1n be a positive integer and suppose ijfF is an nn matrix of complex

valued functions satisfying the basis conditions:

(1) 0ijf a. e. baI , for ;12 nji

(2) ,Lfij for all ji, and all , in baI , , i.e. iLf locij for

;,1 nji (3) 01, iif a. e. on baI , for 11 ni .

We define the quasi-derivatives ky . Let

i

j

jij

iii

i yfyfyyy1

1111,

0 , for y such that

1,...,1,1 niIACy i . The quasi-differential expression is defined by

n

i

ini

n yfyy1

11 for all y with jy in 1,...,2,1,0, njIAC . For this

purpose we assume ijfF satisfies, in addition to (1), (2), (3), the symmetry condition

JFJF *1 where F is the adjoint of F and J is the constant

,,11 1, njiJ jnii with denoting the Kronecker delta.

Resolvents of linear operators, generated by generalized quasi-differential expression

n

i

ini

n yfyy1

11 are described.

The dripping laser: quantum chaos in a phase transition in light

Ruben Fossion, Emmanuel Landa, Victor Velazquez, Alfred U’Ren, Alejandro [email protected]

Classical chaos is characterized by patterns of order, in terms of strange attractors. A paradigm of classical chaos is the dripping faucet. With as a control parameter the water flux, one can observe a phase transition from a regular regime (periodic drops) towards another regular regime (a continuous stream of water), over a chaotic regime (non periodic but correlated drops).Quantum chaos is less well defined. It has been conjectured that fluctuations in the spectrum of quantum systems, e.g. in atomic nuclei, also show patterns of order, that can be described with Random Matrix Theory [1]. More recently, another conjecture states that a quantum spectrum, when interpreted as a time series, behaves like 1/f noise in its power spectrum, if it is a chaotic system [2].We propose a “dripping laser” as the quantum equivalent of the classical dripping faucet. It is possible to produce pseudothermal light (bunched photons) from coherent laser light (random photon time series), using a ground glass disc rotating in the laser beam [3]. Now, the rotation speed of the disc serves as a control parameter in the transition between the two light regimes. We observe a fractal photon-bunching pattern, resulting in a 1/f photon time series in the pseudothermal regime [4]. Key Words: Phase transition, quantum optics, time series, quantum chaos, 1/f noiseReferences


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[1] O. Bohigas, M.J. Giannoni y C. Schmit, Phys. Rev. Lett. 52 (1984) 1.[2] A. Relaño, J.M.G. Gómez, R.A. Molina, J. Retamosa y E. Faleiro, Phys. Rev. Lett. 89 (2002) 244102.[3] W. Martienssen y E. Spiller, Am. J. Phys. 32(12) (1964) 919.[4] E. Landa, R. Fossion, I. Morales, C. Hernández, V. Velázquez, J.C. López Vieyra, and A. Frank, Rev. Mex. Fís., in print.

On the Statistical Independence in the Context of the Rössler Map

Mădălin Frunzete1 , Adrian Luca1 , Adriana Vlad1,2

1Faculty of Electronics, Telecommunications and Information Technology,POLITEHNICA University of Bucharest, 1-3, Iuliu Maniu Bvd., Bucharest 6, Romania

2The Research Institute for Artificial Intelligence,Romanian Academy, 13, Calea 13 Septembrie, Bucharest 5, Romania

[email protected], [email protected], [email protected]

The paper mainly focuses on the statistical dependence/independence relationship existing in the Rössler map and on the possibility to sample the chaotic system as to obtain experimental data complying with the i.i.d. model (data coming out from independent and identically distributed random variables). The investigation considered the following definition of the Rössler map, [1]:

))(1()1(

)1](1))(1[(

)1(

321223313

34321212

221111

bxxbcxxcx

xbbxxbbx

xaxxax

where ),,( 321 xxx represents the system state vector at a certain discrete time moment k

and ),,( 321 xxx is the state vector at the previous time moment 1k . The set

),,,,,,,( 21432121 ccbbbbaa denotes the system parameters (the chaotic behaviour of the

Rössler map depends on these parameters). For a fixed set of parameters, but different initial conditions, three random processes assigned to the three state variables (the outputs of the Rössler map) are obtained. The main theoretical and experimental results provided by this study refer to the following:1) the computational measurements of the transient time - the time elapsed from the initial conditions (initial state vector) of the system up to its entrance in stationarity. Note that the stationarity feature is contained in the ergodicity assumption of the Rössler map. 2) the possibility to sample the three random processes (assigned to the three outputs of the system) in order to obtain i.i.d. data sets.3) the evaluation of the statistical dependence/independence existing between two different outputs of the system (e.g. the pair ),( 31 xx ). Determining a minimum sampling distance that

enables statistical independence between the outputs of the system is of interest in cryptography, especially when the original message is included in a state variable and the cryptogram is obtained as another state variable. The overall investigation relies on: Smirnov tests on two experimental data sets, a Monte Carlo analysis and an original independence test applicable to all kinds of continuous variables, normal or not, even of unknown statistical law, [2], [3].

Keywords: stochastic chaos, statistical independence in chaotic systems, transient time, Rössler system.References[1] Perruquetti W., Barbot J.P. (Eds.): Chaos in Automatic Control, CRC Press, Boca Raton, 2006

[2] Badea B., Vlad A.: “Revealing statistical independence of two experimental data sets. An improvement on Spearman’s algorithm”. LNCS, vol. 3980, pp. 1166-1176, 2006

[3] Vlad A., Luca A., Frunzete M.: “Computational Measurements of the Transient Time and of the Sampling Distance That Enables Statistical Independence in the Logistic Map”, LNCS, Vol. 5593, pp. 703-718, 2009


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Analysis of homoclinic bifurcation in Duffing oscillator under two-frequency excitation: Peculiarity of using Melnikov method in combination with averaging technique

Kenta Fukushima, Vladimir RyabovFuture University-Hakodate, Hokkaido, Japan

[email protected]

We study the Melnikov conditions for the appearance of chaos in Duffing oscillator with hardening type of non-linearity under two-frequency excitation acting in the vicinity of the principal resonance. Since Hamiltonian part of the system contains no saddle points, Melnikov method cannot be applied directly. After separating the external force into two parts, we develop a two-step perturbation analysis that allows recasting the original system to the form suitable for Melnikov analysis. At the initial step, we perform averaging of the system at one of the frequencies of the external force. The obtained system of averaged equations is then analyzed by traditional Melnikov approach, considering the second frequency component of the external force and dissipation as perturbations. Contrary to previous works that were not focused on the analysis of implications of the analytic formulas obtained by Melnikov method, we perform an extensive analysis of the homoclinic bifurcation conditions under the variation of control parameters. The results of calculations reveal that there is an asymmetry in the position of bifurcation with respect to frequency detuning between the excitation frequencies; -the threshold of homoclinic bifurcation depends on the initial assumptions made at the initial step of analysis, i.e. in the averaging procedure;- there are two types of chaotic motions in the system that are caused by the presence of double homoclinic loop in the Hamiltonian part of the averaged system. The Melnikov conditions for the two loops are different, that results in multistability, when several attractors coexist;-in order to apply perturbation methods, we made certain assumptions on the values of parameters (perturbation terms are small). This restricts substantially the areas in the control parameter space where the Melnikov method can be efficiently used.Finally, we formulate an optimal procedure for using Melnikov method in combination with averaging method in the analysis of nonlinear oscillators similar to Duffing system and verify our predictions with numerical experiments. Key Words: Melnikov method, Duffing oscillator, Chaos, Averaging, Global homoclinic bifurcation.

Creativity of information systems from the standpoints of synergetics

Gennady G. GalustovTaganrog Institute of Technology – Southern Federal University,

44, Nekrasovky str., Taganrog, 347928, Russia;

The questions of the possibility of constructing a mathematical model of creativity to produce creative result when used in an automated information system are considering. Also the involvement of dynamic chaos to the possibility of obtaining the elements of creativity, the ability of modern automated information systems to creativity is discussing.


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Gas-vapour discharge between jet electrolyte cathode and solid anode at low pressures

Al.F.Gaysin, Az.F.Gaysin, F.M.GaysinKazan State Technical University

Amirkhan Street, 33-65Kazan, Russian Federation

[email protected]

Studied are the structure and shapes of an electrolyte discharge between liquid anode and metal cathode in the pressure range of 7.6 -608 Torr, discharge voltage 200÷1500 V. Key Words: Electric discharge, electrolyte

Processes ordering in nonlinear automatic phase control system

Y. А. Gelozhe, A. V. SemenovTaganrog Institute of Technology – Southern Federal University, Russia

[email protected]

Processes controlling in the discrete phase control system at frequency detuning, exceeding capture range limits, when establishment of required quiescent state becomes a stochastic event, are concerned. Methods of synergetic control theory are used for solving of processes control tasks. Developed control strategy provides establishment of synchronism mode with probability equal to 1.

Key words: Invariant manifold, attractor, domain of attraction

Pre-fractal patterns in Iannis Xenakis’ algorithmic composition: a critical approach

Αnastasia Georgaki and Cristos TsolakisMusic Department, University of Athens, Greece


Iannis Xenakis, one of the most genious composers of the XXth century, a real bridge maker between science and art (Georgaki 2005) tackles first the questions arising from determinacy and indeterminacy, repetition and variation, symmetry and structure in music composition, as also the multidimensional musical space (Xenakis 1992, 1996). Having applied various mathematical models in his compositions, he has also used cellular automata and other fractal patterns before Benoit Mandelbrot introduces his theory (Mandelbrot, 1983). The scope of this article is to examine in which way Xenakis has been using pre-fractal patterns in his work, giving an holistic interpretation of his scientific and philosophical world. The technology of the stochastic laws constrains him within the margins of disorder and statistic order. According to Discipio Xenakis’ music incarnates the utopia of an art which aims at resolving the dialectic between material and form-between Nature and culture-by means of an integrally constructivist disposition sound (Discipio, 1999). In the first part of our paper we will make a literature review presenting the most interesting aspects about the algorithmic innovation in Xenakis micro/macro- composition techniques. (Discipio 1999; Solomos 2005; Hoffman 2002). In the second part, we will examine the most common way to categorize algorithms in Xenakis works (by their structure and the way of processing musical data) like mathematical models, knowledge-based systems grammars, evolutionary methods, etc. In the third part we will present those different compositional approaches (developed in the environment Max/Msp) in order to outline the pre-fractal patterns that Xenakis has introduced in selected works in the 60s and 70s.


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Synergetic potential of developmental education concepts

G.I. Gerasimov Southern Federal University,


On the basis of synergetic methodology the comparative analysis of different concepts which are available in educational reality of modern Russia is carried out in the article. The matters of organizing social and pedagogical support of transition from traditional forms of educational process organization to developmental paradigm as foundation of organizing cultural and educational space.

Structural-scaling transitions and nonlinear chaotic dynamics of DNA ensembles

Evgeniya Gerasimova, Oleg NaimarkInstitute of Continuous Media Mechanics of RAS, Perm, Russia

[email protected]

The role of finite-amplitude fluctuations in the mechanisms of DNA functioning is the subject of long standing interest [1,2]. Specific functions of DNA are linked with nonlinearity and nonlocality of base interaction. Simulation of DNA dynamics established the multiscale scenarios of open complex formation (transcription bubbles) related to localized denaturation dynamics. The breaking of hydrogen bonds proceeds as generation of multiscale collective modes localized on the spectrum of spatial scales and revealed qualitative different chaotic dynamics that can be linked with DNA specific functions (correlation between the sequence-dependent propensity for bubble formation, transcription initiation, regulatory effects in viral DNA including the ability to built and repair proteins). It was shown in [3,4] that DNA functions can be analyzed as specific type of critical phenomena that is characteristic for large class of out-of-equilibrium systems –structural-scaling transitions. Two order parameters are responsible for thermodynamic and dynamic properties of these systems: structural-scaling parameter and localized distortion mode parameter (defect density parameter). Specific nonlinear dynamics was established for defect density tensor for corresponding ranges of structural-scaling parameter associated with DNA open complex dynamics. Dynamic chaos of DNA functionality is linked with finite degrees of freedom related to collective modes of defect density parameter: breathers, autosolitary waves, blow-up dissipative structures. Transcription and denaturation mechanisms of DNA evolution are analyzed in terms of mentioned collective modes with application to DNA sequencing and gene transformation. References1.Peyrard M. and Bishop A.R. Statistical mechanics of a nonlinear model for DNA denaturation, Phys.Rev.Lett. V.62 (1989), p.2755-2758.2.Peyrard M. Nonlinear dynamics and statistical physics of DNA, Nonlinearity.V.17 (2004), R1-R40.3.Naimark O.B., Defect Induced Transitions as Mechanisms of Plasticity and Failure in Multifield Continua (Review Paper), In “Advances in Multifield Theories of Continua with Substructure”, Birkhauser Boston, Inc., Eds: G.Capriz, P.Mariano , 2003.-P.75-114;4.Naimark O.B., Structural-scaling transitions and localized distortion modes in the DNA double helix, Physical Mesomechanics, 10, 1-2 (2007), P.33-45Keywords: DNA chaotic dynamics, Structural-scaling transitions.


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Forced Chemical Confinement Fusion in Two Layers of Hydrogen Isotopes: Using A Difference Equations Approach

R. GheisariPersian Gulf University, Bushehr 75169, Iran


This paper investigates forced muon catalyzed fusion in the two layers of H/T and D2 (with density and )( x , respectively ). After injection of muons into the H/T inhomogeneous

mixture, start slowing down and are finally captured by the atoms of the mixture or decay with the rate of 16

0 10455.0 s . This means that the muonic atoms are formed, i.e. )1( st .

Due to Ramsauer-Townsend effect, the t muonic atoms leave the first layer of H/T, enter D2

layer where chemical fusion of produced ion of dt may be performed. As before, the

balance equations were written as point kinematic equations were made under simplified assumptions, most important of which were. Since the t atoms are not moderated promptly,

transport equations must be written. Very interesting physical results arise in this theory when time-space dependent transport equations are applied. As sequences, we analytically obtained the balance equation of

),0())0(()(78.0),0( 2.2.

02.2 tNtNtNt

tE

nondta

teVE

at the boundary of two layers where corresponds with experiment result. ),( txN tE and )(tN

are the numbers of )1( st muonic atoms (in 31cm ) having energy of E and, that of the

produced muons from the first layer, respectively. 112104 sa is the rate of muonic

atom formation and, 18. 103 snondt being non-resonant formation rate of the dt three

body. Fick law was not applied here, for the moderated muonic atoms. For the numerical calculations we used Backward Implicit Method. More details of the numerical method are described in this conference, separately. Keywords: Forced chemical cofinement fusion, Two layers of hydrogen isotopes, Time-space dependent, Transport equations, Muonic atom, Analytical result of boundary.

Solution of Time-space Dependent Equations As Balance Transport Equations and Stability of The Numerical Method in Two Layers Reactor Design of Muon Catalyzed

Fusion

Gheisari R., Mohamadsalehi F.Persian Gulf University, Bushehr 75169, Iran


Forced muon catalyzed fusion in the two layers of reactor, H/T and D2 ( with density

0 ), is proposed. After injection of muons into the H/T (localized at 0x ) , start slowing

down and are finally captured by the atoms. This means that the muonic atoms are formed, i.e. )1( st . Due to Ramsauer-Townsend effect, the t muonic atoms leave H/T and enter

the second layer. The time-space dependent transport equations are applied and solved for the reactor media by Backward implicit method(BIM). The numerical method of BIM is used to obtain the number densities of ),( txN t

E at the resonance collision energies 1,47.0E ,

eV5.1 and, also for the )1( st mean energy, eV2.2 . The variable x denotes the space-

coordinate measured from the H/T slab. The chemical cofinement formation rates are very high in the resonance energies. In order to obtain a converged solution we needed a large number of discritization points, the step sizes for x and time variables are, respectively, 2000

and 1510 . As more sequence, the balance equation reported at the bounary of the two layers in this conference, corresponds the our numerical results and would be applied for the

space interval of 2/580 cmgx . The x= 2/58 cmg means m )0(

2

.


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Keywords: Forced fusion, Two layers of reactor, Time-space dependent, Transport equations, muonic atom, Backward implicit method, Step size, Numerical.

Arithmetic Modelling of Stochastic Dynamics

N.M. GlazunovNational Aviation University, 1, Prospect Komarova, 03680, Kiev-680 GSP Ukraine

[email protected]

We define and investigate maps from moduli spaces of algebraic curves and coverings to n-dimensional cubes (n > 0) in m-dimensional (n≤m) real space. These maps are constructed from two families of generic maps: Hasse maps and Kloosterman maps. We review chaotic-like properties of the maps and present results of computer modelling.

Time Variant Chaos Encryption

Victor Grigoras1, Carmen Grigoras2

1Faculty of Electronics, Telecommunications and Information Technology‘Gheorghe Asachi’ Technical University of Iasi, Iasi, Romania

2Faculty of Medical Bioengineering‘Gr.T. Popa‘ University of Medicine and Pharmacy of Iasi, Iasi, Romania

Romanian Academy – Iasi Branch, Institute of Computer ScienceE-mail: [email protected]

Chaos synchronization was extensively studied the last two decades leading to several synchronization and modulation methods. The main aim of the research was to develop wide bandwidth, spread spectrum like, secure communication systems. Taking into account the high sensitivity of all synchronization and modulation methods to both channel noise and parameter mismatch, digital implementations aiming at chaos encryption were preferred lately. Several authors developed in their studies different encryption approaches, most of them being successfully cryptanalized, due to the direct influence of the constant system parameters onto their nonlinear dynamics.The present contribution proposes a time variant approach to chaotic encryption. The proposed method is based on chaos synchronization and plaintext modulation onto the chaotic dynamics of the emitter. In order to improve communication confidentiality, one or several parameters of the emitter system are modulated with pseudo-random digital sequences, thus drastically increasing the length of the encryption key. At the decryption end, the corresponding receiver parameters are also time variant. Exact knowledge of the emitter pseudo-random digital sequence shape and timing are necessary for correct decryption of the cipher-text.It is also worth noting the importance of the modulating sequence amplitude or dynamic range due to its influence on the instantaneous value of the emitter sensitivity and, by consequence, its capacity in hiding the transmitted plaintext. Thus a parametric analysis is presented in order to find a valid parameter range for possible modulation. For the digital implementation of the proposed encryption/decryption systems, although input and output are fixed point, the internal structure of both emitter and receiver must be implemented in floating point to obtain the closest behavior with the chaotic prototype that has analog valued state variables.Both analog and discrete examples for the encryption/decryption system are analyzed and checked for standard attack types. Presented simulations confirm the theoretical results and highlight the great improvement of the communication security by the proposed approach. The concluding remarks point towards some directions in further research.Keywords: Chaos synchronization, Chaos encryption, Parameter modulation.


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The Computer simulation for electromagnetic properties control of the metamaterial structures

Sergey G. Grishchenko, Nataliya N. Kisel’Taganrog Institute of Technology – Southern Federal University,

44, Nekrasovky str., Taganrog, 347928, Russia [email protected]

At present rapidly increasing interest composite structure could possess, in a given frequency interval, a negative effective magnetic permeability and permittivity.

The electromagnetic scattering properties of structures with negative indices of refraction were studied numerically. To perform this analysis, Method of Moment Solver was used (from software product FEKO).The scattering of electromagnetic waves from several structures whose permittivity and permeability are both negative were numerically investigated. Some exotic effects for near fields were shown.

The consistency of the simulations presented here provides evidence that software products such as FEKO, CST STUDIO, HFSS will indeed be reliable when it needs to analyzing more complicated negative index structures.

Quasy-optic simulation of multilayer objects in the problems of the electromagnetism

Sergey G. Grishchenko, Nataliya N. Kisel’Taganrog Institute of Technology – Southern Federal University,

44, Nekrasovky str., Taganrog, 347928, Russia [email protected]

Radar and antennas problems of electromagnetic wave transient and scattering by multilayered objects to be placed on boundary (up boundary or under boundary) are very important.

Quasy-optic algorithm improving ray methods of multilayered media electromagnetic analysis is developed. A description of that method including some details about multilayered media such as structure material lossings, multireflected in structure rays and incident wave front curvature are presented. The ray method coupled quasy-optic algorithm is more efficient than a classic ray method for analyzing arbitrarily shaped objects.

Results for three-dimensional problems involving arbitrary shaped bodies of revolution structures have demonstrated the validity of the ray method coupled quasy-optic algorithm.

Investigation Chaotic Dynamic of Biochemical Process using Lyapunov indices

Valerii I. GrytsayBogolyubov Institute for Theoretical Physics, 14b, Metrolohichna Str., 03680, Kiev, Ukraine


By the example of a mathematical model of the biochemical process, the structural instability of dynamical systems is studied by calculating the full spectrum of Lyapunov indices with the use of the generalized Benettin algorithm. For the reliability of the results obtained, the higher Lyapunov index determined with the orthogonalization of perturbation vectors by the Gram--Schmidt method is compared with that determined with the overdetermination of only the norm of a perturbation vector. Specific features of these methods and the comparison of their efficiencies for a multidimensional phase space are presented. A scenario of the formation of strange attractors at a change of the dissipation parameter is studied. The main regularities and the mechanism of formation of a deterministic chaos due to the appearance of a fold or a funnel, which leads to the uncertainty of the evolution of a biosystem, are determined.


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Keywords: Chaos, Structural instability, Biochemical process, Full spectrum of Lyapunov indices, Self-organization, Strange attractor, Dissipative system.

COMPARISON OF DIFFERENT APPROACHES TO SHOCK CAPTURING TURBULENT FLOW SIMULATIONS

A.R. Guzhova, V.I. Kozlov, V.P. Statsenko, G.S. Firsova, Yu.V. YanilkinRFNC-VNIIEF, Sarov, Russia, [email protected]

On the basis of simulations of a number of experiments, strengths and weaknesses of two approaches to turbulent flow simulations are discussed: direct numerical simulations that use difference solution of Euler equations, and statistical modeling that uses a finite number of first moments of the joint probability distribution function for turbulent velocity and density fluctuations. Direct 3D numerical simulations were carried out by 3D TREK code [1]. Statistic modeling is performed using the k- [2] and the Nikiforov-Kozlov [3] models that belong to RANS models (Reynolds Averaged Navier-Stokes equations).

1. Stadnik A.L., Shanin A.A., Yanilkin Yu.V. The Eulerian Technique TREK for Simulation of 3D Hydrodynamic Multimaterial Fuid Flows // VANT. Ser.: Math. Model. Phys. Process. 1994. Issue 4, pp. 71-78.

2. A.R. Guzhova, A.S. Pavlunin, V.P. Statsenko Specification of k- constants for the turbulence model basing on the direct numerical simulation of the simplest turbulent flows and measurements result;VANT, Ser.: Theor. And Appl.Phisics,Issue 3,2005, pp.37-48.

3. V.I.Kozlov, Simulations of SW turbulence interaction; Proceedings of the 10 International Workshop on The Ptisycs of Compressible Turbulent Mixing, Paris, 17-21 July 2006, France.

Aesthetic Considerations in Algorithmic and Generative Composition

Kerry L. HaganCentre for Computational Musicology and Computer Music

University of Limerick, Limerick, Ireland Email: [email protected]

Models of chance operations, random equations, stochastic processes, and chaos systems have inspired composers as historical as Wolfgang Amadeus Mozart. As these models advance and new processes are discovered or defined, composers continue to find new inspirations for musical composition. Yet, the relative artistic merits of some of these works are limited. This paper explores the application of extra-musical processes to the sonic arts and proposes aesthetic considerations from the point of view of the artist. Musical examples demonstrate possibilities for working successfully with algorithmic and generative processes in sound, from formal decisions to synthesis.Keywords: Algorithmic and generative composition, aesthetics, random and stochastic processes, chaos systems, sound synthesis.


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AN ANALYTICAL AND NUMERICAL INVESTIGATION OF THE DISSIPATIVE CHAOS IN SEMICONDUCTOR SUPERLATTICES

Alireza Heidaria , O. Anwar Bé gb & P. Oseloka Ezepuec

aComputational Physics, Department of Chemistry, Ferdowsi University of Mashhad, Mashhad 91775-1436, Iran. Email: [email protected] Research Leader: Biomechanics, Biotechnology and Computational

Magnetohydrodynamics, Mechanical Engineering Program, Department of Engineering and Mathematics, Room 4112, Sheaf Building, Sheffield Hallam University, Sheffield, S1 1WB,

England, UK. Email:[email protected] Research Leader: Business Intelligence & Quantitative Modelling, Department of

Computing, Room 2211 Harmer Building, Sheffield Hallam University, Sheffield, S1 1WB, England, UK. Email: [email protected]

The transport of electrons in a semiconductor superlattice miniband under the influence of electrical and magnetic fields, which are applied in different directions on the superlattice, is investigated. The time series diagrams and the Lyapunov exponent are computed using the fourth-order Runge-Kutta method. The numerical computations show that for particular values of the parameters, which depend on the superlattice characteristics and the fields applied on them, electrons show chaotic behaviors. In addition, for some other parameter values these behaviors become regular and non-chaotic. The presence of a magnetic field, perpendicular to the electrical field, is shown to reduce the chaotic areas in the motion of the electron. An alteration in electron average energy and velocity is attributed to application of the external fields, carrier scattering from other carriers, and the phonons’ and lattices’ faults. The study has important applications in computational physics and semi-conductor chaotic simulations.

Keywords: Dissipative chaos; Semiconductor superlattices; Miniband; Electrons transport; Lyapunov exponent; fourth-order Runge-Kutta method

PACS: 02.; 02.60.-x; 02.70.-c; 05.; 05.10.-a; 05.45.-a; 05.45.Gg; 05.45.Pq; 05.45.Tp; 05.45.Vx

Unstable periodic spatio-temporal states of spatial extended chaotic systems

Alexander E. Hramov, Alexey A. KoronovskiiFaculty of Nonlinear Processes, Saratov State University,

83 Astrakhanskaya Saratov 410012 RussiaE-mail: [email protected]; [email protected]

Unstable periodic orbits embedded into chaotic attractors are wellknown to play an important role in the dynamics of the non-linear chaotic systems. In the spatial extended systems the unstable periodic spatio-temporal states (UPSTSs) also exist which are similar to the unstable periodic orbits in the chaotic systems witha small number of the degree of freedom. In particular, the chaotic dynamics of spatial extended systems may be controlled by stabilizing such unstable periodic spatio-temporal states [PRE. 59 (1999) 6574; CHAOS. 16 (2006) 013123]. One of the important problem connected with the study of the spatial extended chaotic system is finding these UPSTSs. It is appropriate to suggest that the methods aimed at the search of unstable periodic orbits of the dynamical systems with small dimension of phase space may be adapted to the spatial extended systems.

In this report the method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems have been proposed. This method has been based on the modification of the method of P. Schmelcher and F. Diakonos [PRL. 79 (1997) 4734; PRE 64 (2001) 026214] allowing precise detection of UPSTSs in the spatial extended chaotic systems. The application of this method has been illustrated by the consideration of two different systems: (i) the fluid model of Pierce diode being one of the fundamental system of the physics of plasmas and (ii) the complex one-dimensional Ginzburg-Landau equation demonstrating different regimes of spatio-temporal chaos. The application of this method has


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been also discussed in context of chaos controlling in spatially extended systems by means of stabilization of unstable periodic spatio-temporal states.

Key Words: spatial extended chaotic systems, unstable periodic orbits, chaotic oscillations, controlling chaos

Comparison of the Characteristics of Eyelet Intermittency and Type-I intermittency with Noise

A.E. Hramov, A.A. Koronovskii, M.K. Kurovskaya, O.I. MoskalenkoSaratov State University, Saratov, Russia


In this article we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency) supposed hitherto to be the different phenomena. We prove that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is proven by the consideration of sample systems.

Keywords: Fluctuation phenomena, random processes, noise, synchronization, chaotic oscillators, dynamical system, intermittency.

1. IntroductionIntermittency is well-known to be an ubiquitous phenomenon in nonlinear science. Its arousal and main statistical properties have been studied and characterized already since long time ago, and different types of intermittency have been classified as types I--III, on-off intermittency, eyelet intermittency and ring intermittency.

Despite of some similarity (the presence of two different regimes alternating suddenly with each other in the time series), every type of intermittency is governed by its own certain mechanisms and the characteristics of the intermittent behavior (such as the dependence of the mean length of the laminar phases on the control parameter, the distribution of the lengths of the laminar phases, etc.) of different intermittency types are distinct. There are no doubts that different types of intermittent behavior may take place in a wide spectrum of systems, including cases of practical interest for applications in radio engineering, medical, physiological, and other applied sciences.

Our report is devoted to the comparison between characteristics of type-I intermittency in the presence of noise and eyelet intermittency taking place in the vicinity of the phase synchronization boundary. These types of the intermittent behavior seem to be different and determined by the distinct causes. First of them is observed near the saddle-node bifurcation point in the system enforced by the external stochastic signal. The second one takes place in the vicinity of the phase synchronization boundary in two coupled deterministic chaotic oscillators and it is explained in terms of the synchronization of the unstable periodic orbits embedded into chaotic attractors. Moreover, these types of intermittency are known to be characterized by the different theoretical laws. Nevertheless, we show that these two types of the intermittent behavior considered hitherto as different phenomena are, in fact, the same type of the system dynamics.

The linguo-combinatorial simulation of complex chaotic systems

Mikhail B. IgnatyevSt-Petersburg State University of Aerospace Instrumentation,67 Bolshaja Morskaja uliza, St-Petersburg, 190000, Russia,

E-mail: [email protected] Fax (812)710-65-10.

It is considered the systems with structured uncertainty which is determined by mean of number of the arbitrary coefficients. The arbitrary coefficients defines the chaotic behavior. Any complex system interacts with its changing environment and its viability depends on its adaptability. The number of arbitrary coefficients in the structure of equivalent equations of complex system changes in the process of learning. In systems with more than six variables,


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the number of arbitrary coefficients increases first, and then, passing through the maximum, begins to decrease. This phenomenon makes it possible to explain the processes of system growth, complication and death in biological, economical and physical-engineering systems. We use the linguo-combinatorial method of investigation of complex systems, in taking key words for building equivalent equations. This phenomenon is able to increase the adaptability of different chaotic systems.

Keywords: Adaptability, Combinatorial simulation, Uncertainty, Appearance, Essence, General systems theory, Chaos, Physics, Biology, Social-economics.

Recovering a vector field with the aid of controlled noise

Gabriele IngleseIAC-CNR, via Madonna del Piano 10, Sesto Fiorentino, 50019 Firenze, Italy

[email protected]

We derive an inversion formula for stationary Fokker-Planck equation that can be used for studying some inverse problems in dissipative dynamics.Key Words: Stochastic perturbation of ODE,inverse problems in dynamics

COMPUTATIONAL STANDPOINT OF MIXING FLOWS – FROM TURBULENCE TO CHAOS

Adela IonescuUniversity of Craiova, Romania

[email protected], www.imst.ro

This paper aims to exhibit some of recent challenges in computational approach of modeling the excitable media. Computational Fluid Dynamics (CFD) becomes more and more mature and its tools are increasing in importance. However, how CFD develops remains unpredictable, and it is making itself an exciting research area.

Nowadays, the mixing flow study takes part of CFD. Studying a mixing for a flow implies the analysis of successive stretching and folding phenomena for its particles, the influence of parameters and initial conditions. In the previous works, the study of the 3D non-periodic models exhibited a quite complicated behavior. In agreement with experiments, they involved some special events - the so-called “rare events”. The variation of parameters had a great influence on the length and surface deformations. The experiments were realized with a special vortex installation, it was used a well-known aquatic algae as biologic material, and the water as basic fluid. It must be noticed that both the experimental and analytical analysis worked for any biological material.

A recent challenge is to unify the mixing theory. In this order, CFD brings the computational approach of the turbulence in mixing flows. There are used widespread appliances of MAPLE11 soft, in order to achieve the statistical information necessary to collect the data.

This paper aims to exhibit some of recent work in this area. The fast tools of MAPLE 11 give rise to interesting comparative analysis, both from analytical and numeric standpoint.


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Analysis of Coupled Oscillators Applied to 1-D Antenna Arrays

Mihai Iordache1, Lucia Dumitriu1, Jean-Marie Paillot2, Iulia Dumitrescu1

1 Politehnica University of Bucharest, Electrical Department2Unifersity of Poitiers, LAII

[email protected], [email protected], [email protected]

In the last years, coupled oscillators have shown their efficiency as simple methods for phase control in microwave antenna arrays, and hence as alternatives to conventional electronic beam steering methods. In this paper, a new writing of the nonlinear equations to describe the oscillators’ locked states is presented. These equations are in time domain and in frequency domain. This region is plotted versus the oscillators’ tunings referred to the resonant frequency of the coupling circuit. A prototype circuit consisting of a six oscillators array is currently under test to validate the theory. It is compared the obtained results by the analysis in time domain and by the analysis in frequency domain.

Understanding Chaos using Discrete-Time Map for Buck Converter

Sajid Iqbal1, Kashif Ali Khan2, Shahid Iqbal31Department. of Electrical Engineering, Faculty of Engineering., University of Gujrat.

2Department of Mathematics., University of Gujrat3Department of Computer Science., Virtual University

[email protected] Research in nonlinear dynamics and complexity has made remarkable progress in recent years. Almost all power electronic circuits exhibit some kind of nonlinear behavior e.g., quasi-periodicity, sub-harmonic oscillations, bifurcation, chaos. The aim of this paper is to investigate the nonlinear phenomenon and chaotic behavior in a DC-DC buck converter. The derivation of the discrete-time map for the buck converter is given. This map is simulated and the results infer chaotic behavior.

Key Words: Bifurcation, chaos, buck converter, strange attractor.

Self-ordered front under aperiodically oscillating zero-mean ac force: front dynamics with time delays

V. Jasaitis1, F. Ivanauskas1 and R. Bakanas2

1Faculty of Mathematics and Informatics, Vilnius University, Vilnius, [email protected]

2Semiconductor Physics institute, A. Goštauto 11, 2600 Vilnius, Lithuania

The rectified oscillatory motion (ratchet-like transport) of the self-ordered “bistable” fronts (BFs) joining two states of the different stability in a bistable system of the reaction-diffusion type, being under the action of the quasi-periodically oscillating force of zero time average is investigated. In considering the front dynamics we approximate the ac force acting on the front in the system by multi-harmonic forcing function being a superposition of the single-harmonic (Fourier) modes with incommensurable frequencies. The average characteristics of the spurious drift of BFs versus both the amplitude and the frequency of the fundamental mode of the ac drive are presented. By comparing the average characteristics of the spurious drift of BFs, derivable in both cases of the irregular (quasi-periodic) and regular (periodic) forcing functions we show that the occurrence of the irregular fluctuations in the oscillatory force leads to a lower performance of the ratchet-like shuttling of BFs. Furthermore, we find that the retardation effects (the moment velocity delays) in the front dynamics shrink the spurious drift discussed; the unforced dc motion of BFs practically disappears if the frequency


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of the fundamental mode of the quasi-periodically oscillating force exceeds the characteristic relaxation rate of the system.Keywords: nonlinear dissipative systems, self-ordered fronts, ratchet-like transport, partial differential equations.

Identifying Time-Series Candidates for Efficient Nonlinear Projective Noise Reduction II

N. Jevtic [a,b], P. Stine [a], J.S. Schweitzer [b] [a] Physics and ET, Bloomsburg University

400 East Second St, Bloomsburg, PA 17815-1301 [b] Physics Department, University of Connecticut2152 Hillside Rd, U-3046, Storrs, CT 06269-3046

One of the principal problems in nonlinear time-series analysis of real-world data is

noise. Two new results in the application of nonlinear projective noise reduction in astrophysics will be discussed: (a) In the search for extrasolar planets in resonance using the transit method, the choice of delay can be made to either lower noise at maximum dimming or as the transits begin and end, where one would actually look for planets in resonance. To achieve the most useful results, a discussion of the trade-offs in the selection of the delay to either lower the white noise tail or to lower the power at lower frequencies will be presented. (b) For some white dwarfs with noise-like power spectra, surprisingly good noise reduction is reported. This unexpected result is shown to be the result of a predominantly two-dimensional phase-space reconstruction over short time scales, time-scales that are not accessible by any other method.

In both contexts, simulated time-series data and quasiperiodic light curves will be analyzed.

Basic deformation principles based on transformations of atomic systems of crystalline materials

Audrius JutasKTU, Department of mechanics of solids, Kaunas, Lithuania

[email protected]

The main aim of this paper is calculation of physical constants and engineering characteristics of crystalline materials using lattice deformation model-LDM at nano-, micro- and macro-scales. The objective of this work is the creation of methodology that allows to prevent the physical characteristics such like modulus of elasticity and shear modulus, Poisson’s ratio (till now obtained as experimental results) for metallic alloys contained different chemical compositions using lattice architecture; for the next, on the computer to draw the experimental curves (tension, compression, torsion…) that could be used for engineering solutions by the chosen material properties (strength, thermal resistance, other) and dimensions of specimens; for the third, to create methodology for visualization of stresses and strains used in design according to the chosen loading type.Key Words: Atomic systems, simulation, physical constants of crystalline


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Dissipative Solitons: Perturbations and Chaos Formation

Vladimir L. KalashnikovInstutute for Photonics, Technical University of Vienna, Vienna, Austria


The perturbations of chirped dissipative solitons are analyzed in the spectral domain. It is shown, that the structure of the perturbed chirped dissipative soliton is highly nontrivial and has a tendency to an enhancement of the spectral perturbations especially at the spectrum edges, where the irregularities develop. Even spectrally localized perturbations spread over a whole soliton spectrum. As a result of spectral irregularity, the chaotic dynamics develops due to the spectral loss action. In particular, the dissipative soliton can become fragmented though remains localized. Keywords: Dissipative soliton, Complex nonlinear Ginzburg-Landau equation, Perturbation theory, Chaotic soliton dynamics.

LUMINESCENCE OF STRUCTURES FORMED IN AQUEOUS ALCOHOL SOLUTIONS OF ANTHRAQUINONE

Svetlana KaritskayaUrals State Technical University (USTU-UPI)

Mira,19, Ekaterinburg 620002, Russian [email protected]

The investigation of the properties of micellar systems is of great practical importance, since the microheterogeneous structure, in particular, of aqueous-organic solutions can be used to create reaction centers with designed properties, which will make it possible to increase the efficiency of processes associated with the intra-molecular conversion of the electronic excitation energy of a molecule. In the present paper, such model systems are the spatial-temporal structures (STS) formed as a result of photophysical and photochemical reactions, whose time characteristics are highly sensitive to a change in the solvent compositions.Previously, the phenomenon of heat-and-mass transfer in the form of redistribution of concentrations of reagents and photoreaction products in the reaction-space volume in alcohol solutions of anthraquinone at various ketone concentrations was investigated. It was shown that the luminescent photoproduct (ketyl radical) of anthraquinone is responsible for the formation of structures in this system. The STS evolution processes are slow and the structures formed have macroscopic sizes, which makes the system under consideration a convenient object for experimental studies.One promising method for controlling energy photo transformations in the system under consideration is the use, as a solvent, of water-alcohol mixture, which, on the one hand, is a hydrogen atom donor and, on the other hand, (due to the micro heterogeneity of its structure caused by the presence of density gradient at the interface) exhibits properties radically differing from the properties of homogeneous media and true solutions.It was shown; a change in the mass content of alcohol in the water-alcohol mixture produces a strong effect on the time characteristics of different stages of STS evolution. For instance, the development of UV-radiation-initiated structures in water-alcohol solutions of anthraquinone proceeds without the third (vibrational) stage characteristic of alcoholic solutions. The influence of the structure of water-alcohol solutions is most clearly traced by the induction period of STS formation.The micro heterogeneous structure of aqueous alcohol solutions produces a strong effect on the intermolecular energy transfer rate, which in turn affects the behavior of luminescent STSs: a change in the induction period of the appearance of structures and their evolutionary development in space and time is observed. Such a behavior is associated with the micelle formation and solubilization processes proceeding in aqueous alcohol solutions


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Nature inspired language modelling for text analysis solutions

Marcin KarwinskiUniversity of Silesia, Jaworzno, Poland

[email protected]

The aim of this paper is an analysis of the inter-language dependency and effects of simulated evolutionary processes on linguistic model's grammar class recognition efficiency. 'Static' models propounded by linguists prior to the advent of the Internet are focused on error-proof written forms. Though the 21st century becomes dominated by ubiquitous English language, it is in its various non-standard forms. As a result, existing methods require seemingly 'chaotic' modifications to the 'regular' language modelling approach to ensure resilience to such users' linguistic impurity through condoning the malforms according to the grammar correctness and phrase acceptability paradigms, further increasing performance and dependability of text analysis systems. Key Words: language modelling, T-rules, evolution, text analysis

Modified Chaotic Shift Keying using Indirect Coupled Chaotic Synchronization for Secure Digital Communication

Rupak Kharel, Krishna Busawon, Z. GhassemlooyNorthumbria Communication Research Lab, Northumbria University

Newcastle Upon Tyne, United [email protected]

In this paper, a new method for synchronizing two chaotic systems based upon indirect coupling is proposed which is used to generate same keystream at both the transmitter and the receiver side. Based upon this, a modified chaotic shift keying method is developed to transmit digital bits securely over a communication channel. The scheme is based upon encrypting the digital bits 0 and 1 into infinite levels by applying the keystream such that there is no pattern whatsoever in the encoded transmitted signal. The encoded transmitting signal generated is shown to resist popular attack method (return map method) therefore realizing asecure and trustworthy digital communication system. Simulation result also confirms that the digital bits are successfully recovered on the legible receiver.Key Words: chaotic shift keying, chaotic synchronization, secure communication, return map

NONLINEARITY OF EARTH: ASTONISHING DIVERSITY AND WIDE PROSPECTS

O.B. Khavroshkin, V.V. TsyplakovSchmidt Institute of the Earth Physics, RAS

Moscow, Russia; [email protected] diversity of nonlinearity of seismic waves, fields and processes really have many peculiarities which in common are similary nonlinear effects of other scientific division. Only a seismic acoustic emission and the modulation of high frequency seismic noise are belonging for seismology. Therefore description of its is general and other direction will be shortly mention.

1. THE SEISMIC-ACOUSTIC EMISSION AND MODULATION.

The modulation of high frequency seismic noise (15-300 Hz) by long-time deformation processes of the Earth are being studied experimentally from the very moment of its discovery in 1975 till present. A method of a narrow band filtration and singling out an envelope curve for recording some noise characteristics has been first grounded and applied


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by Khavroshkin and Tsyplakov. According to definition and characteristics of an enveloping curve variations of the accidental process at the output of narrow-band filter the data of registration of envelope amplitude give information about process intensity and its low-frequency changes. The relation of these variations (a modulation effect) of regional noise level to the processes which deform the Earth’s lithosphere: the lunar-solar tides, the Earth’s proper oscillations, microseism storms and wave packets from earthquakes and explosions has been found and studied [1-3]. A qualitative mechanism of generation of a part of high frequency noise has been considered. A model of a local distraction and/or reconstruction of various scale defects of the deformed stressed geophysical media has been used. The concept of a seismic acoustic emission (SAE), analogue of acoustic emission has been introduced. Long-duration research revealed that usually the anomalous variations of SAE relate tectonic activity growth (earthquakes) in specific form [4]. These SAE anomalies were found to exceed considerably the variations resulting from the other known regional noise effects (like tides, changes of meteorological and fluid-dynamic conditions) [1]. Tectonic activity of region is adequately represented by SAЕ envelope. 2. Seismic self-oscillations; self-chaotic and self-order of vibroseismic signals.3. Solitary sign and peculiarity of seismic waves and fields.4. Seismic waves’ interraction; conversion of seismic wave front.5. Applied and fundamental using of seismic nonlinearity.6. Cosmogonic nonlinearity.

REFERENCES

1. Khavroshkin O.B. Some problems of nonlinear seismology. 1999. United Institute of Physics of the Earth Press., Moscow. P.286

2. Rykunov L.N., Khavroshkin O.B., Tsyplakov V.V. The effect of modulation of high frequency noise of the Earth // Discovery Diploma 282 Goskomizobreteniy USSR. 1983 Moscow. P.1

3. Rykunov L.N., Khavroshkin O.B., Tsyplakov V.V. The modulation of high frequency microseism // J. Dokl. Science Section. 1978. V.238. Translated from Reports of the Academy of Sciences USSR. V.238, p.303-306

4. Diakonov B.P., Karryev B.S., Khavroshkin O.B., Nikolaev A.V., Rykunov L.N., Seroglasov R.R., Trojanov A.K., Tsyplakov V.V. Manifestation on earth deformation processes by high frequency seismic noise characteristics // Physics of the Earth and Planetary Interior. Amsterdam. 1990. 63. 151-162

REDUCING OF SEISMIC VULNERABILITY & SHORT TIME EARTHQUAKE PREDICTION:METHODS AND INSTRUMENTS OF NONLINEAR SEISMOLOGY

O.B. Khavroshkin, V.V. TsyplakovSchmidt Institute of the Earth Physics, RAS

Moscow, Russia; [email protected]

Elimination of human losses is the main and immediate task in the seismic vulnerability problem. We suggest the ways of development of seismic research and discussion of defense problems for reducing of seismic vulnerability. It is the ways of nonlinear seismology region. Unconditionally seism zoning and the theory of catastrophes allow reduce human losses and building destruction. But well-known isoseists are the private case of caustic catastrophe theory or seismic-acoustics, so seism zoning can be amounted to 6 elementary catastrophe forms. It will better help to predict seismic actions.

The short-time local prediction of seismic events is general method for strong reducing of human losses. This method takes into account chaotic properties of stress fields and waves and the peculiarities of urban area. It bases on the natural seismic-emission phenomenon and is realized by long-time monitoring, which gives statistically and geographically continuous picture (chart) of seismic noise level inside geologic media. The instruments of this strategy are shock- and pressure- proofed seismometers for long-time monitoring and control the state of geological media including underwater shelf areas.


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We think that the active protecting for cities and buildings as the best modern form of people safety consists in stress discharge of geologic media. Ultrasonic wave defense includes and bases on strong interaction between powerful waves from earthquake and ultrasonic wave train. We want to point out that the technical objects may be used for the investigation of earthquakes induced and some reasons of seismic vulnerability. Also reducing of seismic vulnerability contain as component kinetic acting on volcano at the pre-explosive stage.

The interesting and important aspect of defense problem is observation of the inharmonic wave processes in the soil and quasi-constant forces as the nearest seismic analogue of radiation forces in nonlinear acoustics under powerful earthquake seismic tremor.

Seismic lunar nonlinearity: peculiarities and Moon as astrophysic and cosmogonic detector

Khavroshkin O.B., Tsyplakov V. V. (IPE RAS)Schmidt Institute of the Earth Physics, RAS

Moscow, Russia; [email protected]

The moon as the cosmogonic and astrophysical mega detector has given essentially new information which initial form is received through seismicity (Nakamura Catalogue). Deeper understanding of lunar seismicity gives the analysis of time characteristics of last and integrated parameter of nonlinearity of the Moon as heavenly body as a whole. The parameter of nonlinearity was defined as the relation of squares of amplitudes determined on each year interval of the second tidal harmonic to the basic. The seismic factor of filling of intervals of breakdown of the Catalogue and parameter of nonlinearity are entered, the analysis of their numbers (series) with use of testing signals - solar - terrestrial tides and their harmonics is carried out. As testing the periods in 412 and 206 day (Tsandler`s nutation) and the orbital period of rotation of Venus (225day) were used also because Venus modulates gas dust and meteoroid streams. In result it is revealed: on years the parameter of nonlinearity can vary in 2-3 times, but last 2 years of supervision it is practically stable. Venus harmonic in realizations of number seismic impact and seismic factor changes smoothly but with significant depth of modulation; the harmonic in 206 day is deeply modulated and shifted on a phase be relative Venus period. The harmonic on the period of 412 day - is stable. So the seismic response of the Moon to various "testing" influences has the significant time variations probably caused by internal properties and the parameter of nonlinearity exceeds terrestrial.

Results of previous research linked lunar seismicity (Nakamura Catalogue) and cosmogonic objects and processes are briefly outlined.

The Mapping of Impact Processes from Meteoroid Streams and Solar Wind on the Moon into Durations of Seismograms: Data of annual constructed histograms (distributions) for durations of seismograms from exogenous acting on the Moon were analyzed. Peculiarities of these acting and its comparison with data of optic lunar events were taken into consideration. It has been found that dust-gas plasma of meteoroid streams and solar wind are modulated by Sun free oscillations and histograms from meteoroid streams with intensity of 4-8 impact/days contain durations according to periods of free lunar oscillations.

The Temporal Structure of Meteoroid Streams and Lunar Seismicity; peculiarity of shape of histograms envelops: The shapes of histograms envelops for anneal interval are changed from Gauss to more complicated curve. It betokens unsteady-state of seismic processes and at times similarity of these to earthquake recurrence curve for region of mines and/or to energy distribution for high power solar bursts.

Simple estimation for nongravitational effects on the Moon: assessments of integral pressure to the Moon by solar wind (under undisturbed Sun and Sun burst) and gas-dust component of meteoroid streams have been made. Energy of these disturbances (under Sun bursts or its maximum stream density) is enough for free Moon oscillations initiation and recording lunar seismic events.


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Chaos problems in Observer’s Mathematics

Boris Khots and Dmitriy Khots Compressor Controls Corporation, Des Moines, Iowa USA, [email protected]

Kaplan University, Omaha, Nebraska USA, [email protected]

This work considers the solution of Cauchy problem (initial value problem) in a setting of arithmetic, algebra, topology provided by Observer’s Mathematics (see www.mathrelativity.com) and applies this solution to free wave equation, the linear (time-dependent) Schrodinger equation, the nonlinear Schrodinger (NLS) equation, the (time-dependent) Airy equation, the Korteweg-de Vries (KdV) equation, the generalized Korteweg-de Vries (gKdV) equation, quantum theory of two-slit interference, wave-particle duality for single photons, the uncertainty principle, complementarity in the energy-time uncertainty. Certain results and communications pertaining to solution of these problems are provided.Key words: Cauchy, wave, Schrodinger, Airy, Korteweg-de Vries, two-slit interference, uncertainty, observer2000 MSC: 81Q99

Hindcast of Storm Surge in the South Sea of Korea

Cha-kyum Kim and Jong Tae LeeGyeongnam Provincial Namhae College, Namhae-gun, Gyeongnam, Republic of Korea

[email protected]

A three dimensional numerical models were established to calculate the storm surges which were observed in the south sea of Korea during Typoon "Maemi" and "Rusa". Maemi and Rusa landed on the southern coast of Korean Peninsula on 12 September 2003 and 31 August 2002, respectively. Maemi and Rusa recorded not only tremendous economic loss but also historic weather survey in Korea. The storm surge including tide was hindcasted by 3D numerical model using an ADI (Alternating Direction Implicit) finite difference scheme. All numerical experiments were compared with observed sea surface elevations. Model results were sensitive to meteorological forcing, which were calculated from a parametric typhoon model. The simulated storm surge showed good agreement with tidal records. Key Words: numerical model, storm surge, typoon, hindcast

Bifurcation of countable number of periodic solutions in singularly perturbed differential-difference equations

Ivan KlevchukChernivtsi National University, Chernivtsi, Ukraine


We consider the singularly perturbed system

)),(),(),(,())(),(),(( tytytxthtytytxfdt

dx

)).(),(),(,())(),(),(( tytytxtPtytytxGdt

dy

(1)

Here is a small positive parameter and is a fixed positive number, ,2Rx nRy ,

functions ),,,,( zyxth ),,,( zyxtP are 2 periodic with respect to t ; 0)0,0,0()0,0,0( Gf ;

equation 0),,( yyxG has an isolated solution ),(xy .0)0( We assume that the

function )(x is thrice continuously differentiable and bounded, functions ),,,( zyxf

),,,,( zyxth ),,,( zyxG ),,,( zyxtP are thrice continuously differentiable and bounded as ,Rt

,2Rx ,|)(| xy .|)(| xz Let ))(),(,( xzxyxG ),,,()()( 121 zyxGzxByxB


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where )|||(|),,( 221 yxOzyxG when ;0|||| yx all roots of the characteristic equation

0))exp()()(det( 21 IxBxB lie on the half-plane .02Re Then the integral manifold of system (1) can be represented in the form

),(),,()( 2 Oxtgxyt where

))(),(,())([()]()([),,( 21

21 xxxfx

xBIxBxBxtg ))](),(,,( xxxtP

)),(),(,( xxxfx

.0 We show that, under certain conditions on the right-hand

side, the Poincare map for a perturbed system possesses a transversal homoclinic point [1]. The Melnikov method is used to analyze saddle-node bifurcations. If degenerate system is hamiltonian, then we obtain a countable number of periodic solutions. The stability of these periodic solutions is also investigated. We consider some examples.[1] Klevchuk I.I. Homoclinic points for a singularly perturbed system of differential equations with delay, Ukr. Math. J. 54, No. 4, pp. 693-699 (2002).

Statistical complexity of low-and high-dimensional dynamical systems

R. Kobayashi and V.B. RyabovFuture University-Hakodate, Hakodate, Hokkaido, Japan

[email protected]

We propose a new method of analyzing experimental time series that allows to distinguish between the cases of high-dimensional dynamics and stochastic motion. It is based on the idea of statistical complexity, i.e. the Shannon entropy of the so-called epsilon-machine (a Markov-type model of the observed time series). This approach has been recently demonstrated to be efficient for making a distinction between a molecular trajectory in water and noise. In this paper, we analyze several low- and moderate- dimensional dynamical systems demonstrating chaotic behavior to elucidate the basic mechanism that makes high the value of complexity in deterministic systems. In particular, we show that the value of statistical complexity is high for the case of Hamiltonian systems, such as the standard map, and attains intermediate values between the former case and that of stochastic noise (zero complexity) in dissipative systems, such as Hé non and Ikeda maps. We further study the transition between low-dimensional and high-dimensional motion with the purpose of finding a link between dimensionality of motion and its complexity. Key Words: time series, computational dynamics, statistical complexity, ε-machine

Space flying vehicles orbital motion control system synthesis: power invariants

Alexander A. KolesnikovTaganrog Institute of Technology – Southern Federal University,

Dept. of Synergetics and Control Processes44, Nekrasovky str., Taganrog, 347928, Russia; [email protected]

We solve an applied problem of “low-trust” space vehicles control by using system’s law of gravity. Control laws synthesis procedure as well as simulation results are provided.

Keywords: modeling, space vehicle, nonlinear dynamics, nonlinear systems, nonlinear control.


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Synthesis method for new class of oscillators with inertial nonlinearity

Alexander A. Kolesnikov

Taganrog Institute of Technology – Southern Federal University, Dept. of Synergetics and Control Processes

44, Nekrasovky str., Taganrog, 347928, Russia; [email protected]

Basing on the power approach we develop synthesis method of new models for oscillators with inertial nonlinearity. This oscillator dynamics properties surpass ones for known types generators. So, proposed oscillator models may be applied to self-oscillatory system design including ones with dynamics chaos.

Synthesized generator engineering implementation can be performed by means of modern analog and microprocessor element base.

The theory and methods of regular and chaotic fluctuations generator design is rapidly developed branch of modern science and engineering.

Synergetics and scientific cognition

Anatoly A. KolesnikovTaganrog Institute of Technology – Southern Federal University,


Accounting the existing narrow specialization of many modern technical sciences it is necessary to state the important task of formation of such a holistic outlook. It turned out that in the past years the logic of scientific development lead to significant acceleration of the integration processes connected to studying of cooperative phenomena in the systems of various nature. So the synergetics as a science of cooperative processes began to play the role of a basic paradigm of the modern natural science. The difference of synergetic approach from the classical scientific methods is in identification of the fundamental role of self-organization in nonlinear dynamic systems. Synergetics becomes an evolutionary natural science that allows talking about creation of a meta-language in the problem of holistic understanding of various natural, technological, social and economic notions basing on a single scientific concept. This concept gives us ability to create a new attitude to the process of integral comprehension of various sciences.

Problem of synthesis of new natural laws: introduction in the system physics. Synergetics approach

(plenary report)

Anatoly A. KolesnikovTaganrog Institute of Technology – Southern Federal University,


As system's physics we define the field of modern science that develop system's approach to searching of new laws and regularities in nature, engineering and society. Basis of system's physics are conception of unity for self-organization and control processes. Virtually, any process in nature, engineer and society may be interpreted from this conception


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point of view. This conception provides unified description of various processes in surrounding world.

The method of adaptive control for amphibian aircraft motion under conditions of external environment extreme action

Anatoly A. Kolesnikov1, Victor A. Kobzev2, Phuong Nguyen3

1Taganrog Institute of Technology – Southern Federal University, Dept. of Synergetics and Control Processes

44, Nekrasovky str., Taganrog, 347928, Russia; [email protected] Aircraft Company, 1 Aviatorov Square, Taganrog, 347923, Russia,

[email protected] Chi Minh University of Technical Education, 01 Vo Van Ngan St.,

Ho Chi Minh City, Vietnam, [email protected]

We have developed new synergetics approach providing solution of amphibian aircraft motion adaptive control complex problem under conditions of external environment extreme action. This approach is based on method of analytical design of aggregated regulators (АDАR). By this approach we have solved following problems: (i) by exploring nonlinear dynamics math. model we get amphibian aircraft longitudinal motion fundamental laws providing longitudinal motion control laws for sufficiently general class of amphibian aircrafts; (ii) we get amphibian aircraft longitudinal motion fundamental laws with external perturbation observers providing amphibian aircraft stable motion and implementation of desired control goals as well as sufficiently improving of amphibian aircraft movement dynamics and structural adaptation to heavy sea worst conditions.Keywords: amphibian aircraft, motion control, adaptive control, nonlinear state observer, a-static control, synergetics theory of control.

Crisis control of risk society: synergetics conception

Tatiana A. KolesnikovaRussian railways company

Moscow, [email protected]

We propose new model of crisis control. Base category of this model is directed self-organization. We postulate the synergetics principle of social systems harmonization basing on gold section properties that we use as fundamental main system invariant; we explore risks in social-labor sphere providing definition this sphere point of tenderness; we propose the law of labor pay (award stimulating) system that provide identification of such risk parameter as social strain.

Based on this law we propose most optimal control mechanisms of social-labor sphere for social inequality society.

Keywords: golden section, social-economics system, invariant, self-organization, social strain, social risks, labor pay system.


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Structural Heterogeneity of Detonation Diamond – Containing Material

Anatoly Korets*, Alexandr Krylov, Evgeny MironovSiberian Federal University, 26, Kirensky str., Krasnoyarsk, 660074 Russia,

Institute of Physics SB RAS, Akademgorodok, Krasnoyarsk 660036Krasnoyarsk Institute of Railway Transport (a Filial of Irkutsk State University of Railway

Engineering.), 660028 Krasnoyarsk, 89 L. Ketskhoveli str., RussiaEmail: [email protected]; [email protected]

Diamond-containing material (DCM) synthesized by detonation were separated into fractions. Raman and infrared spectra (IR) and X-ray diffraction patterns (XRD) of the individual fractions were measured. The particles of this material were characterized by the variable ratio of the diamond (sp3) and non-diamond components. The distribution of sp3-grains in the particles was of complicated character. The fine DCM particles contained insignificant amount of diamond. The experiments allow discussing the fluctuations influence on the DCM formation.

Keywords: diamond-like carbon, density fluctuations, impurity characterization.

An Energy Based Investigation of Chua's Circuit

Mustafa Kosem and N. Serap SengorElectronics and Communication Engineering Department, Faculty of Electrical and Electronic

Engineering, Istanbul Technical University, Maslak, TR-34469 Istanbul, [email protected]

In order to deal with nonlinear systems, energy functions have been considered in many applications. In this paper, the analysis of Chua's circuit will be given based on energy functions. The aim is to set an approach based on energy functions to understand the mechanism behind the chaotic behavior of Chua's circuit. In order to explain the effect of nonlinear resistor on the behavior through energy function, different nonlinearities are considered and the simulation results are given. Key Words: Energy shaping, Chua's circuit

Movement of the linear configuration of the five vortices

Korniy KostkinTaras Shevchenko National University of Kyiv, Kyiv, Ukraine.


The paper deals with the configuration of the five dotted vortices located on a straight line at equal distances from each other. In such a situation system undergoes a symmetrical rotation around the central vortex. In this case the trajectories described by the extreme vortices are in the form of petals. Also, we study stability of the system. It is proved that the system is in unstable equilibrium, and if you extract any of the vortices from the initial position, the system breaks down. In the second part the dependence distance between the vortices, in which the vortices begin to rotate being on the same line, was found. The exact dependence was unknown before. The motion of the system was numerically modeled.

Keywords: Vortex, Vortex chain, Unstable equilibrium, Stability.


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2D VERSION OF THE MODIFIED NIKIFOROV MODEL

V.I.Kozlov, A.R.Guzhova, Yu.V.YanilkinRFNC-VNIIEF, Sarov, Russia

The papers [1,2] offer the modified Nikiforov model, which provides an adequate description of the physics of shock wave/turbulence interactions and, thereby, provides convergence of difference solutions to the model equations. The modification performed allows noticeable expansion of the set of flows that can be simulated. The paper presents the modified Nikiforov model’s generalization to include 2D turbulent flows. The given paper supplements the paper [3], which contains the Nikiforov model description generalized for a 2D case. The paper discusses restrictions imposed on the dissipative terms of the turbulent value balance equations that result from availability of the joint fluctuation distribution function for velocity vector and density components.

The model has been implemented numerically within EGAK codes [4]. The model efficiency is illustrated with results of computations. The paper considers the Meshkov experiments on studying the mixing process at the interface of different-density gases caused by the convergent cylindrical shock wave passed across the interface and the submerged turbulent jet.

References

1.V.I.Kozlov. Simulations of SW/turbulence interations // Proceedings of the 10th International Workshop on the Physics of Compressible Turbulent Mixing, Paris, 17-21 July, 2006, France.

2.V.I.Kozlov, I.V.Sapozhnikov. Non-steady turbulent flow simulation on the base of modified Nikiforov model // Proceedings of the 10th International Workshop on the Physics of Compressible Turbulent Mixing, Paris, 17-21 July, 2006, France.

3.A.R.Guzhova, V.I.Kozlov, Yu.V.Yanilkin. 2D turbulent flow computation techniques based on Nikiforov model // VANT, Ser.: Theor. and Appl. Physics, Issues 1-2, 2003, pp.29-35.

4.N.S.Darova, O.A.Dibirov, G.V.Zharova, A.A.Shanin, Yu.V.Yanilkin. EGAK code system. Lagrangian-Eulerian techniques for 2D gas dynamic multicomponent fluid flows. // VANT, Ser.: Math. Model. Phys. Process., Issue 2, 1994, pp.51-58.

Method of State Space Expansion in Non-interacting control

Svetlana A. Krasnova, Victor A. Utkin and Anton V. UtkinInstitute of Control Sciences, Russian Academy of Sciences

Profsoyznya, 65, Moscow, [email protected]

The results of constructive analysis and block design of the problem of non-interacting control in the nonlinear dynamic systems were presented. As compared with the well-known results of the control theory, the method of state expansion enabled augmentation of the class of systems that are controlled autonomously in the output variables. The state observers on sliding modes were used for the dataware of the basic algorithms. The procedure developed feature multilevel decomposition of the problem of high-dimensionality design into smaller independent subproblems.

Key Words: Non-interacting control, Nonlinear system, State space expansion


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Adaptive control of the nonlinear dynamic object at the stage of breaking under indefinite contact surface conditions

Olga D. Kreerenko“Beriev Aircraft Company” JSC, Technological Institute of Southern Federal University,

Taganrog, RussiaEmail: [email protected]

Effective control of the wheel slip during braking is one of the most known and at the same time this issue arising during design and development of the aircraft technique and transport is still far from resolution. This research deals with a minimization of the airplane length of brake path while mowing along the runway surface. The contact conditions of the surface are supposed to be unknown and varying with the distance covered by the object. The solution is based on applying of friction coefficient curves obtained from experimental results as a function of velocity and slip combined in compliance with proposed procedure for identification of the current parameters of the contact surface conditions. There is shown that the control algorithm have been developed assures slip handling to calibrated value, and thereat indentifying characteristic of the adaptive (self-tuning control - STC) algorithm represented as exponentially fast convergence allows verify exact value of real-time calibrated slip. Thus there is compliant implementation of effective breaking control together with estimation of the breaking parameters in real-time processes. Keywords: adaptive (self-tuning) control, identification, nonlinear dynamic object, friction coefficient.

Freedom and Necessity in Computer Aided Composition:A Thinking Framework and its Application

Johannes KretzZentrum für innovative Musiktechnologie (ZiMT) der Universität für Musik und darstellende

KunstWien, Vienna, AustriaEmail: [email protected]

This paper presents some of the author’s experiences with computer aided composition (CAC): the modeling of physical movements is used to obtain plausible musical gestures in interaction with constraint programming (rule based expert systems) in order to achieve precisely structured, consistent musical material with strong inner logic and syntax in pitch material. The "Constraints Engine" by Michael Laurson implemented in OpenMusic (IRCAM) or PWGL (Sibelius Academy) can be used to set up an interactive framework for composition, which offers a balance of freedom (allowing chance operations and arbitrary decisions of the composer) and necessity (through strict rules as well as through criteria for optimization). Computer Aided Composition is moving far beyond being ”algorithmic” or ”mechanical”. This paper proposes an approach based on evolutionary epistemology (by the Austrian biologist and philosopher Rupert Riedl). The aim is a holistic synthesis of artistic freedom and coherent structures similar to the grown order of nature.Keywords: Computer Aided Composition, CAC, physical modeling, music, composition, artificial intelligence, expert systems, evolutionary epistemology.


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A nonlinear Schrödinger equation in the statistical theory of spheroidal bodies

Alexander M. KrotLaboratory of Self-Organization System Modeling, United Institute of Informatics Problems,

National Academy of Sciences of Belarus, Surganov Str. 6, 220012 Minsk, [email protected]

A quantum mechanical interpretation of the statistical theory is proposed for initial gravitational interactions of particles inside the forming cosmological bodies (molecular clouds), which have fuzzy contours and are represented by spheroidal forms [1], [2]. The equation for quasi-equilibrium gravitational compression of a spheroidal body in a vicinity of its mechanical equilibrium is derived initially using the “vibrating strainer” model. The main contribution of this work is to show that interactions of oscillating particles inside a spheroidal body lead to a resonance increase of gravitational compression.

According to the proposed model of “vibrating strainer”, the special quantum mechanical conditions stimulate the coherent motion of oscillatory particles inducing an antidiffusion mass flow inside a slowly compressible gravitating spheroidal body. In this connection, the notions of antidiffusion mass flow density as well as antidiffusion particle velocity in a spheroidal body are introduced. The equations for calculating the partial derivative of the antidiffusion velocity (in the cases of absence or presence of an ordinary hydrodynamic velocity) as well as the complete derivative of the common (hydrodynamic plus antidiffusion) velocity with respect to time are obtained. As shown in this work, these equations are more general than the analogous equations derived in Nelson’ stochastic mechanics.

The linear Schrödinger equation as well as its generalization are considered in this work in connection with the Nelson’s statistical mechanics and the Nottale’s scale relativity. Moreover, both these equations of Schrödinger have been derived in the special case of a constant of gravitational compression function )(tG in the proposed antidiffusion equation when

02/)( mDt G and 2/)( MDt G respectively. This work considers mainly

the case of 2/)( tGt G which is different from the Nelson’s and Nottale’s considerations. In

this connection the derived equations for calculating the partial derivatives (relative to t ) of antidiffusion velocity and ordinary hydrodynamic velocity are used to obtain a nonlinear Schrödinger equation by analogy with the Nelson’s and Nottale’s theories. Really, nonlinear phenomena arise owing to self-organization processes into a spheroidal body under its formation. These nonlinear phenomena lead to nonlinear auto-waves [3] satisfying a nonlinear undulatory Schrödinger-like equation.

Keywords: molecular clouds, initial gravitational interactions, spheroidal bodies, quasi-equilibrium gravitational compression, “vibrating strainer” model, special quantum mechanical conditions, coherent motion of oscillatory particles, antidiffusion mass flow, antidiffusion velocity, nonlinear Schrödinger equation

References1. Krot A.M. A statistical approach to investigate the formation of the solar system / А.М. Krot

// Chaos, Solitons and Fractals. – 2009. – Vol.41 – 3. – P. 1481-1500.2. Krot A.M. On the principal difficulties and ways to their solution in the theory of gravitational

condensation of infinitely distributed dust substance / А.М. Krot //Proc. of the 2007 IAG General Assembly in the book "Observing our Changing Earth ", Vol.133 (Ed. by M.G. Sideris), Springer: Berlin, Heidelberg, 2009, pp. 283-292.

3. Krot A.M. Self-organization processes in a slow-flowing gravitational compressible cosmological body/ А.М. Krot //Selected papers of the CHAOS-2008 International Conference in the book "Topics on Chaotic Systems" (Ed. by C.H. Skiadas, I. Dimotikalis, C. Skiadas), World Scientific: Singapore, New Jersey, London, HongKong, 2009, pp. 190-198.


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On the relation between Vicsek and Kuramoto models of spontaneous synchronization

V.L. Kulinskii, O.O. ChepizhkoDepartment of Theoretical Physics, Odessa National University, Ukraine, Odessa, Ukraine

[email protected]

Two basic models of spontaneous synchronization, the Vicsek model for the self-propelled particles and the Kuramoto Model (KM) are investigated with respect to the introduction of the stochastic perturbation of the dynamics. In essential they are isomorphic at least within the mean-field approach. The isomorphism between two models allows to investigate the influence of the stochastic perturbation of the dynamic in the KM in a manner similar to that for Vicsek model. Within the mean-field approach it is shown that the type of the order-disorder transition is determined by the type of the stochastic noise. Two types of noise the scalar and the vector ones give qualitatively different behavior. New type of the stochastic perturbation -``mixed`` noise is proposed. It is the weighted superposition of the scalar and vector noises. The corresponding phase diagram ``noise amplitude vs. interaction strength`` is obtained.Key Words: self-propelled particles, self-organization

Electronic computing equipment blocks placement based on synergetics principles

Victor M. KureychikTaganrog Institute of Technology – Southern Federal University,

44, Nekrasovky str., Taganrog, 347928, Russia; [email protected]

Problems of electronic computing equipment blocks placement on a surface (chip) based on genetic algorithms are considered. The algorithm construction is based on evolution model and synergetic principles of completeness and blocks interaction in the search process. The construction of order of chaos during the placement process is based on analysis of exact and rough models. The rough model is sensitive to the start conditions. Big building blocks are placed on the basis of its analysis. The exact model allows making order inside the blocks. The experiments made have shown the algorithm effectiveness.

Synergetic ideas in innovative education

Victor M. Kureychik, Veronika I. PisarenkoTaganrog Institute of Technology – Southern Federal University,

44, Nekrasovky str., Taganrog, 347928, Russia; [email protected], [email protected]

New approaches in modern education system are considered. One of them is based on synergetic paradigm which is considered to be very important in the development of modern science and research. Different points of view on pedagogical synergetics are considered. Some ideas of foreign languages teaching based on synergetic ideas are presented.


46

Chaotic Oscillations Control in Microwave Virtual Cathode Oscillators

Semen A. Kurkin, Alexander E. Hramov,Alexey A. Koronovskii, Igor I. Magda

Saratov State University, Saratov, RussiaKharkov Applied-Physics Institute, Kharkov, Ukraine


Study of the controlling chaotic microwave oscillators is an important problem of nonlinear dynamics, microwave electronics and telecommunications. Firstly such investigations are important with a point of view of analysis of complex dynamics control in spatially extended electronic and plasma systems [1, 2]. On the other hand significance and timeliness of creation of controlling microwave sources of chaotic wideband signals is determined by wide application of such devices in various systems of information transmission based on the ideas of dynamical chaos [3], noise radiolocation [4], non-linear antennas [5], etc. Among the most interesting for nonlinear dynamics and prospective sources of chaotic signals of the microwave range there are systems using intensive beams of charged particles with virtual cathode (low-violtage vircators). The analysis of chaotic oscillation processes in spatially extended systems with intensive beams of charged particles in the regimes of virtual cathode (VC) formation attracts great attention of scientific community [6-8]. The systems with VC are well known to be characterized by the complex dynamics and can demonstrate a wide range of nonlinear phenomena, including dynamical chaos [6-9]. At present among the different electronic systems with VC the special interest is caused by vircators with external controlling feedback (virtodes) [10, 11].

Now there are two different principal types of virtodes: 1) virtode where the feedback mechanism is based on a feeding of a portion of the microwave signal from the virtual cathode region directly back into the anode–cathode gap and 2) virtode with collector replaced by a slow-wave structure with a beam collector downstream where backward waves from the slow-wave structure provide the necessary feedback. Tuning the parameters of external feedback in virtodes it is possible to increase power and to control the spectral characteristics of output microwave radiation in the generator. So, recent experiments have demonstrated that by tuning the phase in the feedback circuit, the power output could be varied by as much as 5 dB [10]. On other hand, the controlling of output microwave radiation characteristics in virtodes is important open problem with a view to fundamental research and practical applications mentioned above.

The physical processes occurring in virtodes and the nonlinear dynamics of such generators have been still investigated well. Particularly it hasn’t been studied the influence of virtode’s feedback parameters on the dynamics of electron beam with virtual cathode. The numerical simulation is an effective method for analysis of nonlinear dynamics in electron beam with virtaual cathode in the vircators with external controlling feedback .

In present report the results of numerical simulation of vircator with external controlling feedback (virtode) are presented. Nonlinear non-stationary processes in such electron beam system are investigated by means of the numerical analysis of 2D model based on self-consistent set of Vlasov and Maxwell equations. The nonlinear dynamics of relativistic electron beam in virtode with the change of feedback parameters have been investigated numerically. It has been discovered that the dependence of virtode’s nonlinear dynamics onfeedback parameters is connected with the complex process of premodulation of electron beam and as consequence formation of various spatial electron patterns connected with kinematic unstability of pre-modulated beam.

This work has been supported by Russian Foundation for Basic Research (project 09-02-00255-a, 10-02-90432) and Federal special-purpose program “Scientific and educational personnel of innovation Russia” (2009-2013).

References

[1] A.E. Hramov, A.A. Koronovskii, I.S. Rempen. Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback, CHAOS, 16: 013123, 2006.


47

[2] A.E. Hramov, I.S. Rempen. Investigation of the complex dynamics and regime control in Pierce diode with the delay feedback, Int. J. Electronics, 91 (1): 1-12, 2004.

[3] A.S. Dmitriev, A.I. Panas. Dynamic chaos: novel type of information carrier for communication systems, Fizmatlit, ISBN 5-94052-052-9, 2002.

[4] R.M. Narayanan, M. Dawood. Doppler estimation using a coherent ultrawide-band random noise radar, IEEE Trans. Antennas and Propagation, 48: 868, 2000.

[5] B.K. Meadows, T.H. Heath, J.D. Neff et al. Nonlinear antenna technology, Proceedings IEEE, 90 (5): 882-897, 2002.

[6] A.E. Dubinov, V.D. Selemir. Electronic Devices with Virtual Cathodes (Review), Journal of Communications Technology and Electronics, 47 (6): 575, 2002.

[7] V.D. Alyokhin, A.E. Dubinov, V.D. Selemir et al. Theoretical and experimental studies of virtual cathode microwave devices, IEEE Trans. Plasma Sci., 22 (5): 954, 1994.

[8] Yu.A. Kalinin, A.A. Koronovskii, A.E. Hramov et al. Experimental and Theoretical Investigations of Stochastic Oscillatory Phenomena in a Nonrelativistic Electron Beam with a Virtual Cathode, Plasma Phys. Reports, 31 (11): 938-952, 2005.

[9] V.G. Anfinogentov, A.E. Hramov. On the mechanism of occurrence of chaotic dynamics in a vacuum microwave generator with virtual cathode, Radiophysics and Quantum Electronics, 41 (9): 1137, 1998.

[10] P. Gadestski, I.I. Magda et al. The virtode: a generator using supercritical REB current with controlled feedback, Plasma Phys. Rep., 19: 273, 1993.

[11] S.A. Kitsanov et al. S-band vircator with electron beam premodulation based on compact pulse driver with inductive energy storage, IEEE Trans. Plasma Sci., 30: 1179, 2002.

A Predator - Prey Model with the Nonlinear Self Interaction Coupling xky

I. Kusbeyzi†*, O. O. Aybar†*, A. S. Hacinliyan†‡*

†Yeditepe University, Istanbul, TurkeyDepartment of Information Systems and Technologies, [email protected]

*Gebze Institute of Technology, Kocaeli, Turkey, [email protected] of Mathematics

‡Yeditepe University, Istanbul, TurkeyDepartment of Physics, [email protected]

A class of Predator – Prey Models suggested by the continuous form of the two dimensional map of the form

nnn

nnnn

YaXY

YXaXX

1

1 )1(.

After passing to the continuous time form of this map that generalizes the classical Lotka Volterra model by a quadratic self interaction term; an additional coupling of the form xky in the prey equation is added. The motivation for this is the fact that there is a simple relation between quadratic and cubic self interactions. If one lets x = u2 and y = v2, we get the interaction coupling uv2 in the prey and u2v in predator equation. It would therefore be of interest to study the simplest nontrivial generalization before this, namely couplings of the form xyk in the prey equation. The predator equation is that of the classical Lotka Volterra. The prototype form of the model involving this generalization, after making the variable changes x → ax and y → ay is:

xyyy

yxaxyxaxx kk

12)1(.

The model is shown to have resonant normal forms corresponding to the added coupling terms for integer values of its parameter a. For a given value of the number k we define the following family of systems of differential equations. Stability and bifurcation properties of


48

these models are examined. It is also shown that they have limit cycles irrespective of the etailed form of the coupling. Time series derived from these models are examined for invariant parameters such as Lyapunov exponents, fractal dimension as a function of its parameters. The techniques used for this analysis include time series analysis, rescaled range analysis and detrended fluctuation analysis. In order to examine the robustness and the stability of our results; the effects of noise on the analyzed systems are evaluated.

Keywords: Predator Prey Models, Bifurcation Analysis, Stability and Normal Form, Time Series Analysis, Detrended Fluctuation Analysis

References

[1] D. Ghosh and A. R. Chowdhury. On the Bifurcation Pattern and Normal Form in a Modified Predator - Prey Nonlinear System. Journal of Computational and Nonlinear Dynamics, 2: 267-273, 2007.

[2] Kusbeyzi I., Hacınlıyan A. Bifurcation scenarios of some modified predator-prey nonlinear systems. J. Appl. Funct. Anal. 4, 3, 519-527, 2009.

[3] P. Yu and G. Chen. The simplest parametrized normal forms of Hopf and generalized Hopf bifurcations. Nonlinear Dynamics, 50:297-313, 2007.

[4] H. Zhu, S. A. Campbell and G. S. K. Wolkowicz. Bifurcation Analysis of A Predator-Prey System With Nonmonotonic Functional Response. SIAM J.APPL. MATH., 2 63:636-682, 2002.

[5] H.W. Broer, V. Naudot, R. Roussarie and K. Saleh. Bifurcations of a Predator - Prey Model With Nonmonotonic Response Function. R. Acad. Sci. Paris, Ser. I 341:601-604, 2005.

[6] D. Xiao. Multiple Bifurcations in a Delayed Predator - Prey System with Nonmonotonic Functional Response. Journal of Differential Equations, 176:494-510, 2001.

[7] Y. Nutku. Hamiltonian Structure Of The Lotka - Volterra Equations. Physics Letters A, I:145, 1990.

[8] A. J. Lotka. Elements of Physical Biology. Baltimore, Williams and Wilkins Company, 1925.

[9] B. Hernndez-Bermejo and V. Fairn. Lotka-Volterra representation of general nonlinear systems. Mathematical biosciences, 1 140:1-32, 1997.

[10] C. Christopher. Normalizable, Integrable and Linearizable Saddle Points in the Lotka-Volterra System. Qualitative Theory Of Dynamical Systems, 5:11-61, 2004.

[11] X. Huang, Y. Wang and A. Cheng. Limit cycles in a cubic predator-prey differential system. J. Korean Math. Soc., 43:4:829-843, 2006.

[12] X. Huang, Y. Wang and L. Zhu. One and three limit cycles in a cubic predator-prey system. Math. Meth. Appl. Sci., 30:501-511, 2007.

[13] E. C. Zeeman and M. L. Zeeman. An n-dimensional competitive Lotka-Volterra system isgenerically determined by the edges of its carrying simplex. Nonlinearity, 15:2019-2032, 2002.

Problem of electrical power system nonlinear control synthesis: synergetics approach

Andrew A. KuzmenkoTaganrog Institute of Technology – Southern Federal University,

Dept. of Synergetics and Control Processes44, Nekrasovky str., Taganrog, 347928, RUSSIA [email protected]

Basing on synergetics approach to problem of nonlinear system synthesis we explore method of electrical power system (EPS) nonlinear control law synthesis providing suppression of external piecewise-constant disturbance acts to EPS from the side of power system.

Keywords: electrical power system, turbogenerator, synergetics control theory, invariant, disturbance, zero-constant-error control law.


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Andrew A. Kuzmenko, Vitaly V. OzerovTaganrog Institute of Technology – Southern Federal University,

Dept. of Synergetics and Control Processes44, Nekrasovky str., Taganrog, 347928, Russia [email protected]

One of the modern science key problems is nonlinear adaptive regulator design for complex engineering objects. Turbine of autonomous power system is one of these complex nonlinear, multilinked and multi-dimensional objects. Turbine load torque is changed in unpredictable manner because of turbine load alteration due to electrical energy consumers connecting or disconnecting. So we need to build nonlinear control algorithms providing equilibrium of generating and consuming power at load unpredictable alterations. Therefore these algorithms must provide load change adaptive control. In this work we have developed turbine nonlinear adaptive regulator design. That design is based on synergetics conception principles of modern control theory [1, 2].

Keywords: power system, turbine, synergetics control, adaptive regulator, attractor -invariant.

References

[1] Kolesnikov A.A. Synergetic Control Theory. Moscow: Energoatomizdat, 1994.

[2] Kolesnikov A.A., Kuzmenko A.A., at all. Synergetics Methods of Complex Systems Control: Power Systems. Moscow: URSS, 2006.

The stabilization of chaos in the Rössler system by pulsed and harmonic signals

A.P. Kuznetsov, N.V. StankevichSaratov State University, Saratov, Russia

[email protected]

The stabilization of chaos in the Rössler system by external signal is investigated. Different types of external action are considered: pulsed and harmonic. There are illustrations: charts of dynamical regimes, phase portraits, stroboscopic section of Poincaré , spectrums of Lyapunov exponent. Comparative analysis of efficiency of stabilization of band and spiral chaos by different signals is carried out. The dependence of synchronization picture on the direction of acting pulses is shown. Key Words: nonlinear dynamics, chaos, external action

About transitional processes in penetrative convection

Kuznetsova D., Sibgatullin I.Insitute of Mechanics of Moscow State University


Nonlinear dependence of density of a fluid on temperature is widely spread in natural water reservoirs, in magma and different astrophysical models. The corresponding convective motions of fluid are characterized by penetration of unstable layers to stable layers. We consider a model of convective flow in a plain layer with quadratic dependence of density on temperature. This type of dependence corresponds to the density of water for temperaturefrom 0 to 15C and with the maximum of density around 4C for atmospheric pressure. Variations of density in this case are even smaller than for linear dependency, so we can take as a model Boussinesq approximation with taking into account compressibility only in


50

buoyancy term. Appearance of convective motions and convective motions themselves are qualitatively different from those of usual convection because of two layers in static solution stable and unstable. Nondimensional parameter appears which corresponds to asymmetry of the position of point of maxima in static solution. Behavour of arising periodicals motion is also very different, visually it reveals itself as oscillating temperature “tails”. By direct numerical simulation different two-dimensional modes of are investigated. Appearance of chaotic motions and stability of three-dimensional structures are analyzed. Dependency of Nusselt number on supercriticality parameters and wave number is shown for stationary, periodical and stochastic motions. For high supercriticality (Ra~10^8) in turbulent flow major motions are visualized with characteristic motions of hot and cold “thermals”.

Dissipation Rate of Kinetic Energy of Turbulence Inferred for the Upper Atmosphere from Sporadic-E Parameters

Yurij KyzyurovMain Astronomical Observatory NASU, Kiev, Ukraine

[email protected]

Sporadic-E is a thin layer of enhanced ionisation in the E-region ionosphere. The mechanism of the layer formation is explained by wind-shear theory [1, 3, 10]. According to the theory, the sporadic-E results from the interaction of plasma embedded in the neutral wind with the geomagnetic field under appropriate vertical profile of the horizontal wind velocity. The sporadic-E ion composition differs from that of the normal E-region. The ions in the layer are metallic with a very slow recombination reaction [3, 4, 10]. It is known that atmospheric turbulence exerts an essential influence on the layer if its height is below the homopause [2, 3, 10]. The homopause (or turbopause) can be defined as the level where the energy dissipation by molecular processes becomes larger than that of turbulent processes. At the homopause, mixing stops and diffuse separation sets in. The turbulence defines mean characteristics and fine structure of the layer [2, 3, 7, 10]. Intensification of the turbulence leads to reduction of the peak amplitude of the layer and to the increase in the sporadic-E thickness. From sporadic-E parameters one may derive parameters of the turbulence. The mean rate of turbulent energy dissipation is a basic parameter of turbulence [5, 6, 8]. Determination of the rate from sporadic-E parameters is the purpose of this report. The results of wind-shear theory [1, 3, 10] and the Richardson-Obukhov law for turbulent diffusion [8] were used to obtain an expression that connects the dissipation rate with sporadic-E parameters. The obtained expression has allowed us to estimate the dissipation rate when the sporadic-E was formed by a neutral wind with a sinusoidal vertical profile (under the amplitude velocity u=70 m/s and the wavelength L=10 km) near 100 km altitude of mid-latitude ionosphere (the magnetic dip angle of 52.5 degrees) [9], for two variants of the sporadic-E ion composition (the mean ion mass took values 31 and 51 a.u.m.) [4]. Estimates were made for the layer under variation in plasma density of its peak from 1 to 5 times relative to the background E-region. It was shown that in the first case of ion composition the rate changed from 104.8 to 4.2 mW/kg, and for the second from 23.5 to 0.9 mW/kg. The obtained results do not contradict to experimental data [5, 6].Key Words: Turbulence; Upper atmosphere; Ionosphere

References

[1] W.I. Axford. The formation and vertical movement of dense ionized layers in the ionosphere due to neutral wind shears. J. Geophys. Res., 68(3): 769-779, 1963.

[2] G. Chimonas. Turbulent diffusion as a controlling factor in sporadic-E. J. Atmos. Terr. Phys., 36(2): 235-244, 1974.

[3] B.N. Gershman. Dynamics of Ionospheric Plasma (in Russian), Nauka, Moscow, 1974.

[4] H. Haldoupis, D.T. Farley, and K. Schlegel. Type-1 echoes from the mid-latitude E-Region ionosphere. Ann. Geophys., 15(7): 908-917, 1997.

[5] C.M. Hall, S. Nozawa, A.H. Manson and C.E. Meek. Determination of turbulent energy dissipation rate directly from MF-radar determined velocity. Earth Planets Space, 52: 137-141, 2000.


51

[6] Yu.A. Kalgin and A.D. Danilov. Small-scale turbulence input into the energy balance of the mesosphere and lower thermosphere. Geomagn. Aeron., 35(5): 665-670, 1996.

[7] Yu.V. Kyzyurov. On the spectrum of mid-latitude sporadic-E irregularities. Ann. Geophys., 18(10): 1283-1292, 2000.

[8] A.S. Monin, A.S. and A.M. Yaglom. Statistical Fluid Mechanics: Mechanics of Turbulence 2 (in Russian), Nauka, Moscow, 1967.

[9] K. Schlegel and H. Haldoupis. Observation of the modified two-stream plasma instability in the midlatitude E region ionosphere. J. Geophys. Res., 99(A4): 6219-6226, 1994.

[10] Whitehead, J.D. Recent work on mid-latitude and equatorial sporadic-E. J. Atmos. Terr. Phys., 51(5): 401-424, 1989.

Evidence for Deterministic Chaos in Aperiodic Oscillations of Acute Lymphoblastic Leukemia Cells in Long-Term Culture

George I. Lambrou, Aristotelis Chatziioannou, Spiros Vlahopoulos, Maria Moschovi and George P. Chrousos

1st Department of Pediatrics, Univeristy of AthensThivon & Levadeias, Athens, 11527 Greece

[email protected]

Biological systems are dynamic systems whose properties depend on their initial conditions and response over time. Extending this concept to tumor models can have a major impact on the conclusions derived regarding disease initiation and progression. The present study examines the implications of the size of the initial cancer cell line population on the proliferation rate of the in vitro culture system, as well as how different initial conditions reshape dynamically the properties of proliferating tumor cells. The present work tests the hypothesis posed by Wolfrom et al., that proliferation shows evidence of deterministic chaos, granted that subtle differences in the initial conditions of the cell system may give rise to non-linear response behaviors. This hypothesis, tested on adherent Fao rat hepatoma cells, provided evidence that these cells manifested aperiodic oscillations in their proliferation rate. We tested the same hypothesis but added some modifications to the experimental setup. We used the acute lymphoblastic leukemia cell line CCRF-CEM, as it provides an excellent substrate for modeling proliferation dynamics. Several studies have dealt with the complex dynamic behavior of animal populations and we used this model in our analyses. We took measurements at time points varying from 24h to 48h. We conducted flow cytometry studies to examine the apoptotic and necrotic rate of the system, as well as the DNA content changes of the cells through time. The cells exhibited a proliferation rate of a nonlinear nature reflecting oscillatory behavior. The data gained were put in known models of growth such as logistic and Gompertzian growth.Keywords: Proliferation, deterministic chaos, aperiodic oscillations, non-linearity, CCRF-CEM.

Testing the different chaotic trajectories predicted by special-relativistic and Newtonian mechanics for a slow-moving dynamical system

Boon Leong Lan

School of Engineering, Monash University, 46150 Bandar Sunway, Selangor, Malaysia

It is shown that in order to experimentally test the different chaotic trajectories predicted by special-relativistic and Newtonian mechanics for a slow-moving dynamical system, the parameters and initial position and momentum of the system must be measured to quite high accuracy so that the calculated chaotic trajectories are sufficiently accurate. Such an experiment is therefore highly challenging.


52

Scale Invariance in Chaotic Time Series: Classical and Quantum Examples

E. Landa,1 R. Fossion,1 P. Stransky,1 I. Morales,1 V. Velazquez,2

J.C. Lopez Vieyra,1 and A. Frank1

1Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico,Apartado Postal 70-543, 04510 Mexico, D.F., Mexico

2Facultad de Ciencias, Universidad Nacional Autonoma de Mexico04510 Mexico, D.F., Mexico

Important aspects of chaotic behaviour appear in systems of low dimension, as illustrated by the Logistic Map and the Map Mod 1. It is indeed a remarkable fact that all systems that make a transition from order to disorder display common properties, irrespective of their exact functional form. We discuss evidence for 1/f power spectra in the chaotic time series associated with the Map Module1, also a Detrended Fluctuation Analysis (DFA) method is applied to investigate the scaling properties of these time series.The same analysis is showed to the energy uctuations in the spectrum of 48Ca obtained with a large realistic shell model calculation (ANTOINE code) and with a random shell model (TBRE) calculation. We compare the scale invariant properties of the 48Ca nuclear spectrum sith similar analyses applied to the RMT ensambles GOE and GDE. A comparison with the corresponding power spectra is made. We discuss the possible consequences of these analyses.

Research of chaotic synchronization phenomena on the field of visual processes in ophthalmology

Rosário Laureano, Clara Grácio (É vora University), Diana A. Mendes (Department of Quantitative Methods, IBS - Business School, IUL - ISCTE Lisbon University Institute)

Fátima Laureano (Instituto de Microcirurgia Ocular)Department of Quantitative Methods, IBS -- Business School

IUL -- ISCTE Lisbon University Institute, [email protected]

The study of nonlinear dynamics has a long history. However, real applications that make direct use of Chaos Theory have not been fully developed. For other side, the current rapid development of efficient imaging techniques has led to a growing interest in the study of chaotic synchronization phenomena in biological systems, particularly on the field of visual processes in ophthalmology. In this perspective, the purpose of the present research is to demonstrate the feasibility of using unidirectional or bidirectional coupling mechanisms to a better understanding of diseases affecting human vision. Besides the analysis of synchronization error defined by the transversal system, yet we considered the use of measures of Chaos Theory that sheds light on the possibility of improving these couplings and performing control of chaos. Key Words: synchronization error, eye, electroretinogram (ERG), glaucoma

Asymptotic and practical synchronization of one-dimensional chaotic quadratic maps using a non-symmetric coupling

Rosário Laureano, Diana A. Mendes and Manuel A. Martins FerreiraDepartment of Quantitative Methods, IBS -- Business School

IUL -- ISCTE Lisbon University Institute, Lisbon, [email protected]

We consider synchronization phenomena of chaotic discrete dynamical systems with unidirectional and bidirectional coupling mechanisms.


53

We present a systematic study of the nonlinear coupling scheme between two one-dimensional chaotic quadratic maps that appears in natural way from the family of analytic complex quadratic maps when we proceed to the decomposition into real and imaginary parts. It is an asymmetric coupling, since we use different values of the control parameters chosen in the region of chaos of the real quadratic map. The nonlinear coupling term is defined by the square of the difference between the variables of the subsystems times the coupling strength. The dynamical system obtained by coupling two chaotic quadratic maps exhibits a richer dynamics that the single one, but it is still possible to study its behaviour. We are not aware about any studies of this type of coupling. When not even practical synchronization (in the Kapitaniak sense) is achieved, but the difference between the dynamical variables of the subsystems is bounded, we still can apply to the coupled system a chaos control technique based on the well-know OGY-method, the pole-placement control technique, developed by Romeiras et al., in order to decrease the difference between the variables of the subsystems. Moreover, we obtain yet stable identical and generalized synchronization considering some versions of that original coupling, highlighting the absence of symmetry. Two of them are generalizations promoting the use of different coupling parameters. By numerical simulationsof the coupled chaotic maps, we identify the range of coupling strengths for which is allowed practical synchronization and locally stable asymptotic synchronization. The attractive effect of enough coupling can counterbalance the trend of the individual chaotic trajectories to separate, due the sensitive dependence on initial conditions, and makes them to approach. By analysing the difference between the dynamical variables of the systems, we obtain some results leading to stable synchronization. In case of coupling with two different coupling parameters, these results are relations between the coupling parameters and the initial conditions that guaranteed the linear stability of the synchronous state. Key Words: quadratic map, stable asymptotic synchronization, practical synchronization

Acoustic Emission within an Atmospheric Helium Corona Discharge Jet

V J Law1, C E Nwankire2, D P Dowling2 and S Daniels1

1Dublin City University, National Center of Plasma Science and TechnologyCollins Avenue, Glasnevin, Dublin 9, Dublin, Ireland

(e-mail: [email protected] )2School of Electrical, Electronic and Mechanical Engineering

University College Dublin, Belfield, Dublin 4, Ireland

This paper describes the thermal gas effluent and ion acoustic pressure wave interaction between the fundamental drive frequency and its harmonics within an atmospheric helium Corona discharge. Deconvolution of the acoustic signal and the electrical signals reveal that the plasma jet undergoes a change in operational mode from chaotic (where the plasma is spatially and temporally inhomogeneous at the electrode surface) to stable (periodic in nature) when the plasma expands away from the electrodes and into the reactor cylinder. This effect is strongly influence by the helium flow and input power. In addition the generated acoustic signals is found to have a frequency response to that of a closed-end cylinder column which supports antinodes of n = 1 and 3. Decoding of the acoustic signal allows the helium thermal gas temperature to be obtained: Tgas ~ 290 K. The signal allows the axial gap distance between the jet nozzle and work surface to be estimated which has technology importance in terms of plasma metrology and in the basic understanding of atmospheric pressure plasma jet physics.Keywords: Corona discharge, phase-space diagrams, and acoustic emission


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Experimental investigation of the cross-correlation function and the enhancement factor for graphs with and without time reversal symmetry

Michał Ławniczak, Szymon Bauch, Oleh Hul, and Leszek SirkoInstitute of Physics, Polish Academy of SciencesAl. Lotników 32/46, 02-668 Warszawa, Poland


Quantum graphs are widely used to investigate properties of quantum chaos [1]. Experimentally, quantum graphs are simulated by microwave graphs (networks) consisting of joints and microwave cables [2-3]. This is possible due to an equivalency of the one-dimensional Schrödinger equation describing a quantum system and the telegraph equation describing an ideal microwave network.

We present the results of the experimental study of the cross-correlation function vc12 :

vv

v

vvSvvS

vvSvvSvc

2

21

2

12

21*

12

12 .

In the case of TRS systems, 112 vc while for the systems with broken TRS vc12 is less

than 1.

The enhancement factor [4-5]:

ab

bbaa

S S

SSW

var

)var(var, was also determined for

irregular fully connected hexagon microwave graphs in the presence of absorption.

To determine the enhancement factor ,SW we measured the matrix S for the microwave

graphs with time reversal symmetry (TRS), which statistical properties of eigenfrequenciescan be described by Gaussian Orthogonal Ensemble (GOE), and for the graphs with broken time reversal symmetry described by Gaussian Unitary Ensemble (GUE). The measurements were performed as a function of absorption, which was varied by microwave attenuators.

This work was supported by the Ministry of Science and Higher Education grant No. 72645.

[1] T. Kottos, U. Smilansky, Phys. Rev. Lett. 79, 4794 (1999).[2] O. Hul, S. Bauch, P. Pakoński, N. Savytskyy, K. Życzkowski, L. Sirko, Phys. Rev. E 69,

056205 (2004).[3] M. Ławniczak, O. Hul, S. Bauch, P. Seba and L. Sirko, Phys. Rev. E 77, 056210 (2008).[4] D. V. Savin, Y. V. Fyodorov, H.-J. Sommers, Acta Phys. Pol. 109, 53 (2006).[5] M. Ławniczak, S. Bauch, O. Hul and L. Sirko, Phys. Rev. E, accepted for publicaction

(2010).

The model of energy transport in turbulent under critical laser plasma of porous target

I.G. Lebo, A.I. Lebo Technical university-MIREA, Moscow, Russia

[email protected]

We have proposed a physical-mathematical model of power laser pulse interaction with low density porous targets (see in details [1]). We have carried out the simulations of the "hydro-thermal wave" expansion in laser plasma by using 2D Lagrange code "ATLANT" [2]. The good agreement between of numerical results and experimental data [3] has been got. Using this model it is possible to explain some challenging phenomena, which have been observed at "PALS" experiments (weak irradiation at t=0.15-0.2 ns and bright irradiation in optical spectrum with time delay 1-1.5 ns after laser pulse closing from rear side targets).


55

We have discussed the opportunities to study the whirls and spontaneous magnetic fields in the plasma with help of electron bunch tomography [4-5].

The work is supported by RFBR, project #08-02-00913a.Key Words: laser pulse interaction with porous matter

References

[1]. Lebo I.G., Lebo A.I. Matematicheskoe Modelirovanie (in Russian), v.21, 75-91, (2009).

[2]. Lebo I.G., Popov I.V., Rozanov V.B., Tishkin V.F. Journal of Russian Laser Research, v.15, 136-143, (1994)

[3] Borisenko N, Akunets A., Khalenkov A. et al. J. Russian Laser Res. 28, 548-566, (2007).

[4] Konash P.V., Lebo I.G. Quantum Electronics, 36(8), 767-772, (2006)

[5] Lebo Ivan. The 5-th Internat. Conference on IFSA -2007. IOP Publishing Journal of Physics: Conf. Ser. 112 (2008) 022018

Attractors, limit cycles and homoclinic orbits of low dimensional quadratic systems

Gennady A. LeonovMember (corresponding) of Russian Academy of Science

Dean of Mathematics and Mechanics FacultySaint-Petersburg State University, Russia

Low dimensional quadratic systems play an important role in the mathematics and different applications. Recall here a question, on the number of limit cycles of quadratic two-dimensional systems, which has been set in Hilbert's sixteenth problem. A widely known Lorenz system, which describes three-mode convection of two-dimensional flows and in which a strange attractor first was discovered, is three-dimensional quadratic system. In the last decades together with analytic results for these systems, the computer-assisted proofs and computer calculations and experiments take more places. However the obtaining of simple analytic estimates and formulas for low dimensional quadratic dynamical systems is of great importance and attraction.The presentation is devoted to the consideration of such results. In the report the methods of localization of attractors of two-dimensional and three-dimensional quadratic systems are considered. The criteria of existence of four limit cycles in two-dimensional quadratic systems are obtained. The criteria of existence of homoclinic orbits in two-dimensional and three-dimensional quadratic systems are formulated. Scenarios of passage to chaos via homoclinic bifurcation are discussed. Dimensional characteristics of attractors are considered. Formulas of Lyapunov dimension for Hé non and Lorenz attractors are obtained.

Dynamics of Steel Turning by Recurrence Plots*

G. Litak, R. RusinekLublin University of Technology

Nadbystrzycka 36, 20-618 Lublin, [email protected]

The machining technology is the most important component in the modern massive production. Over the past years, its fast development gave way to a reliable high-speed cutting procedure. Consequently, elimination and stabilization of the associated chatter oscillations have become a high interest in science and technology [1]. The plausible adaptive control concept, based on relatively short time series, has been studied to gain deeper understanding. We investigate dynamics of a turning process by the recurrence plot technique [2]. The experimental time series of a steel cutting process enable us to distinguish different types of the system response. This method, supplemented by recurrence quantification analysis (RQA), was used to analyze relatively short time series [2,3]. Changing


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the single system parameter, cutting depth, we observed qualitative change of the system response.[1] Y. Altintas, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Cambridge University Press, Cambridge 2000.[2] N. Marwan, M.C. Romano, M. Thiel, and J. Kurths, Recurrence plots for the analysis of complex systems, Physics Reports 438, 237 (2007).[3] G. Litak, M. Wiercigroch, B.W. Horton, and X. Xu, Transient chaotic behaviour versus periodic motion of a parametric pendulum by recurrence plots Z. Angew. Math. Mech. 90, 33 (2010).*This work has been partially supported by European Union within the framework Integrated Regional Development Operational Programme as the project POIG.0101.02-00-015/08.

Multichannel discharges between turbulence current and porous material

N.A.Loginov, Az.F.Gaysin, F.M.Gaysin, E.E.Son , Al.F.GaysinKazan State Technical University named after A.N.Tupolev

Russia, Kazan

Multichannel discharges in porous medium with turbulence current are uninvestigated and physical processes at the border and differentiation between turbulence current and drop of electrolyte. Basic forms of glow discharge with turbulence current are uninvestigated. Therefore experimental researching of characteristics of multichannel discharge in porous medium with turbulence current is the main task. In this article we give test studies of structure, characteristics and extension of multichannel discharge with turbulence current in broad band parameters: Pressure (P) = 7.6 - 760 torr, length of current (lc) = 12 mm, diameter of current (dc) = 1.5 mm, discharge current ( I ) = 1 –4 мА, voltage (U) = 100 – 200 V, electrolyte is industrial water mixed with NaCl in different concentration. TV camera (MMC – F220) was used for visually researching of multichannel discharge.Analysis of test studies showed that multichannel discharge in porous medium with turbulence current create plasmic vortex on the surface of porous material. Plasmic vortex is the result of mixing the plasma with electrolyte.

Non-classical model of historical research and synergetic ideas

Anatoliy V. LubskiySouthern Federal University,


In the network of non-classical model of historical investigation synergetic ideas and methods have become widespread and these ideas and methods enable in the most effective way to learn matters connected with historical transition from social chaos to order and manifestation in it everything historically necessary and casual. With using the theory of self-organization of society as comprehensive whole, synergy gives an opportunity in an innovative way to consider such matters of historical development as possibility and reality, traditions and innovations, the past and the future, alternative and choice.

Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Valerio Lucarini, Klaus Fraedrich Department of Mathematics & Department of Meteorology, University of Reading, UK

[email protected]

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a


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decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec^(-1)) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f^(3/2) power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Multifractal Turbulence in the Solar System Plasma

Wieslaw M. Macek1,2

1Faculty of Mathematics and Natural Sciences Cardinal Stefan Wyszynski UniversityWoycickiego 1/3, 01-938 Warsaw, Poland

2Space Research Centre, Polish Academy of Sciences Bartycka 18 A, 00-716 Warsaw, Poland

E-mail: [email protected]

. We consider a solar wind plasma with frozen-in interplanetary magnetic fields, which is a complex nonlinear system that may exhibit chaos and intermittency, resulting in a multifractal scaling of plasma characteristics. We analyse time series of plasma quantities obtained during space missions onboard various spacecraft, such as Helios, Advanced Composition Explorer, Ulysses, and Voyager, exploring different regions of the Solar System. To quantify the multifractality of solar wind turbulence, we use a generalized two-scale weighted Cantor set with two different rescaling parameters [1]. We investigate the resulting spectrum of generalized dimensions and the corresponding multifractal singularity spectrum depending on the parameters of this new cascade model [2]. In particular, we show that intermittent pulses are stronger for the model with two different scaling parameters, where the multifractal scaling is often rather asymmetric, and a much better agreement with the solar wind data is obtained, as compared with the one-scale model.We hope that the generalized multifractal model will be a useful tool for analysis of intermittent turbulence in the Solar System plasma. We thus believe that multifractal analysis of various complex environments can shed light on the nature of turbulence.Keywords: Multifractals, Turbulence, Solar wind plasma, Interplanetary magnetic fields.References1.W. M. Macek and A. Szczepaniak. Generalized two-scale weighted Cantor set model for

solar wind turbulence. Geophys. Res. Lett., 35, L02108, 2008.2.W. M. Macek and A.Wawrzaszek. Evolution of asymmetric multifractal scaling of solar wind

turbulence in the outer heliosphere. J. Geophys. Res., 114, A03108, 2009.


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Sensitivity Analysis of Chaos Synchronization in Colpitts Oscillators

Vlad Maftei, Victor GrigorasFaculty of Electronics, Telecommunications and Information Technology

‘Gheorghe Asachi’ Technical University of Iasi, RomaniaE-mail: [email protected]

Chaotic dynamics in grounded base bipolar junction transistor Colpitts oscillator was extensively studied due to its implementation simplicity and high frequency capability. Some synchronization methods were also proposed, but they suffer from high sensitivity both to channel noise and parameter mismatch.

The present paper proposes two novel synchronization topologies based on voltage-mode implementation. The central aspect of the research is the estimation of the sensitivity performance for the proposed chaotic carrier modulation for analog transmission systems. We also perform a parametric analysis to deduce the optimum component values for the proposed application with respect to noise immunity and component tolerances. In order to improve communication speed, we used a demodulation equalizer, thus drastically increasing the maximum frequency of the modulating signal. The conclusion of this comparative study points to the most efficient synchronization and modulation / demodulation methods in order to achieve practical chaos communication based on analog modulation.

Keywords: Chaos synchronization, Colpitts oscilator, synchronization sensitivity.

Random network of coupled chaotic maps for economic dynamics

Rakesh Mahla, Manish Shrimali, Anup Poonia, Chirag Jain The LNM Institute of Information Technology, India

[email protected]

We investigate a network of coupled chaotic maps for economic dynamics, with varying degrees of randomness in coupling connections. It is observed that the network shows a power-law behavior for a non-zero value of re-wiring probability similar to actual scaling behavior of actual economy. The network consists of a set of interacting agents and the wealth of the agents is represented by the dynamical variables at each node. The dynamics of the system is controlled by two parameters. One parameter expresses the growth capacity of the agents and the other describes the local environmental pressure. A very well studied coupling form in coupled chaotic maps is nearest neighbor coupling. While some degree of randomness in spatial coupling can be closer to physical reality than strict nearest neighbor scenarios. In fact, many systems of biological, technological, and physical significance are better described by randomizing some fraction of the regular links. Some alternate scenarios have been suggested, such as the small-world network. Here one starts with a regular structure on a lattice, for instance nearest neighbour interactions. Then each regular link from a site is rewired randomly with probability p. This model is proposed to mimic real life situations in which non-local connections exist along with predominantly local connections.For simplicity, we shall assume that the agents are distributed on a one-dimensional lattice with periodic boundary conditions. The state of an agent i is characterized by a real variable x denoting its wealth or richness at the discrete time t. The system evolves in time synchronously. Each agent updates its state x according to its present state and the states of its nearest or random sites. In this paper we consider a homogeneous system with a uniform capacity r and a fixed selection pressure a for all the agents. The collective behavior of the system is characterized through the instantaneous mean field of the network. The synchronized system displays a sequence of bifurcations through different periodic and chaotic attractors. As the re-wiring probability p increases, bifurcation is suppressed and shifted in the parameter space. The nontrivial collective behavior, where macroscopic order coexists with local disorder, can emerge in this system. The probability distribution of wealth in the asymptotic regime shows a transition to power law behavior for non-zero value of re-wiring probability p near the 'small-world' region for given parameter values.

Key Words: Random network, Coupled chaotic maps, Economic dynamics, Small-world network, Bifurcations, Power law behavior.


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The systematic as heuristic principle in synergetics

Marina V. Maksimova Southern Federal University, department of philosophy

Rostov-on-Don, RussiaEmail: [email protected]

The needs in objective description of modern processes of science with helps of synergetic tools led to necessity of methodological understanding of fundamental synergetic categories. It’s suppose conceptualization of such ideas as integrity and systematic. The synergetic system approach as totality of cognitive principles fulfils own heuristic functions, based on the search of mechanisms of integrity and exposures of connect technologies. This scientific orientation permit to clear not only subject qualities of local processes but also to unite observed laws in holistic sphere. The systematic as one of the fundamental heuristic principles in synergetic contribute to adequate and effective opening of problems essence and their successful decision in different areas of science.

The constructive potential of social chaos in modern society: regional peculiarity

M.B. MarinovSouthern Federal University,


Within the framework of synergetic theory and oriental philosophy there was conceptualized in the article the constructive potential of social chaos in modern society. Also there was specified its selective peculiarity concerning the South-Russian region.

Dynamical Analysis of AFM Micro-Cantilever and Control of Its Chaotic Behaviour via AFSMC Algorithm

Amirhossein Davaie Markazia , Ali Abbasib

a Mechanical Engineering Department, Iran University of Science and TechnologyTehran, Iran,

Email:[email protected] Engineering Departmentt, Iran University of Science and Technology

Tehran, Iran,Email:[email protected]

In this paper, the nonlinear dynamics and chaotic behaviour of Atomic Force Microscopy (AFM), being run in the non-contact mode (TM), were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The micro-cantilever was modelled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. Then a robust adaptive controller for control of its chaotic motion has been used. The controller incorporates a fuzzy system which imitates an ideal controller and a sliding mode controller (SMC) to cope with the difference between the fuzzy controller and the ideal controller. The parameters of the fuzzy system, as well as uncertainty bound of the robust controller, are tuned adaptively. Then compare the results obtained from Adaptive Fuzzy Sliding Mode control (AFSMC) with Sliding Mode Control of AFM micro-cantilever. The results show that AFSMC has remarkable success in controlling the chaotic behaviour of AFM micro-cantilever, relative to SMC approach due to its robustness against unknown model.

Keywords: AFM, Lennard-Jones,AFSMC, SMC,microcantilever,robust control.


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Dynamic Modelling and Comparative Analysis for Life Table Data of non-European Countries

George Matalliotakis1, Christos H. Skiadas2 , Vardoulaki Maria3

Technical University of Crete, Chania, Crete, GreeceEmail : 1 [email protected], 2 [email protected], 3 [email protected]

In this article we study the mortality data of some non-European countries. The study isfocused on analysis of life table data taking into account the different mortality features between male and female population during the time.The method uses a dynamic model introduced by Janssen and Skiadas (1995) and a new form proposed by Skiadas and Skiadas (2010). The later is a three parameter model based on a stochastic methodology and especially in the first exit time theory. We discuss the impact of the proposed model and the results obtained in the insurance science. The Health State Function H(t) of a population is modeled as the mean value of the health states of the individuals. Then we use the life table data and apply the specific methodology. Important conclusions are extracted and compared to Weibull and Gompertz models. We have studied and analyzed the graphs (curves) formed by the mortality data of the population. We comment on their form and finally give important conclusions about the different mortality features. The study shows that the S-model gives lower errors, and fits to the data with greater accuracy than the Weibull and Gompertz models.1. Janssen, J. and Skiadas, C. H., Dynamic Modelling of Life-Table Data. Applied Stochastic Models and Data Analysis, vol. 11, No 1, 35-49, 1995.2. Skiadas, C. and Skiadas, C. H., Development, Simulation and Application of First Exit Time Densities to Life Table Data, Communications in Statistics - Theory and Methods, Volume 39, Issue 3 January 2010, pages 444 - 451.

Nonlinear Dynamics in CNN’s with Second Order Cells

Radu Matei1, Carmen Grigoras2,3

1Faculty of Electronics, Telecommunications and Information Technology‘Gheorghe Asachi’ Technical University of Iasi, Iasi, Romania

E-mail: [email protected] of Medical Bioengineering, ‘Gr.T. Popa‘ University of Medicine and Pharmacy of Iaşi,

Iasi, Romania3Romanian Academy – Iaşi Branch, Institute of Computer Science


Cellular neural networks (CNNs) may be regarded as special cases of recurrent neural networks architectures, having only neighboring connections, and a variety of cell structures, based on simple nonlinear analog circuits. Due to their high order nonlinear equations, CNNs can develop rich dynamics, including limit cycles, N-torus and chaotic behavior, for certain choices of the parameters values and nonlinear functions. Such complex behavior was reported by many researchers for several CNNs with first order cell.

In this paper, we present some recent results on the nonlinear dynamics of second order cell CNNs, with 1D low order structure. The CNN cell consists of a circuit with two linear capacitors and nonlinear dependent current sources. In the array of cells, interconnections are achieved by means of the nonlinear sources. We conducted the analysis at the variation of different circuit parameters in order to discriminate conditions for quasi-periodic and chaotic behavior. Poincaré maps and bifurcation diagrams highlight the capability of the proposed class of CNNs to develop complex nonlinear dynamics. We also highlight the system performance in space-time pattern formation, for possible signal processing applications.

Keywords: cellular neural networks, nonlinear dynamics, chaos


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Mutual Information and Dynamics

Massimo Materassi1, Giuseppe Consolini2 and Nathan Smith3

1Istituto dei Sistemi Complessi ISC-CNR, via Madonna del Piano 10, 50019, Sesto Fiorentino (Italy); [email protected]

2INAF- Istituto di Fisica dello Spazio Interplanetario, via del Fosso del Cavaliere, 100, Roma (Italy); [email protected]

3Department of Electronic and Electrical Engineering, University of Bath, BA2 7AY, [email protected]

In studying the dynamics resulting from the interaction of two or more systems with stochastic elements, the use of information theory quantities, as the mutual information or the transfer entropy, has been growing in importance in the last decade. Those quantities are naturally de.ned for discrete-time systems, while must be generalized to continuous evolutions with some care. The goal of using the Mutual Information Analysis (MIA) and the Transfer Entropy Analysis (TEA) in physics of complex interactions is to de.ne the best mathematical form of a dynamical system mimicking the evolution of two unknown physical processes X and Y, of which one only knows that they do interact, and measures as proxies the time series x (t) and y (t) respectively.Here we propose a discussion of MIA and TEA, in which the role of non-linearity and memory properties of the dynamics is stressed: after a brief review of their de.nition, and of the problems arising in applying them to continuous processes (e.g. the binning problem), the more fundamental matter of unbiasing MIA and TEA from the potentially different degree of stochasticity in the processes X and Y is faced. In order to do this, some new quantities are introduced, which are the central result of this paper. Their application to some controversial natural and numerical cases is then showed.

Reliability of bioelectric activity (EEG, ECG and HRV) researches of the deterministic chaos by the nonlinear analysis methods

Oleg Yu. Mayorov1,2,3, Vladmir N. Fenchenko 1,3,4

1Institute of Medical informatics and Telemedicine, Kharkiv2Kharkiv Medical academy of postgraduate educations, Ministry of Health of Ukraine, Kharkiv

3Institute of Children and adolescents health protection, АМSc of Ukraine, Kharkiv4Institute of Low temperatures NАSC of Ukraine, Kharkiv


There has been proposed a new approach to the process of investigation of bioelectric activity in the human and animal brain, basing on the use of multidimensional spectral analysis methods to detect cerebral hemisphere and subcortical structure regions involved temporarily in a certain functional system (according to P.K. Anokhin) for the purpose of realization of behavior acts, and the subsequent analysis and modeling of their nonlinear-dynamic parameters from the position of the deterministic chaos theory.

The possible reasons of errors occurrence are analyzed at research deterministic chaos in bioelectric activity of man and animals organism (EEG, ECG, HRV, etc.) by methods of the nonlinear analysis. The complex approach is offered, allowing to increase accuracy and reliability of received results at a correct choice of stationary sites of a signal, a delay and scale of consideration, use of adequate parameters during attractor reconstruction (an estimation of dimension of reconstruction and embedding dimension), for estimating entropy process and maximal Lyapunov exponent. Corresponding software NeuroResearcher® is created and examples of «chaos parameters» calculations of typical EEG and ECG signals illustrated.

Keywords: bioelectric activity of organism, EEG, ECG, HRV analysis, multidimensional spectral analysis, deterministic chaos, attractor reconstruction, attractor dimensions, delay, entropy, maximal Lyapunov exponent.


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SHOCK TUBE INVESTIGATIONS OF THE INSTABILITY OF A TWO-GAS INTERFACE ACCELERATED BY A SHOCK WAVE

E.E. MeshkovSarov State Phisycal and Technical Institute, Sarov

The Report sets out the main results of shock tube experiments for investigating the instability of an interface of two gases having different densities, accelerated by a shock wave:1 regularities of the development of initial perturbation of an unstable interface;2 peculiarities of the discontinuity break-up arising when a shock wave is passing through a

perturbed interface of two gases having different densities; 3 development of the instability mechanisms;4 peculiarities of the development of a turbulent mixing of gases at an unstable interface;5 peculiarities of the instability development when the interface is being accelerated by

steady and unsteady shock waves.

The Report is based on the results of experiments conducted by, and with direct participation of, the author

Concept of “self organization” in the light of cosmological problems

Larisa A. MinasyanSouthern-Russian State University of Economics and Service, Russia, Rostov-on-Don


Methodology of “determinated chaos”’s examination can be essentially enriched thanks to study of non-line dynamic processes which give variant of Universe’s evolution where the top of development have become appearance of a Human (entropic principle). All modern cosmological models use in their base the idea about the Universe as a self-organized integrity and direct to the construction of the ontological idea of our world. Ontological aspect comes to the question about vacuum stage of the cosmological expansion of the Universe which is a priority in the theoretical formations and experimental researches. In 1998 extravagant results were received, radically changed our idea about matter’s structure. It was determined that usual substance makes only 4% of Universe’s energy, 20% is non-identified “dark substance” and 76% is “dark energy” which is compared with energy dominated and broke vacuum able to the gravitational repulsion. In the case if the bearer of the “dark energy” is really cosmological vacuum, we will receive complimentary arguments in the rightness of chosen strategy in the consideration of the cosmological vacuum as an object where in the beginning all the energy of our super symmetrical Universe was concentrated. Dissipative nature of the vacuum has provoked that the part of energy during the Universe’s evolution has been given to bear birth other structural units of matter known as usual substance and “dark energy”. Based on the results received during theoretical and experimental stages of modern researches we can put the question about consideration the vacuum as a primogenitor of our world and in quantity of the origin abstraction of the physical theory. To show the peculiarities of the complicated heterogeneous vacuum’s structure serves the complex of experiments planned to be done at the Large Hadron Collider. Special importance will have the results of planned experiment’s realization “SNAP”. We can maintain that the modern science is at the threshold of radical changes of ideas not only about of our Universe’s formation but also about Human’s place in it. In the article the typical traits of modern ideas about the world are considered and the attempt of their synergetic understanding is made.

Key words: self-organization of the Universe, “dark energy”, heterogeneous vacuum’s structure, bifurcations, relativition phased passages, chaos and symmetry.


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Algorithmic Sound Composition using Coupled Cellular Automata

Jaime Serquera and Eduardo R. MirandaInterdisciplinary Centre for Computer Music Research (ICCMR)

University of Plymouth, [email protected], [email protected]

In this paper we introduce a new approach to algorithmic sound composition using a bespoke technique combining coupled Cellular Automata (CA) and Histogram Mapping Synthesis. Two CA are used: a hodge podge machine and a growth model. The latter serves as control of the former. The hodge podge machine can exhibit different kinds of behaviour depending on the values of a set of rule parameters. Our method explores the fact that different simultaneous behaviours can be evolved within the same automaton if we bring into play different sets of parameter values. However, we restrict the number of parameter sets to two. Therefore, the CA growth model will have only two states and will delimit two dynamic zones in the hodge podge machine, each of which governed by a different set of parameter values. The predictable evolution of the two zones will produce a controlled dynamic sound spectrum. Among all the possibilities that this process affords for the composition of a variety of sounds algorithmically, we highlight its application to the attack portion of a sound, making it dynamically more complex than the rest of the sound.

Keywords: sound synthesis, cellular automata, histogram mapping synthesis, hodge podge machine.

Analysis of generalized synchronization in mutually coupled dynamical systems

Olga I. Moskalenko, Alexey A. Koronovskii,Alexander E. Hramov, Svetlana A. Shurygina

Saratov State University, Saratov, RussiaEmail: [email protected]

Synchronization of chaotic oscillations is one of the most relevant directions of nonlinear dynamics attracting great attention of modern scientists [1]. The interest to it is connected both with a large fundamental significance of its investigation and a wide practical applications, e.g. for the transmission of information, diagnostics of dynamics of some biological systems, control of chaos in the microwave systems, etc. Several types of the synchronous chaotic system behavior are traditionally distinguished. They are phase, generalized, lag, complete, time scale synchronization and others.One of the most interesting types of the synchronous chaotic system behavior is the generalized synchronization (GS) regime [2-4]. Such type of chaotic synchronization has been firstly proposed for two unidirectionally coupled chaotic oscillators [2]. Later the concept of GS has been extended to the mutually coupled systems and networks of coupled nonlinear elements [3-4]. At that, it should be noted that the GS regime has been investigated in detail only in unidirectionally coupled chaotic oscillators, whereas such type of chaotic synchronization in mutually coupled dynamical systems and complex networks has been analyzed poorly enough. Known works (see, e.g. [3-4]) are directed to the development of new methods for the GS regime detection in such systems on the basis of the auxiliary system approach [5] proposed for unidirectionally coupled oscillators. At the same time, the concept of the GS regime, mechanisms of its arising and possibility of application of auxiliary system approach even in two mutually coupled dynamical systems remain still unclear. In present report we analyze the possibility of the GS regime onset in systems with a mutual type of coupling. Thereto we compute the spectrum of Lyapunov exponents (LE) and analyze its variation with the coupling parameter value increasing. The choice of Lyapunov exponents for such purposes is caused by the well-known fact that they are a powerful tool for the analysis of the complex system dynamics. In particular, the spectrum of Lyapunov exponents


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allows to detect the qualitative changes of the system behavior with its control parameter varying [6, 7]. It is clear that appearance of any type of chaotic synchronization could be defined by the changes in the behavior of Lyapunov exponent spectrum. In particular, the GS regime in unidirectionally coupled dynamical systems is known to take place when the highest conditional Lyapunov exponent becomes negative [7, 8]. The analogous situation takes place in mutually coupled dynamical systems, i.e. with the coupling parameter value increasing one of the positive Lyapunov exponents passes through zero [9]. Transition of the positive Lyapunov exponent in the field of the negative values has been explained in literature by the appearance of the lag synchronization (LS) regime. At the same time, the difference between the coupling parameter values corresponding to the regimes mentioned above could be a bigger one that has been explained in [9] by the presence of intermittency near the boundary of LS regime. Our calculations (using the examples of coupled Rossler and Lorenz oscillators) show that the threshold value of the LS regime onset grows with the value of the control parameter mismatch increasing, whereas the moment of transition of the positive LE towards the negative values depends slightly on the value of parameter detuning. At that, intermittent LS can both be observed and non-observed in coupled dynamical systems. One can assume that transition of the positive LE to the negative values is connected with the GS regime onset in mutually coupled dynamical systems. To prove our assumptions we propose the modification of the nearest neighbor method [2, 10] and apply it to the system under study. We approve our method on unidirectionally coupled dynamical systems and obtain a good agreement between obtained and well-known results. This work has been supported by Russian Foundation for Basic Research (project 10-02-00341) and Federal special-purpose program “Scientific and educational personnel of innovation Russia” (2009-2013).

References

[1] S. Boccaletti, J. Kurths, G. V. Osipov, D. L. Valladares, C. S. Zhou. The synchronization of chaotic systems. Physics Reports, 366: 1-101, 2002.

[2] N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, H. D. I. Abarbanel. Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E, 51(2): 980-994, 1995.

[3] Z. Zheng, X. Wang, M. C. Cross. Transitions from partial to complete generalized synchronizations in bidirectionally coupled chaotic oscillators, Phys. Rev. E, 65:056211, 2002.

[4] S. Guan, X. Wang, X. Gong, K. Li, C.-H. Lai. The development of generalized synchronization on complex networks, CHAOS, 19:013130, 2009.

[5] H. D. I. Abarbanel, N. F. Rulkov, M. M. Sushchik. Generalized synchronization of chaos: The auxiliary system approach, Phys. Rev. E, 53(5): 4528-4535, 1996.

[6] A. E. Hramov, A. A. Koronovskii, M. K. Kurovskaуa. Zero Lyapunov exponent in the vicinity of the saddle-node bifurcation point in the presence of noise, Phys. Rev. E, 78:036212, 2008.

[7] K. Pyragas. Conditiuonal Lyapunov exponents from time series, Phys. Rev. E, 56(5): 5183-5188, 1997.

[8] A. E. Hramov, A. A. Koronovskii. Generalized synchronization: a modified system approach, Phys. Rev. E, 71(6):067201, 2005.

[9] M. G. Rosenblum, A. S. Pikovsky, J. Kurths. From phase to lag synchronization in coupled chaotic oscillators, Phys. Rev. Lett., 78(22):4193-4196, 1997.

[10] U. Parlitz, L. Junge, W. Lauterborn. Experimental observation of phase synchronization, Phys. Rev. E, 54(2):2115-2117, 1996.


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Search for chaos in black holes and neutron stars

Banibrata MukhopadhyayIndian Institute of Science, Department of Physics, Indian Institute of Science,

Bangalore 560012, [email protected]

The accretion disk around a compact object in universe is a nonlinear general relativistic system involving magnetohydrodynamics. Naturally the question arises whether such a system is chaotic or stochastic which might be related to the associated transport properties whose origin is still not confirmed yet. By computing correlation dimension based on observed data, we have been analysing the nonlinear nature of such compact sources over the past half a decade. We show that the black hole system GRS 1915+105 behaves as a low dimensional chaos in certain temporal classes. We also show that neutron stars, which are unique for their kHz QPOs arised presumably from nonlinear mechanisms around them, such that Sco X-1, Cyg X-2 are low dimensional chaotic systems. Based on our analysis, we argue that Cyg X-3 may be a black hole.

Investigation Chaotic Dynamics of Nonlinear System

Iryna V. Musatenko Kyiv National Taras Shevchenko University, Faculty of Cybernetics

Department of Calculus Mathematic, Vladimirskaya Street, 64, Kyiv 01033, Ukraine [email protected]

The goal of the paper is numerical and analytical investigation chaotic dynamics of nonlinear system. The system describes population dynamics. It was found that, under certain conditions, the system displays chaotic behavior. Also bifurcation diagram and the chaotic behavior of the model is demonstrated. Key Words: Logistic model, Lotka-Volterra system, chaos, bifurcation

Nonlinear adaptive control for aircraft flight under chaotic wind disturbances

Alexey S. MushenkoTaganrog Institute of Technology – Southen Federal University,

Dept. of Synergetics and Control Processes44, Nekrasovky str., Taganrog, 347928, Russia

[email protected]

Wind disturbances are main source of external action affecting aircraft flight control system operation. Mostly these wind disturbances has unpredictable and chaotic manner and therefore are ultimately danger. Usually, methods of distributed-statistical analysis are used for such uncertainties describing and accounting. But these methods do not provide desired control under chaotic wind disturbances in some cases. In the paper we propose design of nonlinear adaptive regulator for aircraft longitudinal or spatial motion control providing withstand to some classes of disturbances. For nonlinear adaptive regulator design we use nonlinear mathematical model of aircraft motion and approaches of synergetics control theory as well as method of analytical design of aggregated regulators [1, 2] were applied. In the paper we present nonlinear regulator synthesis procedure and results of closed-loop system computer simulation. Moreover, in order to successful withstanding such class of disturbances we propose control for additional aircraft wing mechanizing elements. This approach may be applied at new class aircraft control system design.

Keywords: nonlinear control, aircraft control systems, synergetics control theory, disturbances, flight control, ADAR method


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References

[1] Kolesnikov A.A. Synergetic Control Theory. Moscow: Energoatomizdat, 1994.

[2] Kolesnikov A.A., Mushenko A.A., at all. Synergetics Methods of Complex Systems Control: Mechanical and electromechanikal systems. Moscow: URSS, 2006.

TURBULENT MIXING IN GAS-VAPOR DISCHARGE PLASMA WITH JET ELECTROLYTE ANODE

T.B.Mustafin, Al.F.Gaysin, F.M.GaysinKazan State Nechnical University, Kazan, Russian Federation

[email protected]

The particular features of mixing of multichannel discharge plasma and jet electrolyte anode is considered. The experiments were carried out at pressures p = 7.6 – 760 Torr, voltages U = 200 – 1500 V, jet diameter in the range of d = 3 – 5 mm, jet lengths 30 – 40 mm and electrolyte flow rate G = 1.5 – 4.5 g/s. Saturated solutions of NaCl in water were used as electrolyte. The experiments show that the turbulent flow and evaporation of the electrolyte jet significantly influence the burning and shape of the electric discharge between jet electrolyte anode and copper cathode. Key Words: plasma; discharge; turbulent mixing; electrolyte

Chaotic vs Classical Codes for Synchronous TH-UWB Multiple-Access System in IEEE 802.15.4a Multi-path Channel

Anis NAANAA, Zouhair BEN JEMAA and Safya BELGHITHSys’Com laboratory/ENIT. ENIT BP. 37 le Belvé dère, 1002 Tunis, Tunisia

Email:[email protected],[email protected], [email protected]

This paper aims to evaluate the impact of chaotic sequences on the performance of synchronous TH-UWB system when they are used as multiple access keys. We considered the realistic multi-path channel described in the norm IEEE -802.15.4a. Firstly, we will prove the dependence of the performance on the used multiple access codes by expressing the power of multi-user interference with the aid of the Average of Squared Collision Number (ASCN) criteria of the used code set, Then the ASCN of chaotic sequences and the one of classical Gold sequences are computed and compared. The results show that chaotic sequences have better ASCN for some maps. To analyse how this result is reflected on the performance we simulated the system in multipath channel context and with conventional receiver in the two cases, when chaotic and Gold sequences are used for multiple access. We found that the performances in term of binary error rate are better for some chaotic sequences. Keywords: Chaotic sequences, Utra wide band, Time hopping, multi-path channel, Average of squared collision number.

The crisis communication in the space of social chaos

Vera I. NemchinaSouthern Federal University,

105/42, Bolshaya Sadovaya str., Rostov-on-Don, 344006, Russia [email protected]

Social chaos in modern society is a qualitative state of society in which there is a failure and collapse of the past institutional structure with simultaneous absence of socially productive and supported by the society innovative institutional norms.


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The crisis communication performs a mechanism of organizational formation of modern society in the period of institutional transformation. The alternation of the crisis communication’s vector and its exploring character makes this kind of communication structure-forming factor in non-coordinated social space where destabilizing chaotic processes take place.

The crisis communication detects its specific manifestations, with forming micro-, mezzo- and macro-level structures in the space of social chaos.

ON BIFURCATIONS TO LEADING TO CHAOS IN IS-LM MODEL

UMBERTO NERI 1 and BEATRICE VENTURI 21Department of Mathematics, University of Maryland, College Park, MD (U.S.A.)

2Corresponding author: Department of Economics, University of Cagliari, Cagliari (Italy). E-mail: [email protected]

Bifurcations and the structure of limits sets are studied of a non-linear fixed-price disequilibrium IS-LM model, which depends on two parameters, with investment behavior as a general non-linear function avoiding any Kaldor type assumption (see Neri and Venturi 2007).We use graphical, heuristic and rigorous arguments to show that as the parameters vary a wide range of dynamical behavior is displayed.

JEL classification: C62, E32.Keywords: deterministic cycles, Hopf bifurcations, stability of periodic orbits, heteroclinic and homoclinic orbits.

Large Eddy Simulation of Turbulent Drag Reduction over Hydrophobic Surfaces

N.Mohammad Nouri, Alireza Mofidi, Seyyed Mohammad Amin KariminiaTehran, Iran

[email protected]

In this paper, drag reduction by using hydrophobic surfaces in a turbulent channel flow is investigated through Large Eddy simulation. The surface boundary condition was modeled by the Navier slip condition. Also the hydrophobicity of a surface was expressed in terms of a slip length. It is assumed that large slip length can produce large drag reduction. Simulations are performed at Re = 4200. The computational domain of 4πδ×2δ×4/3πδ is used in the x,y,z directions, respectively, with 65×65×65 grids. The results show that the computed drag reduction is in good agreement with results obtained from Direct Numerical Simulation. Smagorinsky and Dynamic-Smagorinsky models which used in Large Eddy Simulation indicate that the slip velocities and drag reduction predicted by Dynamic-Smagorinsky model are in good agreement with Direct Numerical Simulation. Recent results show that large drag reduction is possib! le at Reynolds numbers of practical applications by using a hydrophobic surface. Key Words: Large Eddy Simulation,Drag Reduction, Hydrophobic Surface,Turbulent Flow

Investigation of Performance of Different Sub-grid Scale Models in Improvement of 3D Large Eddy Simulation of Turbulent Near Wall Boundary Layer

N. Mohammad Nouri, Seyyed Mohammad Amin Kariminia, Alireza MofidiTehran, Iran

[email protected]

Turbulent flow field analysis, especially in near wall region is crucial and requires heavy computational costs. In the present research work, analysis of 3D turbulent flow was performed through Large Eddy Simulation by means of Smagorinsky, dynamic and one-


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equation sub-grid scale models. Each model in LES approach has different prediction of turbulent characteristics in near-wall region. Fully developed channel flow for Reynolds number of 2800 based on bulk velocity and channel half width is evaluated. The computational domain is used in streamwise, wall-normal and spanwise directions, respectively, with 274625 grid points (65×65×65). Mesh formation in wall normal direction is set as hyperbolic distribution. Turbulent characteristics such as turbulent intensity in different directions and Reynolds stresses; moreover, the mean velocity profile are examined and compared with Direct Numerical Simulation. Furthermore, efficiency of different procedures in computing flow characteristics in boundary layer is evaluated. The results indicate close agreement.Key Words: Near-wall region, Large Eddy Simulation, Channel flow, Sub-grid scale models

Asymptotic behavior and limit sets of piecewise izometric transformations derived from an Error Diffusion algorithm

Tomasz NowickiIBM Watson Research Center 33-210

1101 Kitchawan Road Rte 134, PO Box 218Yorktown Heights, NY 10598, USA

(e-mail: [email protected])

. We investigate certain piecewise linear maps that are defined in terms of a convex polytope. When the convex polytope is a simplex, the resulting map has a dual nature. On one hand it is defined on RN and acts as a piecewise translation. On the other it can be viewed as a translation on the N-torus. What relates its two roles? A natural answer would be that there exists an invariant fundamental set into which all orbits under piecewise translation eventually enter. We prove this for any N and generic translations. We also prove the structure of theorem on the pieces of the invariant sets. This problem was motivated by investigation of greedy online algorithms for colour printing.Let P be a non degenerate simplex with vertices vi. We can define a partition of the space into Voronoi regions Vi by collecting all the points which are closer (in Euclidean distance) to the vertex vi than to any other vertex. Some tie breaking rules need to be applied but the results are independent on this choice. For γ an internal point of the simplex define the piecewise translation map by

)()( ivxxF for iVx . We will say that:

It is worth observing that the map can be projected onto a torus (space divided by the simplex lattice) where it acts as rotation – translation by a single vector. The typicality condition is represented by ergodicity of this rotation. Theorem (Structure of the invariant set) For a typical point in an acute simplex the minimal absorbing set for the trajectories of Fγ is a fundamental set with respect to the lattice generated by the edges of the simplex.Theorem (Pieces of the invariant set ) Any collection of the pieces (with respect to the Voronoi partition) of the invariant set is a fundamental set with respect to a lattice which can be explicitly expressed by the vertices vi and the point γ.

Efficient Large-Scale Forcing in Finite-Difference Simulations of Steady Isotropic Turbulence

Ryo Onishi, Yuya Baba and Keiko TakahashiEarth Simulator Center

3173-25 Showa-machi, Kanazawa-kuYokohama 236-0001 [email protected]

This study has proposed a new forcing scheme suitable for massively-paralleled finite-difference simulations of steady isotropic turbulence. The proposed forcing scheme, named reduced-communication forcing (RCF), is based on the idea of the conventional large-scale forcing, while requires much less data communication. It has been confirmed that the RCF


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works intrinsically in the same manner with the conventional large-scale forcing. Comparisons have revealed that the fourth-order finite-difference model together with the RCF (FDM-RCF) is as good as the spectral model, moreover it requires less computational costs. Large computations using the FDM-RCF have shown the consistent power-law increase of Reynolds-dependence of flatness factor with past studies. Key Words: Steady isotropic turbulence, Finite-difference simulation, High-performance computing, intermittency

On a Problem of Approximation of Markov Chains by a Solution of a Stochastic Differential Equation

Gabriel V. OrmanDepartment of Mathematical Analysis and Probability

"Transilvania" University of Brasov, [email protected]

It is known that a precise definition of the Brownian motion involves a measure on the path space, such that it is possible to put the Brownian motion on a firm mathematical foundation. Much scientific works has been done on its applications in such diverse areas as molecular and atomic physics, chemical kinetics, solid-state theory, stability of structures, population genetics, communications, and many other branches of the natural and social sciences and engineering. In this sense, many contributions have been done by P. Lé vy, K. Itô , H.P. McKean, Jr., S. Kakutani, H.J. Kushner, A.T. Bharucha-Reid and other. But we refer here only to some aspects concerning the approximation of Markov chains by a solution of a stochastic differential equation to determine the probability of extinction of a genotype. Various situations may exist when the survival of a particular genotype can be very dynamic. And some characteristics of interest, become very hard to calculate. Thus, the Markovian nature of the problem will be pointed out again, and we think that this is a very important aspect.

Keywords: Brownian motion, stochastic differential equations, Markov chains, transition probabilities, binomial distribution.

2000 MS Classification: 60H10, 60H30, 60J65, 60J20, 60J70

An ill-posed problem of determining nonlinearity in diffusion process

Jiaqing Pan Jimei University, Xiamen, P.R.China

[email protected] ; [email protected]

This work is concerned with the solvability of the ill-posed problem of determining the diffusion velocity in nonlinear diffusion process with an additional condition. We first prove the continuous dependence of the solutions with respect to the nonlinearity of the equation and then, give the existence of the solution of the ill-posed problem and calculate the range of the velocity.

Key Words: ill-posed problem; nonlinearity; continuous dependence on nonlinearity

AMS(2000) Subject Classifications: 35K10; 35K20

Supergranular Activity Dependence

U. Paniveni, V.Krishan, Jagdev Singh , R.Srikanth NIEIT, Mysore, Karnataka, India

[email protected]

We study the complexity of supergranular cells using the intensity patterns obtained from the Kodaikanal solar observatory during the Solar maximum. Our data consists of visually identified supergranular cells, from which a fractal dimension D for supergranulation is obtained according to the relation Pα AD/2 , where A is the area and P the perimeter of the


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supergranular cells. We find a difference in fractal dimension between the active and the quiet region cells which is conjectured to be due to the magnetic field. Key Words: Turbulence, Convection, MHD

The complete solution for the classical four-spin Heisenberg ring

Leonidas PantelidisDepartment of Physics and Astronomy, Hanover College, Hanover, IN 47243, USA

E-mail: leon [email protected]. The four-spin Heisenberg ring is a simple integrable model for which a general closed-form solution can be found, however, this classical dynamics is far more complicated than the corresponding quantum dynamics. In this article, we analytically calculate, characterize, and classify all the possible families of trajectories of this dynamical system using an E-T plot. This plan may not be carried out to its end for longer Heisenberg chains. Nevertheless, by employing similar arguments, insight may be gained into certain types of motion of larger systems with additional symmetries.

PACS numbers: 05.45.-a

A bifurcation scenario for large-P Rayleigh-Benard Convection

Supriyo Paul, Sandeep Reddy, Pankaj Wahi and Mahendra K. VermaMechanical Engineering Department

Indian Institute of Technology-Kanpur, Kanpur, [email protected]

We present results of direct numerical simulations (DNS) of Rayleigh-Benard convection (RBC) in a fluid of Prandtl number 6.8. The system shows constant, time-periodic, quasi-periodic and chaotic convective states with a change in the Rayleigh number. Coexisting chaotic and constant convection states are observed. The observed the convective state in such scenarios depend crucially on the initial conditions. We also observe that the convection rolls move chaotically in a direction perpendicular to the roll axis for certain values of the Rayleigh numbers. We propose a possible bifurcation scenario based on the DNS results which include both super- and sub-critical Hopf, Neimarck-sacker and boundary crisis. Key Words: Rayleigh-Benard convection, Bifurcation, Chaos.

Data processing distributed systems

Ivan M. PershinPyatigorsk State Technological Institute,

Pyatigorsk, [email protected]

We consider the mathematical tool providing information extraction from function mudulated distributed data signals. This functions are depended from spatial coordinates, i.e. spatial modes. These extraction is performed by spatial scanners and spatial filters. Spatial scanners provide finding of spatially modulated signal (by means of spatial scanning) in the distributed data signal, but spatial filters extract defined spatial modes (tranks of data transfer) from exploring data signal. In the paper we show examples of data processing system implementations.


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Synergetic Synthesis of Energy Saving Control Systems for Electromechanical Processes

Andrey N. PopovTaganrog Institute of Technology – Southern Federal University,

Dept. of Synergetics and Control Processes44, Nekrasovky str., Taganrog, 347928, Russia;

[email protected]

The paper is devoted to using of synergetic control theory for synthesis of energy saving control for electromechanical processes. The questions of energy invariants finding and synergetic synthesis procedure of energy saving control are considered. Proposed approach application for induction motor is demonstrated.

Keywords: electromechanical energy conversion, energy saving, automatic control, energy invariants, synergetic feedback synthesis.

Chaos as Compositional Order

Eleri A. PoundICSRiM (Interdisciplinary Centre for Scientific Research in Music), University of Leeds


Composition is a combination of determined combinations of notes, durations and timbres usually decided upon in advance by a composer who plans carefully the sounds she desires. There is also always an element of chance present in acoustic music due to the 'human' element of the performance in that the performers will add their own interpretation of the dynamics and errors in terms of precise durations and pitches. Some composers have exploited this chance element more than others, allowing more space within the composition for the performers to make choices during the course of the piece. Composers such as Cage and Bussotti offer varying degrees of freedom within pieces resulting in unpredictability of the resulting sound of the composition. Other composers attempt to control as far as possible every parameter of the music as seen in serialist composers such as Webern and Boulez. This paper is delivered from the point of view of a composer who is intrigued by the relationship between the notation and the resultant sound, specifically, in terms of the relationship between the written elements determined by the composer and the unpredictability that arises due to those elements which cannot or are deliberately not written. These elements are then left to the interpretation and/or choice of the performer during the performance resulting in a composition which differs sonically from performance to performance. Chaos offers this combination of determination and the appearance of disorder: a clear structure within which are a number of elaborate chaotic-appearing options. The paper will focus on a composition-in-progress for voices which will offer the performers some choices based on the idea of sensitivity on initial conditions. Each singer will be provided with a set of headphones through which they will be fed a choice of pitches, the choices made for the first few pitches will determine the choices provided to the singer later on in the composition. The paper will also outline the concepts behind the piece and how the use of chaos will provide compositional parameters with the overall development of the piece being determined by choices made by the performers. The paper will also briefly explain the unusual tuning systems set in place for the piece which is a system proposed by Rob Sturman based on non-linear dynamics.


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Complexity Theory: from Microscopic to Macroscopic level,Concepts and Applications

G.P. Pavlos[1], A.C. Iliopoulos[1], , L.P. Karakatsanis[1], V.G. Tsoutsouras[1], E.G. Pavlos[2]

[1] Department of Electrical and Computer Engineering, Democritus University of Thrace, 67100 Xanthi, Greece.

[2] Department of Physics, Aristotle University of Thessaloniki, 541 24 Thessaloniki, GreeceEmail: [email protected]

The great challenge of the complexity theory emerges from old and essential problems such as: the time arrow, the existence or not of a simple physical level, a unified description of macroscopic and microscopic levels, the relation between the observer and the examined object etc. In general, as far as the complexity theory and every new level of the physical reality is concerned, new concepts and new classifications are required. The first principles of the physical theory modeled the entire cosmos, using a reductionist point of view, as a deterministic, integrable, conservative, mechanistic and objectifying whole.

However, Boltzmann’s probabilistic interpretation of entropy as well as the non-integrability of the large Poincare systems, raised for the first time serious doubts upon the universality and plausibility of the primitive classical physical theory. Moreover, two great revolutions reconfigured the absolute objectifying character of the classical physical theory. The first one, concerning the macrocosm was the Relativity Theory of A. Einstein and the second one, concerning the microcosm, was the Quantum Theory of W. Heisenberg, E. Schrodinger and P. Dirac. Finally, the reductionist character of the physical theory has been disputed after the scientific job of M. Feigenbaum, H. Poincare, E. Lorenz, I. Prigogine, G. Nicolis, D. Ruelle and F. Takens and other scientists who founded the chaos and complexity theory. In particular, Complexity theory includes: chaotic dynamics in finite or infinite dimensional state space, far from equilibrium phase transition, long range correlations, self-organization and multiscale cooperation from the microscopic to the macroscopic level, fractal processes in space and time and other significant phenomena.

In this study, initially we provide a comprehensive description of the novel concepts included in the complexity theory from the microscopic to the macroscopic level and finally we introduce new tools and methods useful for connecting the complexity theory with observational data and various physical problems.

Energy cycle for the Lorenz-63 attractor

Vinicio Pelino, Filippo MaimoneCNMCA AEROPORTO 'M.DE BERNARDI', POMEZIA (ROMA) , ITALY

[email protected]

In 1955 E. Lorenz [1] introduced the concept of energy cycle as a powerful instrument to understand the nature of atmospheric circulation. In that context conversions between potential, kinetic and internal energy of a fluid were studied using atmospheric equations of motion under the action of an external radiative forcing and internal dissipative processes. Following these ideas, in this paper we will illustrate that chaotic dynamics governing Lorenz-63 model can be described introducing an appropriate energy cycle whose components are kinetic, potential energy and Casimir function derived from Lie-Poisson structure hidden in the system Key Words: chaos Lie-Poisson energetics


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Regular variation, Paretian distributions, and the interplay of light and heavy tails in the fractality of asymptotic models

Dinis D. Pestana, J. Leonel Rocha and Sandra M. AleixoMathematics Unit, DEC, Instituto Superior de Engenharia de Lisboa and CEAUL

Lisboa, [email protected]

Classical central limit theorems, culminating in the theory of infinite divisibility, accurately describe the behaviour of stochastic phenomena with asymptotically negligible components. The classical theory fails when a single component may assume an extreme protagonism. The early developments of the speculation theory didn’t incorporate the pioneer work of Pareto on heavy tailed models, and the proper setup to conciliate regularity and abrupt changes, in a wide range of natural phenomena, is Karamata’s concept of regular variation and the role it plays in the theory of domains of attraction, and Resnick’s tail equivalence leading to the importance of generalized Pareto distribution is the scope of extreme value theory.Waliszewski and Konarski (2005) discussed the applicability of the Gompertz curve and its fractal behaviour for instance in modeling healthy and neoplasic cells tissue growth. Gompertz function is the Gumbel extreme value model, whose broad domain of attraction contains intermediate tail weight laws with a wide range of behaviour.Aleixo et al. (2008, 2009) investigated fractality associated with Beta(p,q) models, some of which are generalized Pareto, that span thee possible regular variation of tails. We extend the investigation to other extreme stable models, namely Fré chet’s and Weibull’s types in the General Extreme Value (GEV) model.

References:

Aleixo, S.M., Rocha, J.L. and Pestana, D.D (2008). "Populational Growth Models Proportional to Beta Densities with Allee Effect", Proceedings of the BVP2008, Conference on Boundary Value Problems, Mathematical Models in Engineering, Biology and Medicine, American Institute of Physics AIP Conference Proceedings Volume 1124, 3-12. ISBN: 978-0-7354-0660-5

Aleixo, S.M, Rocha, J.L. and Pestana, D.D. (2009). Dynamical Behaviour in the Parameter Space: New Populational Growth Models Proportional to Beta Densities. In Luzar-Stiffler, V., Jarec, I. and Bekic, Z. (eds.), Proceedings of the ITI 2009, 31th International Conference on Information Technology Interfaces, p. 213-218.

Benoit Mandelbrot, B. (1963). The Stable Paretian Income Distribution when the Apparent Exponent is Near Two, International Economic Review, 4, 111-115.

Pestana, D.D., Aleixo S.M. and Rocha, J.L. (2009). Hausdorff Dimension of the Random Middle Third Cantor Set. In Luzar-Stiffler, V., Jarec, I. and Bekic, Z. (eds.), Proceedings of the ITI 2009, 31th International Conference on Information Technology Interfaces, p. 279-284.

Pestana, D.D., Aleixo, S.M. and Rocha, J.L. (2009). The Beta(p,1) extensions of the random (uniform) Cantor sets. Discussiones Mathematicae Probability and Statistics 29 (in press)

Waliszewski and J. Konarski, J. (2005). A Mystery of the Gompertz Function, in Fractals in Biology and Medicine, G.A. Losa, D. Merlini, T.F .Nonnenmacher and E.R. Weibel (eds.), Birkhäuser, Basel. 277-286.

Key Words: Regular variation, paretian distributions, Gompertz function, fractals and general extreme value model


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Assessing ergodic properties of ecological time series

R. Petritsch, S.A. PietschBOKU - University of Natural Resources and Applied Life Sciences

Peter-Jordan-Strasse 82Vienna A-1190 Austria

[email protected]

We implemented a framework for assessing ergodic properties for a given time series. It enables us to estimate the maximum Lyapunov exponent, Hausdorff-, correlation and information dimensions. Initially, this is done within a Graphical User Interface to obtain suitable parameters for the estimation process. Afterwards, the procedure may be applied in a batch operation with pre-defined parameters for a large number of time series. This is necessary as we are not only interested in the ergodic properties of a single time series, but also a set of time series coming from different scenarios, spatially distributed measurement stations or model runs. In the present study, we assess ergodic properties of ecological time series originating from ozone and climate measurements and outputs of a mechanistic ecosystem model. Key Words: Time series analysis, ecological data, ecosystem modelling

The Ergodic View of Ecosystem Behaviour

S.A. Pietsch, R. PetritschBOKU - University of Natural Resources and Applied Life Sciences

Peter-Jordan-Strasse 82Vienna A-1190 Austria

[email protected]

The changes in global climate expected over the course of the 21st century are among the major challenges natural ecosystems face today. Ergodic theory allows a numerical description of aspects related to system dynamics like the dimensional characteristics of the attractor, the rate of information generation and the temporal and conditional scale of model stability. If a model serves as representation of reality, then unstable model situations should be consistent with instabilities of the real world ecosystem the model intends to mimic. If model instabilities are inconsistent with real world observations, then arbitrary estimates may be more accurate than model predictions. From the applied prospective the separation of the two possibilities is currently one of the main difficulties in forecasting and scenario analysis. In the context of the expected rapid changes in environmental conditions there is an evident! need for tools that allow the assessment of (i) the resilience, (ii) the stability and (iii) the predictability of ecosystem behaviour. Ergodic theory provides that tools. Key Words: resilience, predictability, stability, ecosystems, ergodic theory

Tools for Investigation of Dynamics of DC-DC Converters within Matlab/Simulink

Dmitry PikulinRiga Technical University, Riga, Latvia


In this paper the study of complex phenomenon in buck converter under voltage mode control, operating in discontinious current mode, within Matlab/Simulink simulation environments is provided. To perform simulations different types of models are used: based on discrete-time maps, differential equations and real elements (including different nonidealities). The main goal of this paper is to detect the ability of various Matlab/Simulink models to identify and to explore different types of complex behaviour, such as chaos and


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bifurcataions, in switch-mode DC-DC converters, as system parameters are changed, as well as to estalish the possibilities of each model in this kind of investigation. Simulations are carried out by means of Matlab/Simulink simulation environment that provides wide range of blocks and elements for complete investigation procedure, including the implementation of all types of mentioned models and appropriate result data postprocessing and visualization. The verification of accuracy of developed models is based on the detection of Feigenbaum numbers. All models with definite level of precision are able to reveal that under certain circuit parameters period doubling route to chaos is observed.

Keywords: Bifurcation diagram, buck converter, chaos, simulation tools, subharmonics.

De Broglie-wave chaos

S.V. PrantsLaboratory of Nonlinear Dynamical Systems, Pacific Oceanological Institute of the Russian

Academy of Sciences, 43 Baltiiskaya St., 690041 Vladivostok, Russiae-mail: [email protected]

Coherent motion of cold atomic wave packets in a standing-wave laser field is interpreted in the dressed-state basis as a propagation in two optical potentials. It is shown that the wave-packet dynamics can be either regular or chaotic with transitions between these potentials after passing nodes of the standing wave. Manifestations of de Broglie-wave chaos are found in the behavior of the momentum and position probability-densities and the Wigner function. The probability of those transitions depends on the ratio of the squared detuning to the Doppler shift and is large in that range of the parameters where the classical atomic motion is shown to be chaotic in the sense of exponential sensitivity to small variations in initial conditions or parameters. Varying the strength of the laser field, one can manipulate the regimes of the wave-packet motion.

SYNERGETIC APPROACHES TO PROBLEMS OF EVOLUTION OF PROPERTIES OF MATERIALS AND NANOMATERIALS ON THE BASIS OF SILICON

E.P. ProkopevMoscow State Institute of Electronic Technology (MIET)

d.903, kv.18 Zelenograd, Moscow, [email protected]

The opportunity of synergetic approach to consideration of evolution of properties of modern materials of a science and technics and the silicon, connected with the advent of in a material under influence of an exchange with an environment streams of energy and substance of a new phase (for example, amorphous), breaking its basic properties (for example, durability), caused by nonequilibrium phase transitions of type of crystall amorphous phase is considered. It is shown, that durable and some other properties of technically important materials it is impossible to consider only on the basis of one laws of mechanics. They should be considered as a part of the general problematics of the nonlinear dynamic systems working far from balance (I.R.Prigozhina's postulate). Lead below consideration of evolution of properties of technically important materials used in nuclear and electronic materiology (for example, silicon and structures silicon on an insulator) on the basis of simple models quasichemical Shlögl reactions, confirms Prigozhin's this postulate [1,2].1.E.P.Prokopev. http://www.portalus.ru/modules/science/rus_readme.php 2.E.P.Prokopev. http://yfyf.ru/wp-admin/upload.php Key Words: Synergetics, silicon, defects


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The chaos and order in human ECG under the influence of space weather and other external factors

M.V. Ragulskaya1 , V.V. Pipin2

[email protected], Moscow, Russia, 2ISTP, Irkutsk, Russia

The results of the many-year telecommunication heliomedical monitoring “Heliomed” (2003-2010) show, that space weather and geophysical factor variations serve as a training factor for the adaptation- resistant member of the human population. Here we discuss the specific properties of the human ECG discovered in our experiment. The daily registered parameters include: dynamical characteristics 1-st lead ECG (25 000 measures total), the arterial pressure, the variability cardiac contraction, the electric conduction of bioactive points on skin. The results time series compared with daily values of space weather and geomagnetic parameters.The analysis of ECG signal proceeds as follows. At first step we construct the ECG embedding into 3D phase space using the first 3 Principal Components of the ECG time series. Next, we divide ECG on the separate cycles using the maxima of the ECG's QRS complex. Then, we filter out the non-typical ECG beats by means of the Housdorff distance. Finally, we average the example of the ECG time series along the reference trajectory and study of the dynamical characteristics of the averaged ECG beat.It is found, that the experimental ECG signal embedded in 3D phase space can be considered as a mix of a few states. At the rest, the occurrence of the primary ECG state compare to additional ones is about 8:2. The occurrence of the primary state increases after the stress. The main effect of the external perturbation is observed in structural change of the cardio-cycle and not in the variability of the R-R interval. The number of none-typical cycles increase during an isolated magnetic storm. At the all monitoring centers participating experiment the same type of changes in the cardiac activity parameters is detected to go nearly simultaneously during an isolated magnetic storm.

To understand the origin of the standard cardio-cycle changes we use the dynamical model reconstruction of the individual cardiac beat. The model is constructed as follows. Suppose we have two principal components that are responsible for the system dynamics. Let it be the

signal a and the quantity which is functionally related to the its derivative b . Using the ideas of the stellar dynamo we derive the model for the simple nonlinear oscillator with the parametric excitation. It reads as follows

322 aka(t)asin=akb,a5

4(t)sinΩ=b

The parameters Ω can be identified as power of the driving force, while k is to take into account of diffusion processes in the system. The model demonstrate the different kind of attractor for the internal different parameters of the system from the order to chaos. We find that the stiffness of the beat is important for the general stability of ECG. Thus, the observable changes of the ECG structure can serve as a good proxy for the internal cardiac functioning process. The given results agues for the increase the relative disorder of the human cardiac system under external perturbations due to changes in the space weather and climatic factors. Also, the results of monitoring show that cardiac system can be stabilized by “internal” (physical) stress.


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Scattering by many small inhomogeneities and applications

Alexander G. RammMathematics Department, Kansas State University

Manhattan, KS 66506-2602, [email protected]

http://www.math.ksu.edu/eramm

Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small inhomogeneities per unit volume and their intensities such that embedding of these inhomogeneities in a bounded region results in creating a new system, described by a desired potential. The governing equation for this system is a non-relativistic Schrödinger’s equation described by a desired potential. Similar ideas were earlier developed by the author for acoustic and electromagnetic (EM) wave scattering problems.Key words: wave scattering by small inhomogeneities; metamaterials; nanotechnology; refraction coefficient; negative refraction.PACS 43.20.+g, 62.40.+d, 78.20.-e.MSC 35J10; 45F05; 74J25, 81U10; 81U40; 82C22

REFERENCES:1) A.G.Ramm, Wave scattering by small bodies of arbitrary shapes, World Sci. Publishers,

Singapore, 2005.2) A.G.Ramm, Inverse problems, Springer, New York, 2005.3) A.G.Ramm, Distribution of particles which produces a ”smart” material, Journ. Stat. Phys.,

127, N5, (2007), 915-934.4) A.G.Ramm, Many-body wave scattering by small bodies and applications, J. Math. Phys.,

48, N10, 103511, (2007).5) A.G.Ramm, Scattering by many small bodies and applications to condensed matter

physics, Europ. Phys. Lett., 80, (2007), 44001.6) A.G.Ramm, Inverse scattering problem with data at fixed energy and fixed incident

direction, Nonlinear Analysis: Theory, Methods and Applications, 69, N4, (2008), 1478-1484.

Beta(p,q)-Cantor Sets — Determinism and Randomness

J. Leonel Rocha, Sandra M. Aleixo and Dinis D. PestanaMathematics Unit, DEQ, Instituto Superior de Engenharia de Lisboa and CEAUL

Lisboa, [email protected]

Usually randomness appears as a sophisticated extension of deterministic models, that are then presented as expectation of some class of random models (this approach is exceedingly well managed in the classical Barucha-Reid’s treatise on random functions and stochastic processes). Pestana et al. (2009) summarize previous work by the authors, using stochastic definitions of extensions of Cantor’s fractal to put forward appropriate deterministic models, that in a precise sense are the expectation of a structured class of models, and investigated bifurcations, Allee’ effect, and the Hausdorff dimension. Beta (p,q) models, with either p=1 or q=1, or the classical Verhulst’s model (p=q=2), proportionate interesting computable models for which computations both of Hausdorff dimension and probabilities can be explicitly evaluated, either analytically or using Monte Carlo. The present extension, axed on arbitrary symbolic dynamical systems, further develops new fundamental classes of geometric constructions, and exploit the interplay of determinism and randomness on the richness of the limit fractal set, in a recursive construction.This sheds new light on the sense of Hausdorff dimensionality. We show that the dependence of the random order statistics is at the core of the apparent anomaly of consistently smaller Hausdorff dimensions of the random sets, when compared with the corresponding


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deterministic counterparts. We also recover Falconner’s, Pesin’s and Weiss’ (among others) ideas on recursive geometric constructions as a straightforward approach to important issues is fractality and chaos.

References:

Aleixo, S.M., Rocha, J.L. and Pestana, D.D. (2008). "Populational Growth Models Proportional to Beta Densities with Allee Effect", Proceedings of the BVP2008, Conference on Boundary Value Problems, Mathematical Models in Engineering, Biology and Medicine, American Institute of Physics AIP Conference Proceedings Volume 1124, 3-12. ISBN: 978-0-7354-0660-5

Aleixo, S.M, Rocha, J.L. and Pestana, D.D. (2009). Dynamical Behaviour in the Parameter Space: New Populational Growth Models Proportional to Beta Densities. In Luzar-Stiffler, V., Jarec, I. and Bekic, Z. (eds.), Proceedings of the ITI 2009, 31th International Conference on Information Technology Interfaces, p. 213-218.

Pestana, D.D., Aleixo S.M. and Rocha, J.L. (2009). Hausdorff Dimension of the Random Middle Third Cantor Set. In Luzar-Stiffler, V., Jarec, I. and Bekic, Z. (eds.), Proceedings of the ITI 2009, 31th International Conference on Information Technology Interfaces, p. 279-284.

Pestana, D.D., Aleixo, S. M., and Rocha, J.L. (2009). The Beta(p,1) extensions of the random (uniform) Cantor sets. Discussiones Mathematicae Probability and Statistics 29 (in press)

Key Words: Order statistics, uniform spacings, random middle third Cantor set, Beta spacings, Hausdorff dimension.

Cancellation exponents in helical and non-helical flows

Paola Rodriguez Imazio and Pablo Mininni Dpto. de Fisica, Facultad de cs. Exactas y Naturales, Universidad de Buenos Aires


Helicity is a quadratic invariant of the Euler equation in three dimensions. As the energy, when present helicity cascades to smaller scales where it dissipates. However, the role played by helicity in the energy cascade is still unclear. In non-helical flows, the velocity and the vorticity tend to align locally creating patches with opposite signs of helicity. Also in helical flows helicity changes sign rapidly in space. Not being a positive definite quantity, global studies considering its spectral scaling in the inertial range are inconclusive, except for cases where one sign of helicity is dominant. We use the cancellation exponent to characterize the scaling laws followed by helicity fluctuations in numerical simulations of helical and non-helical turbulent flows, with different forcing functions and spanning a range of Reynolds numbers from approx 670 to 6200. The exponent can be related to the fractal dimension as well as to the first order helicity scaling exponent. The results are consistent with the geometry of helical structures being filamentary. Further analysis indicates that statistical properties of helicity fluctuations in the simulations do not depend on the global helicity of the flow. Key Words: Turbulence, Helicity, cancellation exponent

Predicting chaos with second method of Lyapunov

Vladimir B. RyabovFuture University Hakodate, 116-2 Kamedanakano-cho, Hakodate

Hokkaido, Japan 041-8655Email: [email protected]

We overview several analytic methods of predicting the emergence of chaotic motion in nonlinear oscillatory systems. A special attention is given to the second method of Lyapunov, a technique that has been widely used in the analysis of stability of motion in the theory of dynamical systems but received little attention in the context of chaotic systems analysis. We show that the method allows formulating a necessary condition for the appearance of chaos


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in nonlinear systems. In other terms, it provides an analytic estimate of an area in the space of control parameters where the largest Lyapunov exponent is strictly negative. A complementary area thus comprises the values of controls, where the exponent can take positive values, and hence the motion can become chaotic. Contrary to other commonly used methods based on perturbation analysis, such as e.g., Melnikov criterion, harmonic balance, or averaging, our approach demonstrates superior performance, especially at large values of the parameters of dissipation and nonlinearity. Several classical examples comprising mathematical pendulum, Duffing oscillator, and a system of two coupled oscillators, are analyzed in detail demonstrating advantages of the proposed method compared to other existing techniques.

Keywords: Direct method of Lyapunov, Lyapunov exponents, Melnikov method, Harmonic balance, Averaging, Saddle-node bifurcation, Local expansion rates, pendulum, Duffing

Existence results for flows of slightly compressible viscoelastic fluid in a singular bounded domain

Zaynab SalloumUniversité Libanaise, Faculté des Sciences-Section I, Dé partement de Mathé matiques,

Beirut, [email protected]

Steady flows of slightly compressible viscoelastic fluid of Oldroyd type with zero boundary conditions are considered on a bounded two-dimensional domain with an isolated corner point. We prove the existence and the uniqueness of the solution for small data in weighted

Sobolev spaces kV , where the index ξ characterizes the power growth of the solution near

the angular point. The proof follows from an analysis of a linearized problem through the fixed point theory. We use a method of decomposition for such linearized equations: the velocity field u is split into a non-homogeneous incompressible part v and a compressible part .

Simulation and FEM Analysis of Batch Sugar Centrifuge Shaft

H.Samadzadeh, B. Abdi Khoy, Iran

[email protected]

Batch top suspended centrifuges are a kind of filtering centrifuges. These centrifuges are used in many fields of industry. In this paper the shaft of one type of batch centrifuge has been analyzed which is used in sugar factories for sugar separation. For this purpose, firstly, this centrifuge is modeled. Then for examining the centrifuge operation cycle, an operation cycle has been simulated. This operation cycle was an example which had 2-times operational speed. Another assumption which had implemented was that the separated liquid is not exhausted by centrifuge forces. In the period of simulating, the forces which affects the shaft of centrifuge, has entered in FEA (Finite Element Analysis technique). For one by one instant, this technique has been performed on the shaft of centrifuge. Finally an instant has checked in FEA which had the most probable tension. The critical points have occurred on top of the shaft and in the connection between the shaft and coupling. Because the maximum tension (which had occurred in theses places) was lower than the allowed tension of used material. So we could assure that the shaft can tolerate the loads which resulted from centrifuge rotating. Key Words: Batch Centrifuge Shaft, Simulation, Finite Element Analysis, Stress Analysis, Sugar Industry


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Universal Inverse Power law distribution for Fractal Fluctuations in Dynamical Systems: Applications for Predictability of Inter - annual Variability of Indian Region

Rainfall

A.M.SelvamIndian Institute of Tropical Meteorology, Pune, India

[email protected]

Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and therefore the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory for fractal fluctuations (Selvam, A.M., Fractals, 2009, 17(3), 333-249) which predicts the following. (i) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being generated by the successive integration of enclosed smaller-scale fluctuations. (ii) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the same inverse power law which is a function of the golden mean. (iii) Such a result that the additive amplitudes of eddies when squared represent probability densities is exhibited by the sub-atomic dynamics of quantum systems such as the photon or electron. Therefore, fractal fluctuations are signatures of quantum-like chaos (iv) The model distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean, while for extreme events such as stock market crashes, floods etc., the model predicts much higher (non-zero) probability of occurrence. Continuous periodogram power spectral analyses of available annual total rainfall time series for the period 1900 to 2008 of about 500 Indian stations show that the power spectra and the rainfall distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. Global warming related atmospheric energy input will result in intensification of fluctuations of all scales and can be seen immediately in high frequency (short-term) fluctuations such as devastating floods/droughts resulting from excess/deficit annual, quasi-biennial and other shorter period (years) rainfall cycles. Key Words: fractals, inverse power law, long-range correlations, climate change, global warming

Transition of electromagnetic wave through a warm overdense plasma layer

Babak Shokri, Leila Rajaei,Sedighe MirabotalebiDepartman of physics- Qom university- Qom- Iran

[email protected]

A high transparency condition of an overcritical warm plasma layer due to the excitation of the electromagnetic surface modes is studied. This procedure requires evanescent incident waves on the plasma layer which here is prepared by placing two dielectric layer on the both sides of the plasma film. Key Words: Overdense plasma, surface wave


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VARIETY OF CHAOTIC BEHAVIOUR OF THE DETERMINISTIC NONIDEAL HYDRODYNAMIC SYSTEMS

A.Yu. Shvets, V.A. SirenkoNational Polytechnic University of Ukraine "KPI"

[email protected]

Dynamical systems which consist of the cylindrical tank, partially filled with a liquid, and the electric motor of the limited power, which excites tank oscillations are considered. Mathematical models for such systems have been constructed in [1-2]. The principal attention is given to study of chaotic behaviour of the given systems and description the scenarios of transition to deterministic chaos.

Existence of several types of chaotic attractors of systems "tank-electric motor" is established, their classification is carried out. For the first time existence of hyperchaotic and quasiperiodic attractors is proved. In space of parameters of the considered systems were constructed maps of dynamical regimes which give the exhaustive information about attractors of systems. It is shown that in system all basic scenarios of transition to deterministic chaos, such as Feigenbaum’s scenario, intermittency in the sense of Pomeau–Manneville, et cetera are realized. Possibility of transition to chaos under the scenario of generalized intermittency, described in [1-2], is confirmed. Scenario transition to hyperchaos through destruction of quasiperiodic attractors is described.

1. Krasnopolskaya T.S., Shvets A. Yu. Regular and chaotic dynamics of systems with limited excitation. – Moscow – Izhevsk: R&CD, 2008. – 280p. (in russian)

2. Krasnopolskaya T.S., Shvets A.Yu. Dynamical chaos for a limited power supply oscillations in cylindrical tanks//Journal of Sound and Vibration.-2009.-Vol. 322.-P. 532-553.

A Model of Conflicting Populations for the study of Stock Markets

Christos H. SkiadasData analysis and Forecasting Laboratory

Technical University of Crete, Chania, Crete, Greece(e-mail: [email protected])

This work expands our previous results published in a recent book on “Chaotic Systems: Theory and Applications” [1]. This paper explores an idealized model of two populations conflicting into the same environment (a Stock Market) by following basic rules known from the imitation-innovation diffusion theory, as is the mutual interaction between adopters, potential adopters, word-of-mouth communication. The proposed model is derived by two different approaches that is: 1) the Lotka-Volterra theory and 2) the influence of delays in the communication-decision process. Both methodologies coincide to a set of two coupled nonlinear differential and difference equations including third order terms providingcharacteristic stationary points. The set of the two differential equations is

2122 ))(()( exeyceyax

2211 ))(()( eyexcexby ,

and the corresponding difference equations analogue is:2

1221 ))(()( exeyceyaxx ttttt 2

2111 ))(()( eyexcexbyy ttttt .

Both models show characteristic behavior indicating the presence of limit cycles. Interesting is the stationary behavior and the sensitivity to initial conditions.

Keywords: chaotic modeling, the stock market problem, stock market, innovation diffusion modeling, Lotka-Volterra, simulation, chaotic simulation.

[1] Skiadas, C. H., A Two Population Model for the Stock Market Problem, in Chaotic Systems: Theory and Applications, C. H. Skiadas and I. Dimotikalis, Eds, World Scientific, 302-308, 2010.


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Chaotic Modeling: Lessons and developments during the last decades

Christos H. Skiadas and Charilaos SkiadasData analysis and Forecasting Laboratory

Technical University of Crete, Chania, Crete, [email protected]

Hanover College, Indiana, [email protected]

The rapid growth of the chaotic literature during last decades gave rise to very interesting developments and related applications. However, there are many simple but yet very important issues that we have overcomed in our search for novelty and even complexity. In this note we give few examples on how relative simple improvements in the related theory could have very serious theoretical and real life applications.

Leader-Following Discrete-Time Consensus Protocol on a Buyer-Seller Network

Sunantha Sodsee†‡, Maytiyanin Komkhao†, Zhong Li†, Wolfgang A. Halang†, and Phayung Meesad‡

† Faculty of Mathematics and Computer ScienceFernuniversit¨at in Hagen, Germany‡ Faculty of Information Technology

King Mongkut’s University of Technology North Bangkok, [email protected]

A discrete-time consensus protocol with the leader-following control is proposed, which can drive agents to follow either static or time-varying reference state of the leader. An agent updates its state based on only the current information available from its neighbors. This proposed protocol is applied to the problem of the buyer-seller network, and simulations will illustrate the effectiveness of the proposed consensus protocol. Key Words: Discrete-time consensus, leader-following, static and time-varying state, buyer-seller network

Classical Versus Quantum Dynamical Chaos: Sensitivity to External Perturbations, Stability and Reversibility

Valentin V. Sokolov1;2, Oleg V. Zhirov1;3, and Yaroslav A. Kharkov3;1

1 Budker Institute of Nuclear Physics, Novosibirsk, Russia(e-mail: [email protected])2 Novosibirsk Technical University

3 Novosibirsk State University

. The extraordinary complexity of classical trajectories of typical non-linear systems that manifest stochastic behavior is intimately connected with exponential sensitivity to small variations of initial conditions and/or weak external perturbations. In rigorous terms, such classical systems are characterized by positive algorithmic complexity described by the Lyapunov exponent or, alternatively, by the Kolmogorov-Sinai entropy. The said implies that, in spite of the fact that, formally, any however complex trajectory of a perfectly isolated (closed) system is unique and differentiable for any certain initial conditions and the motion is perfectly reversible, it is impractical to treat that sort of classical systems as closed ones. Inevitably, arbitrary weak influence of an environment crucially impacts the dynamics. This


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influence, that can be considered as a noise, rapidly effaces the memory of initial conditions and turns the motion into an irreversible random process.In striking contrast, the quantum mechanics of the classically chaotic systems exhibit much weaker sensitivity and strong memory of the initial state. Qualitatively, this crucial difference could be expected in view of a much simpler structure of quantum states as compared to the extraordinary complexity of random and unpredictable classical trajectories. However the very notion of trajectories is absent in quantum mechanics so that the concept of exponential instability seems to be irrelevant in this case. The problem of a quantitative measure of complexity of a quantum state of motion, that is a very important and nontrivial issue of the theory of quantum dynamical chaos, is the one of our concern. With such a measure in hand, we quantitatively analyze the stability and reversibility of quantum dynamics in the presence of external noise.To solve this problem we point out that individual classical trajectories are of minor interest if the motion is chaotic. Properties of all of them are alike in this case and rather the behavior of their manifolds carries really valuable information. Therefore the phase-space methods and, correspondingly, the Liouville form of the classical mechanics become the most adequate. It is very important that, opposite to the classical trajectories, the classical phase space distribution and the Liouville equation have direct quantum analogues. Hence, the analogy and difference of classical and quantum dynamics can be traced by comparing the classical (W(c)(I; θ; t)) and quantum (Wigner function W(I; θ; t)) phase space distributions both expressed in identical phase-space variables but ruled by different(!) linear equations.The paramount property of the classical dynamical chaos is the exponentially fast structuring of the system's phase space on finer and finer scales. On the contrary, degree of structuring of the corresponding Wigner function is restricted by the quantization of the phase space. This makes Wigner function more coarse and relatively "simple" as compared to its classical counterpart. Fourier analysis affords quite suitable ground for analyzing complexity of a phase space distribution, that is equally valid in classical and quantum cases. We demonstrate that the typical number of Fourier harmonics is indeed a relevant measure of complexity of states of motion in both classical as well as quantum cases. This allowed us to investigate in detail and introduce a quantitative measure of sensitivity to an external noisy environment and formulate the conditions under which the quantum motion remains reversible. It turns out that while the mean number of harmonics of the classical phase-space distribution of a non-integrable system grows with time exponentially during the whole time of the motion, the time of exponential upgrowth of this number in the case of the corresponding quantum Wigner function is restricted only to the Ehrenfest interval 0 < t < tE - just the interval within which the Wigner function still satisfies the classical Liouville equation. We showed that the number of harmonics increases beyond this interval algebraically. This fact gains a crucial importance when the Ehrenfest time is so short that the exponential regime has no time to show up. Under this condition the quantum motion turns out to be quite stable and reversible.Keywords: Quantum Chaos, Wigner Function, Noise, Fidelity, Stability, Reversibility, Markov's chain, Entropy, Purity.

Composing Chaotic Music from the Letter m

Anastasios D. SotiropoulosSchool of Music, Composition-Theory Division

University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA E-mail: [email protected]

Chaotic music is composed from a recurrence relation depicted by the letter m. Each of the two curves of the letter m is based on the classical logistic recurrence equation. Thus, the resulting recurrence equations of the m- model are xn+1 = r xn(0.5 - xn) for xn between 0 and 0.5 defining the first curve, and xn+1 = r (xn – 0.5)(1 - xn) for xn between 0.5 and 1 representing the second curve. The parameter r which determines the height(s) of the letter m varies from 2 to 16, the latter value ensuring fully developed chaotic solutions for the whole letter m; r = 8 yielding full chaotic solutions only for its first curve. The determining factor for the interplay


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between the two curves is the parameter r. The m- model yields fixed points, bifurcation points and chaotic regions for each separate curve, as well as values of the parameter r greater than 8 which produce inter-fixed points, inter-bifurcation points and inter-chaotic regions from the interplay of the two curves. For r smaller than 8, the m- model map is identical to the classical logistic map if x is doubled and r is divided by two. With increasing r larger than 8 and smaller than 6+4√2, the fixed point for the individual second curve, the resulting map is quite complex being either chaotic or inter-periodic of different degree, alternating at small intervals of r. Based on the above, music is composed from mapping the m- recurrence model solutions onto actual notes. The resulting musical score strongly depends on the sequence of notes chosen by the composer to define the musical range corresponding to the range of the chaotic mathematical solutions x from 0 to 1. Here, two musical ranges are used; one is the middle chromatic scale and the other is the seven-octaves range. At the composer’s will and for aesthetics, within the same composition, notes can be the outcome of different values of r and/or shifted in any octave. The musical meaning of the mathematical results obtained above is discussed. Specific notes corresponding to fixed points are defined in order to avoid them for fully developed compositions. Compositions with endings of non-repeating note patterns result from values of r in the m- model that do not produce bifurcations. Examples of composed chaotic music from the m- model are presented, they are compared with music from the classical logistic map and their recordings are played.

Keywords: Algorithmic composition, chaotic music, m- model music, double logistic map.

On Logistic-Like Iterative Maps

Dimitrios A. Sotiropoulos Department of Sciences

Technical University of Crete, Chania, Greece 73100 Email: [email protected]

Logistic-like first order iterative maps defined by r xλ (1-x)μ are examined. The parameters r, λand μ are positive real numbers, while the variable x and its map range from 0 to 1 giving the upper value of r which yields full chaos. The purpose of the present study is three-fold: first, maps are determined whose fixed and bifurcation points can be expressed in explicit algebraic form; second, for maps of this kind that have not been dealt with in the literature, fixed and bifurcation points are obtained exactly; and third, for other iterative maps near these maps, fixed and bifurcation points are obtained approximately in explicit form from the respective known points of the nearby maps. For maps that are far from them, upper and lower bounds are obtained as a consequence. The approach is based on analyzing the fixed point(s) equation and, in turn, the bifurcation points equations. Values of λ and μ are determined that yield solutions of these equations in explicit algebraic form. The fixed and bifurcation points are then obtained exactly for specific maps including the iterative map defined by the two parameters being equal to one half corresponding to an ellipse. For other values of λ and μ, fixed and bifurcation points are calculated approximately in explicit form by applying the Newton method in their exact equations, one step from the respective known exact fixed and bifurcation points of the iterative map nearest this map. The approximation is tested against the difference between the two sets of λ and μ values for each value of the free parameter r. For differences in the order of one tenth, the approximation yields in general fixed points that are off by an order of one thousandth from their true values. For maps further away, more steps are used in the Newton method for an accurate result. In any case, the fixed and bifurcation points obtained exactly for two neighboring maps, provide upper and lower bounds of the respective points for the iterative maps between them.Keywords: chaotic maps, logistic maps, iterative maps, recurrence equations, fixed points, bifurcation points.


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On the Timbre of Algorithmic Chaotic Sounds

Dimitrios A. Sotiropoulos Department of Sciences

Technical University of Crete, Chania, Greece 73100 Email: [email protected]

Chaotic sound waveforms produced algorithmically are considered to study their timbre characteristics of harmonic and inharmonic overtones. Algorithms employed in the present paper come from different first and second order iterative maps which yield various sound waveforms. To separate the effects of sound onset and fully developed chaotic sound on timbre, the Fourier transform is taken separately for the two corresponding regions of the waveform. The computed amplitude of the Fourier transformed waveform reveals the location and peak of the overtones while the computed frequency dependent phase defines the time shift of individual overtones in the sound waveform. The effects of the map’s free parameter(s) and initial generating sound are studied. Moreover, the higher overtones depend on the path of sound continuity between discrete points of the algorithmically obtained waveform. Higher density in the points results in higher overtones that get affected by the path choice. The effect of the path choice is also examined quantitatively by using different interpolation schemes to connect neighboring discrete points. For the timbre of the sound onset, an attempt is made to represent its overtone content and its phase by an analytical expression derived from approximating the waveform in time by geometrical forms with known Fourier transforms. For example, in the case of the logistic algorithm, the onset waveform is fitted by linear segment(s). The analytical overtones and their phase are compared for several iterative maps with their accurate counterparts obtained numerically, to realize the approximation error involved. The numerical results of the study are depicted graphically.

Keywords: Chaotic sound, sound synthesis, sound analysis, algorithmic music, chaotic maps, music timbre, overtones.

The Rainbow Effect on Composing Chaotic Algorithmic Music

Vaggelis D. SotiropoulosSchool of Music, Composition-Theory Division

University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA E-mail: [email protected]

The effect of rainbow color sequence on composing chaotic algorithmic music is examined. The mathematical range of the chaotic algorithm is mapped onto musical notes whose sequence follows the sequence of the six main rainbow colors and their in-between six auxiliary colors. Each musical note is identified with a color by a frequency shift. As a result, for a single rainbow, the range of the chaotic music comprises an ascending chromatic scale without the thirteenth note, followed by its corresponding descending chromatic scale. This approach contrasts the usual octave- ascending music range. For aesthetic purposes, a note can be shifted in other octaves at the composer’s will. The effect of a double rainbow on composing chaotic music is also studied. It is known from nature that the outer bow has its color sequence reversed. Thus, in this case, the chaotic music range comprises four chromatic scales in a sequence that resembles in shape the letter w. The first scale is a descending chromatic scale without the thirteenth note, followed by its corresponding ascending chromatic scale, which in turn is followed by the same two-scale pattern. Regions of darkness (Alexander’s bands) in the rainbow are included in the musical range as intervals of pauses. As an example and based on the described musical ranges, chaotic music is composed from an algorithm defined by a semi-elliptical recurrence relation. The minor axis of the ellipse is defined by the range of the mathematical variable from 0 to 1 while the semi-major axis by that of the related variable from 0 to r/2; r is a free parameter that varies from 1 to 2 to be chosen by the composer. The lower limiting value of the free parameter r corresponds to a circle yielding no chaos whereas all the other values of r correspond to ellipses. Compositions of chaotic music result from r values between 1.95 and 2, the latter


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value yielding full chaos from an ellipse with its major axis double its minor axis. Fixed notes are obtained for all r’s, i.e., notes to be avoided for a prematurely ending composition. Semi-elliptical rainbow chaotic music is composed and presented in musical notation and colors. Recordings of it are played for the audience together with their corresponding visual effect of colors.

Keywords: Chaotic composition, algorithmic music, rainbow music, color spectrum, elliptical music.

A Highly Chaotic Attractor for a Dual-Channel Single-Attractor, Private Communication System

Banlue Srisuchinwong and Buncha MunmuangsaenSirindhorn International Institute of Technology, Thammasat University

131 M.5, Tivanont Road, Bangkadi, Muang, Pathum-Thani, Thailand 12000E-mail: [email protected]

A one-parameter highly chaotic attractor is presented and its application to a dual-channel, single-attractor, private communication system is demonstrated based on self-synchronization and chaotic masking techniques. Only a single attractor is required for a dual-channel transmitter or receiver, and can be either the well-known Lorenz attractor, the Lorenz-like attractor, or the one-parameter highly chaotic attractor developed in this paper. The latter is particularly well suited for an application to private communications due to the relatively high values of both the maximum Lyapunov exponent of 2.6148 and the maximum Kaplan-Yorke dimension of 2.1921. An advantage of the dual channel is the possibly twice increase in higher speed.Keywords: Highly chaotic attractor, self-synchronization, dual-channel single-attractor private communications.

Compound Structures of Six New Chaotic Attractors in a Modified Only-Single-Coefficient Jerk Model Based on Sinh-1 Nonlinearity

Banlue Srisuchinwong, Teerachot Siriburanon, and Teera NontapraditSirindhorn International Institute of Technology, Thammasat University, Pathum-Thani,

Thailand ,12000, Email: [email protected]

Six new chaotic attractors in a modified only-single-coefficient jerk model are presented based on six new sets of a single coefficient and hyperbolic arcsine nonlinearity. In particular, compound structures of such chaotic attractors are demonstrated through the use of a half-image operation using a control parameter n. The positive value of an appropriate n isolates the right half-image attractors whilst the negative value of an appropriate n isolates the left half-image attractor. Both images can then be merged together as a compound structure. Keywords: Chaos, Jerk Model, Compund Structure, Single Coefficient, Hyperbolic Arcsine Nonlinearity.

Observations and modeling of chaos and solitons in quasi-parallel bow shocks

K. Stasiewicz, M. Strumik, B. ThidèSwedish Institute of Space Physics, Uppsala, Sweden

[email protected]

Using Cluster measurements made in quasi-parallel bow shocks we have analyzed properties of nonlinear soliton-like structures embedded in widespread electromagnetic turbulence. The structures are identified as fast alfvenons propagating with speeds faster than the local Alfvèn speed. They represent large amplitude compressions or rarefactions of the magnetic fieldbeing in phase with structures of plasma density. The observations are modeled both analytically and with time-dependent simulations based on two-fluid equations. We discuss


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the results in the context of chaos theory as well as recent results related to Orbital Angular Momentum (OAM) of electromagnetic fields and its relation to plasma structuring. Key Words: solitons, turbulence, chaos, bowshock, foreshock, data analysis, simulations

Manifestation of chaos in collective models of nuclei

Pavel Stránský1,2, Michal Macek1, Pavel Cejnar1, Alejandro Frank2, Ruben Fossion2, Emmanuel Landa2

1Institute of Particle and Nuclear Physics, Charles University in Prague, Czech Republic2Institute of Nuclear Sciences, UNAM, Mexico City, Mexico


Simple models of nuclear collective dynamics - the geometric collective model and the interacting boson model - exhibit a high degree of variability of regular and chaotic features with energy and control parameters [1, 2]. Our recent analysis of classical and quantum signatures of chaos in both models [3-5] has a revealed good classical-quantum correspondence in measures of chaos, even in the regime with mixed dynamics. Apart from standard techniques (e.g. Lyapunov exponents or nearest neighbor spacing distribution) we also applied (i) the Peres lattices [6] which provide a very efficient way to distinguish ordered and disordered parts of spectra and to reveal main ordering principles of quantum states [7,8], (ii) The geometrical method [9] which allows to determine the position where the transition from order to chaos occurs [10], and (iii) We look for 1/f^alpha power law in the power spectrum of energy level fluctuations [11].

[1] Y. Alhassid, N.Whelan, Phys. Rev. Lett. 67, 816 (1991). [2] P. Cejnar, P. Stransky, Phys. Rev. Lett. 93 (2004) 102502.[3] P. Stransky, M. Kurian, P. Cejnar, Phys. Rev. C 74 (2006) 014306.[4] M. Macek, P. Stransky, P. Cejnar, S. Heinze, J. Jolie, J. Dobes, Phys. Rev. C 75 (2007)

064318. [5] P. Stransky, P. Hruska, P. Cejnar, Phys. Rev. E 79, 046202 (2009).[6] A. Peres, Phys. Rev. Lett. 53 (1984) 1711.[7] P. Stransky, P. Hruska, P. Cejnar, Phys. Rev. E 79, 066201 (2009).[8] M. Macek, J. Dobes, P. Cejnar, Phys. Rev. C 80, 014319 (2009).[9] L. Horwitz, Y.B. Zion, M. Lewkowicz, M. Schiffer, J. Levitan, Phys. Rev. Lett. 98, 234301

(2007).[10] P. Stransky, P. Cejnar, in preparation[11] A. Relano, J.M.G. Gomez, R.A.Molina, J. Retamosa, E. Faleiro, Phys. Rev. Lett. 89,

244102 (2002). Key Words: Hamiltonian system, measure of chaos, nuclear collective model, Peres lattice

Importance of the Chaos for computational processes of Collective Intelligence in social structures.

Tadeusz (Ted) SZUBAAGH University, Dept. of Control, Cracow, Poland, EU


Today, computers are based on automata model of computations i.e. Turing Machine and are designed to be deterministic; chaotic behavior is undesirable when considering the stability of algorithms for example. However, when attempting to build the theory of the phenomena of Collective Intelligence (CI), it appears that molecular models of computations relying on chaotic behavior of its components must be used as the computational model. Moreover, Chaos emerges as the essential component for Collective Intelligence (CI) computational processes, providing some required computational mechanisms and computational properties. The paper attempts to define Collective Intelligence and describe relations between CI and Chaos.

Keywords: Collective Intelligence (CI), models of computations, parallel distributed and unconscious computations, Chaos.


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Experimental and Numerical Investigations of Flow Incidence Effects on Surface Pressure Distributions of Axial Compressor Blades

Reza Taghavi Zenouz and Farzin GhanadiIran University of Science & Technology, Tehran, Iran

[email protected]

Cascade data are essential in design process of any turbomachine blades. These data consist of variations of losses, pressure rise, surface pressure distributions and outlet flow angle in terms of Reynolds number, inlet Mach number and flow incidence. Compressor designers use these set of data not only for selection of profile geometry to suit their predicted on design performance, but also to meet off design conditions. Blade incidence may change due to many factors. These factors mainly consist of rotational speed of the compressor axis and inlet flow conditions. Design point in majority of turbomachines does not necessarily correspond to zero incidence. As a result, cascade data at various incidences would be vital during design performance.In the present research work, intensive investigations were performed on axial compressor blades from experimental and numerical point of views. In this paper, results are confined to variations of surface pressure distributions versus flow incidence. Test model was a cascade consisting of three rotor blades of an axial compressor with profile geometry introduced as NGTE 10C4/30C50 section. Tests were carried out in an open circuit wind tunnel of blowing type. Tunnel walls were modified somehow to fit the proposed intentions. In this respect, a suitable test section together with a secondary nozzle were designed and manufactured. These were connected to the exit section of the original wind

tunnel. The Reynolds number was changed from 2.5 × 10 5 to 4.1 × 10 5 based on the blade chord length. 30 pressure tappings were mounted evenly all around the surface of the middle profile both on the pressure and suction surfaces. A suitable data accusation system was used to log the surface static pressures under different conditions. In parallel to the wind tunnel tests flow characteristics were studied using computational fluid dynamics (CFD) technique. Reynolds averaged Navier-Stokes equations were solved using realizable K-ε turbulence modeling.Finally, numerical results were compared to those obtained through the tests which showed close agreements. Key Words: Axial Compressor, Cascade, Incidence Effects, Surface Pressure Distribution

Superstability and Optimal Matrix Correction of the Class of Chaotic Systems

Yuri V. Talagaev1 and Andrey F. Tarakanov2

1Balashov Institute of Saratov State University, Balashov, RussiaEmail: [email protected]

2Borisoglebsk Teachers Training Institute, Borisoglebsk, RussiaEmail: [email protected]

The paper covers the research of two opposite states of dynamic systems that arise in the course of parameter changes, namely, chaos and superstability. The investigation of this interesting problem leads us to the multiparametrical analysis of the structure of system’s equations. In the paper we defined the conditions of superstability attainability and showed that superstability is a unique feature peculiar to few chaotic systems. On the basis of superstability criterion we formulated the optimal matrix (multiparametrical) correction problem and showed an effective problem solution technique. The offered technique allows finding superstabilizable chaotic systems. It also provides their chaos–superstability transition through the optimal correction of the parameters. Key Words: Chaotic systems, Superstability, Multiparametrical analysis, Optimal matrix correction


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IMPERFECT PHASE SYNCHRONIZATION OF THE WALL TURBULENCE:EXPERIMENTS and DIRECT NUMERICAL SIMULATIONS

Sedat TARDULEGI, B.P. 53 X, 38041 Grenoble, Cé dex, France

[email protected]

The discovery of coherent structures in the early 1960’s has profoundly modified our point of view of the wall turbulence structure. The “incoherent” turbulence occupies only 20% of time and space in the inner layer. The coherent part is simpler to understand, since the coherent vortical structures can be identified, and tracked in time and space, and their direct effect on the wall shear and transport of the shear stresses and passive scalar can be clearlydetermined. The common consensus reached by now points at the existence of quasistreamwise vortices of diameters typically 10 wall units and located at 20 units from the wall. Their streamwise extend is roughly 300 units, and they generate low and high speed streaks at the wall with a spanwise periodicity of 100 wall units. The sweep and ejection events they generate contribute to the Reynolds shear stress by 80%. The time period of their generation is approximately 100 units also and it depends on the distance from the wall.Turbulence in general and the wall turbulence in particular can be seen as an infinite dimensional chaotic system. The quasi-periodicity induced by the coherent structures that areconvecting in the low buffer layer, should logically lead to the synchronization of the turbulent quantities near the wall. Chaos synchronization is a process wherein chaotic coupled (sub) systems subject to external forcing adjust their time scales resulting in common spatial and temporal dynamics. Synchronization can also be defined as the locking between the instantaneous phases of a state variable of the system and the phase of the external periodicforce. A rather weak degree of wall turbulence synchronization is expected in a rush environment partially dominated by incoherence. The weaker synchronization between chaotic systems, namely the phase synchronization occurs when the suitably well-defined phases collapse, while the amplitudes remain highly uncorrelated.

Investigating the effect of structural properties on bifurcation and chaotic behavior of passive walking biped with an upper body

Siavash Tayefi and Abdolreza OhadiMech. Eng. Dept., Amirkabir University of Technology, Hafez Ave., Tehran, Iran

[email protected]

Dynamic behavior of a planar biped robot on inclined slopes, changes gradually by change in its parameters before the bifurcation point; after that, the gait performance of biped intrinsically shifts to a different manner, which finally yields to chaos where no two steps are identical. In the chaos regime, the biped has a rich structure which can be used in control application and that is the natural process that happens in human gait. In this study, a 2-D biped model with an upper body is used. This robot has two knee-legs with point masses as its feet at the end of each leg, a third point mass at the "hip" point, a forth mass, which is connected to the hip joint with a massless link to make the upper body and a rotational spring that is located between the legs. The upper body link is confined to the midway angle of the two legs so the model has only two degrees of freedom. Six parameters, namely the ground slope angles, the normalized masses (ration of foot mass and upper mass to the hip mass), leg length and body link length of the robot and finally stiffness of the spring, describe its gait. In this study, we focus our attention on the effects of normalized masses and spring stiffness on the chaotic behavior of biped. The equations of motion are solved by using the function of ODE45 in MATLAB, with a tolerance of 1e-12 in numerical simulations. With specific initial conditions, stable solutions are obtained. Bifurcation diagram of the system due to each parameter shows that how the parameter affects the boped dynamics. Then with tools such as box counting dimension of the Poincare section during chaotic walking motions, it can be found that in which configuration of parameters, the system has the most chaotic behavior and its details can be used in control manner.


90

Complex Signal Generators based on Capacitors and on Piezoelectric Loads

Horia-Nicolai Teodorescu1,2 and Victor Cojocaru3

1,3 Faculty of Electronics, Telecommunications and Information Technology, ‘Gheorghe Asachi’ Technical University of Iasi, Romania

E-mail: [email protected] Institute of Computer Science of the Romanian Academy, Iasi, Romania

We propose, analyze, and demonstrate several signal generators, which apparently should not oscillate, because they include only capacitors in the positive feedback loops. However, the design attempted to make use of the well-known parasitic elements of the capacitors to create a selective feedback loop with physical capacitors only. The use of the resonant (piezoelectric) load adds a new potential mode of oscillation. The design aimed to make achievable as many as possible oscillation modes, against the rather common belief that a single oscillation mode can be supported at one time in electronic oscillators. For this purpose, we provided variable, independent gains to the positive feedback loops that correspond to the various modes in the circuit. In the paper, we describe the schemes, analyze their behavior, show simulation and experimental results and discuss potential uses. One of the applications is in the generation of large bandwidth ultrasounds for a bio-mimetic system.

Keywords: electronic circuit, multimodal oscillation, parasitic elements

“ANOMAL DIFFUSION” IN THE DYNAMICS OF COMPLEX PROCESSES

S.F. Timashev, Yu.S. Polyakov, S.G. LakeevKarpov Institute of Physical Chemistry, Moscow 105064, Russia

USPolyResearch, Ashland, PA 17921, [email protected]; [email protected]

Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in complex processes by comparing experimental and theoretical displacements at relatively small time intervals. This paper proposes an interpolation expression, which uses the difference moment (transient structural function) of the second order as the average characteristic of displacements, for the identification of anomalous diffusion in complex processes for the cases when the stochastic dynamics of the system under study reaches a steady state (large time intervals). A procedure for identifying anomalous diffusion and calculating its parameters in complex processes, which includes the removal of regular (low-frequency) components from the second-order experimental difference moment built for the source time series and the fitting of the stochastic part of the experimental difference moment to the interpolation expression, was applied to the analysis of the dynamics of electric potential fluctuations in a electromembrane system with overlimitting current density, X-ray emission dynamics of astrophysical objects, and neuromagnetic responses to an equiluminant flickering stimulus of different color combinations applied to a group of control human subjects. The results of this study make it possible to broaden the range of complex natural processes in which anomalous diffusion can be identified. Key Words: Anomalous diffusion, Time series, Transient structural function, Electric potential fluctuations, X-ray emission dynamics of astrophysical objects, Neuromagnetic responses.


91

PARAMETERIZATION OF ATOMIC FORCE MICROSCOPY CHAOTIC IMAGES

1V.A. Timofeeva, 1A.B. Solovieva, 1Misurkin P.I., 2S.F. Timashev 1 Institute of Chemical Physics, Russ. Academy of Sciences, Moscow, Russia

2 Karpov Institute of Physical Chemistry, Moscow, RussiaE-mail: [email protected]

Atomic Force Microscopy (AFM) gives a possibility to study and control the surface structure at submicron spatial scales. The essential problem in studying the surfaces is their adequate parameterization. It is necessary to extract information from the surface roughness profiles h(x) and h(y) along coordinates x and y. These profiles contain regular (resonant) components as well as chaotic (noisy) components with “long memory”. The main questions are how to extract useful information about the surface state and study the effect of various external factors on it by analyzing the spatial series h(x) and h(y) and separate out the information contents of chaotic and resonant components. These problems can be solved by using Flicker-Noise Spectroscopy (FNS) approach. According to FNS, the information hidden in chaotic surface profiles is represented by correlation links in sequences of different types of irregularities: spikes, jumps, and discontinuities in derivatives of different orders at all spatial hierarchical levels of the systems. In FNS, the tools to extract and analyze the information are “structural function” (2)(Δ) (Δ is the space lag parameter) of the 2nd order and power spectrum S(f) (f – spatial frequency) of relief profile heights. In order to determine FNS parameters based on the array of relief profile heights, all the profile hi(x) scans forming the AFM image are split into M groups (usually M = 8-16). For each group, the average profile is calculated and the FNS parameters are determined. The most informative parameters that show the differences in the surface structure are the mean σ square deviation of relief profile height relative to the basic profile (formed by the low-frequency “resonant” component determined from S(f)) and the S(L0

– 1) value, which is defined as the power spectrum corresponding to spike irregularities in the range of spatial frequency L0

– 1 (usually L0– 1 ~ 0.1-

1 nm –1). The values σ and S(L0– 1) could be considered as the measures of the nano-relief

jump-irregularities and spike-irregularities correspondently. In addition, the following parameters are introduced to characterize each averaged relief profile in the nanometer range: L0 and L1 – the correlation lengths of irregularities-spikes and irregularities-jumps respectively, H1 – the Hurst constant used to characterize the rate at which the memory (the information content of a dynamic variable) is lost over spatial intervals less than the correlation length (Δ << L), n – the flicker-noise parameter showing the loss of correlationlinks at spatial scales greater than L0

-1 for the sequences of irregularities-spikes in the averaged nano-relief. Capabilities of the methodology introduced are demonstrated on parameterization of AFM data for double and triple systems produced on mica from water solution of chitosan and demigin (porphyrin photosensitizer). These systems appear in research of organic substrate photoinduced oxidation in water solution.

Keywords: Atomic Force Microscopy, chaotic roughness profiles, phenomenological parameters, irregularities, Flicker-Noise Spectroscopy.

Problem of search of the first integrals in nonlinear dynamics tasks

Dmitry V. TimoshenkoTaganrog Institute of Technology – Southern Federal University,


[email protected]

At research of processes in nonlinear dynamic systems the condition of system in a present situation of time essentially differs from initial, that almost completely excludes direct application of the approached analysis based on linearisation of initial system of the differential equations, describing a condition of system. In this connection the great value gets search of the first integrals of such systems. With their help it is possible to carry out research as at those restrictions at which these integrals are received, and their vicinity.


92

From chaos to self-organization: structure and system of the poetic literary text

Polina P. TkachovaBelarusian State University, Belarus

[email protected]

Self-organization of the literary poetic text is that theme which researchers practically have bypassed by their attention. However, the understanding of processes of self-organization, self-structure, as well as self-renewal of poetic structure is key for an analysis of systems prosody functioning. These processes determine as occurrence of the new poetic texts in belles-lettres, and their interrelation with already known works of art. The functioning of systems prosody directly depends on language environment of their use as well as processes of self-organization occurring in a language under investigation. In the given research the processes of self-organization in Russian and Belarusian poetic literary texts are considered.Keywords: self-organization literary text, chaos, structure, system

Numerical Simulation and Wall Shear Stress Analysis of Pulsating Flowin the Channel of Plate Heat Exchanger

Pichitra Uangpairoj and Kontorn ChamniprasartSuranaree University of Technology

111 University Avenue, Sub district Suranaree, Muang DistrictNakhonratchasima, 30000 Thailand

[email protected]

Pulsed flow has the effect of raising the wall shear stress which is one key parameter of the cleaning enhancement in the cleaning in place (CIP) system. In this study, the effect of type of pulsed flow was considered to improve the cleaning efficiency of the CIP system. To indicate the cleaning efficiency of pulsed flows, wall shear stresses of various types of pulsed flows were investigated by using the finite volume method of the commercial computational fluid dynamics code (FLUENT® 6.3.26). In addition, the influences of pulsation parameters and the geometry of the channel flow on wall shear stress were also investigated. The turbulent pulsating flows of water at 50oC were simulated through the corrugated channel of plate heat exchanger and parallel plates under isothermal condition. Type of pulsed flow was characterized by functions of velocity at the inlet boundary which were periodic function such as rect! angular wave, saw tooth wave, sinusoidal wave, trapezoidal wave and triangular wave. As the results of the study, the numerical simulation of different type of pulsed flows shows that pulsating flow with the rectangular waveform of pulsation gives the greatest wall shear stress. Pulsed flows whose flow velocity suddenly change can generated higher wall shear stresses than the pulsed flows whose flow velocity gradually change. Meanwhile, wall shear stress increases with the amplitude and mean velocity inlet of pulsation. But it is inverse proportion to the frequency of pulsation. This is obviously seen only in the corrugated channel. Moreover, the effect of the geometry of the channel flow shows that the complicated channel of plate heat exchanger also gives higher wall shear stresses than the simple geometry as the parallel plates. Key Words: Pulsating flow, Wall shear stress and Computational fluid dynamics (CFD)


93

Shadowing unstable orbits of the 3-body problem

David UrminskyRochester Institute of Technology, Department of Physics, Rochester, New York, USA

[email protected]

Previous work on finding shadow-orbits for numerical solutions of N-body systems have found that shadowing breaks down during close encounters between two particles. In this study I show a different regime in which shadowing breaks down. It is shown that shadowing can be difficult for orbits near the escape boundary due to the stretching of the phase-space. Key Words: shadowing, 3-body, computational mathematics, chaos

Chaos in corporate governance systems: typology, characteristics and overcoming ways

Maksim A. VaskovSouthern Federal University,

The Affiliation of Institution of Russian Academy of Sciences Institute of Sociology RAN in South of Russia


The chaos category in a corporate governance by the large regional commercial organizations is considered in article. Sociological definition of chaos, in a context of studying administrative systems of the large regional commercial organizations is presented, the sociological analysis of the reasons and mechanisms of its occurrence, classification, social and managerial parameters, and also dysfunctions caused by it and deviations in administrative activity is carried out. The conditions that are necessary for overcoming chaos in a corporate governance and administrative culture are considered.

Glue composition containing micro- and nanosized fillers

Venger, E. F., Lokshyn, B. and Maslov V.P.ISP NAS of Ukraine, 41, Prospect Nauky, 03028 Kyiv, Ukraine

[email protected]

The new approach for glue modification via simultaneous addition of microsized and nanosized fillers in glue formulation is putting forward. The glue joint thermal durability depending on fillers concentration has been studied. It has been revealed that addition of nanosized ZrO2 doped 3% Y2 O3 filling powder to silicon resin glue formulation containing the standard micron sized BN or TiO2 filler results in more than three times increasing of the glue joint thermal durabilityKey Words: glue composition, microsized filler, nanosized filler

The crisis of traditional family and the alternatives of the family institution development in different regions of Russia: theoretical analysis in the network of

synergetic paradigm

Anna Vereshchagina Southern Federal University,


The article is devoted to one of the urgent problems of the present-day Russian reality that is the family institution transformation which progresses in the network of the crisis of traditional family and forming the present-day family pattern. This period is characterized by forming transformational space in domestic and conjugal sphere that is presented with


94

coexistence of traditional and new forms of domestic relations. What is in store for Russia and its diverse in ethnocultural and sociocultural respect regions? What pattern of family is going to be prevailing in Russian society in the nearest future? The author is trying to answer these questions in this article with using the synergetic methodological paradigm of investigation.

Key words: the family institution, the family, the traditional family, the present-day family, egalitarian family, patriarchy, matriarchy, the crisis of traditional family, synergetic paradigm, transformation of family.

Nonlinear complex system’s hierarchical control strategies synthesis tasks

Gennady E. VeselovTaganrog Institute of Technology – Southern Federal University,


[email protected]

We have considered principles of hierarchical structures organization in various nature systems and made a review of existed approaches to the problem of control action determination for such systems. Basing of this researches in the paper we propose new approach for solving the problem of hierarchical synthesis of multi-linked, multi-dimensional and nonlinear control systems. Proposed approach application is shown by manipulating robots hierarchical control systems synthesis example.

Keywords: hierarchical structure, system’s synthesis, nonlinear systems, robotics, synergetics

Synthesis of nonlinear control systems by aircraft operation units: synergetics approach

Gennady E. Veselov, Tatiana A. MotienkoTaganrog Institute of Technology – Southern Federal University,


[email protected]

This report presents synergistics synthesis of nonlinear control systems by aircraft operation units. The complete mathematical models and synergistics regulators for electrical and electro-hydraulic drives are described. This synergetics approach improves the efficiency and accuracy of aircraft control systems.

Keywords: modeling, aircraft, mathematical models, regulators, non-linear dynamics, non-linear systems, non-linear control, robustness, electrical, electro-hydraulic, electro-pneumatic drives.

Chaos in Cataclysmic Variables: Superhumps in the UGSU Dwarf Nova Stars

Natalia A. Virnina

We study superhumps in a group of dwarf nova stars of the SU UMa - subtype. The shape of the superhumps vary with time and luminosity. In an addition to usual studies of the signal itself, we study the evolution of the superhumps at the m - dm/dt plots with a special attention to the influence of trend. For this study, we use few methods for statistically optimal smoothing the (irregularly spaced) signal - global trigonometric polynomial (+polynomial trend) fit, spline fit; local "running parabola", "running trigonometric polynomial + linear trend" fits. Results are compared with that expected for the chaotic limit cycle behaviour and for the multiperiodic processes.


95

The ideas of synergy and Russian identity

Yuri G. Volkov Southern Federal University,


Under radical transformation of Russian society the collapse of Russian identity occurred. The loss of regulatory restrictions and the chaos of basic values has put citizens of Russia in the situation of cognitive, axiological and conative option. This option is defined not only with former social experience but also depends on external conditions.

Mathematical simulation of urbanization processes based on analogies with physical fractals

Vyklyuk YaroslavNational University "L'vivs'ka Politekhnika", S. Bandera str. 12, Lviv, 79013, Ukraine


Proposed attributive and structural analogy between physical fractal and social economic system. Proposed algorithm for growth modeling of social economic system. Researched mechanism of stagnation appearance and system self-organization in evolution process. Specified functional analogy between crystal entropy and average level of system competition.

Keywords: fractal, attractor, self organization, entropy, phase transition.

Patterns and Chaos in low- and zero-Prandtl number convection

Pankaj Wahi, Pankaj K. Mishra, Pinaki Pal, Supriyo Paul, Mahendra K. Verma.Mechanical Engineering Department, Indian Institute of Technology-Kanpur, Kanpur, India

[email protected]

We present a detailed bifurcation structure and associated flow patterns for low-Prandtl number (P = 0.0002, 0.002, 0.005, 0.02) and zero-Prandtl number (P=0) Rayleigh-B´enard convection near its onset. We use both direct numerical simulations and reduced order models for this study. We observe that both low-Prandtl number (low-P) and zero-P convection exhibit similar patterns and chaos, namely stationary squares, asymmetric squares, oscillating asymmetric squares, relaxation oscillations, and chaos. At the onset of convection, low-P convective flows have stationary 2D rolls and associated stationary and oscillatory asymmetric squares. In contrast, for the case of zero-P convection chaos appears at the onset itself. The range of Rayleigh number for which stationary 2D rolls exist decreases rapidly with decreasing Prandtl number and vanishes in the limit of zero-P consistent with our observations. Our results are in qualitative agreement with results reported earlier. Key Words: Convective flow patterns, Low- and zero-Prandtl number convection, Bifurcation Diagrams, Chaos.


96

Drift waves’ synchronization by using an external signal. The stabilization of a chaotic plasma turbulence

C. L. Xaplanteris and E. FilippakiNCSR "Demokritos", Institute of Materials Science

Patriarchou Gregoriou & Neapoleos15310 Aghia Paraskevi, P.O Box 60228, Athens Greece

[email protected]

In a cylindrical cold rf plasma, a variety of drifts and other sort of waves are usually observed; when a turbulence is created the state becomes chaotic and, then the plasma turns out to be more unstable. In the present work, an external signal is enforced on the plasma’s waves (or turbulence), which strongly affects to the physical magnitudes of the plasma instabilities. The final result is that plasma stabilization occurs when plasma waves are synchronized with the external signal. Moreover, nonlinear phenomena occur, such as a vigorous coupling among the waves’ frequencies, which affects to the Hall conductivity. Another significant observation is the influence of boundaries on the interaction waves. Key Words: plasma instabilities, wave-wave interaction, synchronization, stabilization of a chaotic state.

The Interrelation Between Irreversibility and Evolution in the Dynamics of Electrical-Mechanical Systems in the Process of Friction and Cutting-Processing

Vilor L. ZakovorotnyDonskoy State Engineering University1, Gagarin sq. Rostov-on-Don, Russia

[email protected]

In the report it is proposed to analyze the mathematical description of the evolution system in the sort of non-linear differential equations, the parameters of which are presented as the integral operators of Volterra of the second type in the relation of the power trajectory of irreversible transformations fulfilled along the trajectory. Such system has the capacity of the evolution changeability, dynamic restructuration and characterizes the changes of its features including bifurcations in the process of the natural functioning. The algorithms of the calculations of the evolution trajectories are proposed as well as the methods of identification of the nucleus of the integral operators. The concrete examples are given.

Chaos game technique as a tool for the analysis of natural geomorphological features

G. Žibret1 & T. Verbovšek2

1Geological Survey of Slovenia, Ljubljana, Slovenia,Email: [email protected]

2Faculty of Natural Sciences and Engineering, University of Ljubljana, Slovenia,Email: [email protected]

The paper presents a novel method for evaluating the randomness of different natural processes. The method is based on the chaos game technique, and evaluation of the results is based on the measurements of the fractal dimension of the obtained Sierpinski triangles. A higher degree of randomness is expressed as higher fractal dimension of such triangle. Pathways of the natural rivers channels case study have been used for the demonstration of the methodology; however the method can be applied to many natural phenomena. Method is found to be useful and provides additional information about the geomorphological behaviour of analyzed rivers. Authors would like to encourage others to perform similar analysis on other natural phenomena, as more case studies are needed to draw more solid conclusions.Keywords: chaos game, Sierpinski triangle, fractal dimension, rivers


97

Author Index

Abbasi, Ali 59

Abd-el-Malek, Mina B. 1

Abdi, B. 79

Aidanpää, Jan-Olov 1

Aleixo, Sandra M. 73, 77

Amabili, M. 1

Andronov, Ivan L. 2, 14

Aniszewska, Dorota 2

Anwar Bé g, O 18, 28

Arora, Raina 3

Artemyev, A.V. 4

Atsalakis, George 4

Axenides, Minos 4

Aybar, O.O. 10, 47

Baba, Yuya 68

Bagautdinova, L.N. 5

Bak, Zygmunt 5

Bakanas, R. 31

Barbashin, M.U. 6

Barbot, Jean-Pierre 14

Basyrov, R.Sh. 6

Bauch, Szymon 54

Belghith, Safya 66

Ben Jemaa, Zouhair 66

Berezowski, Marek 7

Bhattacharjee, Jayanta K. 6

Biri, Venceslas 7

Bizon, Katarzyna 7

Bogomolov, A. 8

Bolotin, Yu.L. 8

Bondarenko, Volodymyr 9

Borgogno, D. 9

Borkowski, Wojciech 9

Breus, Vitalii V. 10

Busawon, Krishna 34

Cakar, O. 10

Caneco, Acilina 12

Carrassi, Alberto 12

Cejnar, Pavel 87

Chakraborty, Sagar 6

Chamniprasart, Kontorn 92

Chatziioannou, Aristotelis 51

Chavda, N. D. 13

Chepizhko, O.O. 45

Cherkaskiy, V.A. 8

Chernobrovkina, N.I. 13

Chernous, V.V. 14

Chinarova, Lidia L. 14

Chrousos, George P. 51

Cojocaru, Victor 90

Conde, Luis 15

Consolini, Giuseppe 61

Continillo, Gaetano 7

Daniels, S 53

Datcu, Octaviana 14

Del Rio, Ezequiel 15

Dhadke, Vijay 15

Dick, O.E. 16

Dimotikalis, Yiannis 17

Domanska, D. 17

Donoso, Jose M. 15

Dowling, D.P. 53

Dumitrescu, Iulia 31

Dumitriu, Lucia 31

Efimov, N. N. 18

Elaskar, Sergio 15

Farhadi, S. 1

Fenchenko, Vladmir N. 61

Filippaki, E. 96

Filippenko, V.I. 19

Firsova, G.S. 27

Floratos, Emmanouel 4

Fossion, Ruben 19, 52,87

Fraedrich, Klaus 56


98

Frank, Alejandro 19, 52,87

Frunzete, Mădălin 20

Fukushima, Kenta 21

Galustov, Gennady G. 21

Gaysin, Al.F. 22, 56, 66

Gaysin, Az. F 22, 56

Gaysin, F.M. 5, 22, 56, 66

Gelozhe, Y. A 22

Georgaki, Anastasia 22

Gerasimov, G.I. 23

Gerasimova, Evgeniya 23

Ghanadi, Farzin 88

Ghassemlooy, Z. 34

Gheisari, R. 24

Giroud, Anthony 7

Glazunov, N.M. 25

Grácio, Clara 12, 52

Grasso, D. 9

Grigoras, Carmen 25, 60

Grigoras, Victor 25, 58

Grishchenko, Sergey G. 26

Grytsay, Valerii I. 26

Guzhova, A.R. 27, 42

Hacinliyan, A. S. 10, 47

Hagan, Kerry L. 27

Halang, Wolfgang A. 27

Hassan, Hossam S. 1

Heidari, Alireza 18, 28

Hramov, Alexander E. 28, 29, 46,63

Hul, Oleh 54

Ignatyev, Mikhail B. 29

Iliopoulos, A.C. 72

Inglese, Gabriele 30

Ionescu, Adela 30

Iordache, Mihai 31

Iqbal, Sajid 31

Iqbal, Shahid 31

Ivanauskas, F. 31

Ivashkevich, G.I. 8

Jain, Chirag 58

Jasaitis,V. 31

Jevtic, N. 32

Jutas, Audrius 32

Kalashnikov, Vladimir L. 33

Karagiozis, K. 1

Karakatsanis, L.P. 72

Kariminia, Seyyed Mohammad Amin

67

Karitskaya, Svetlana 33

Karwinski, Marcin 34

Khan, Kashif Ali 31

Kharkov, Yaroslav A. 82

Khavroshkin, O.B. 34- 36

Khorshidi, K. 1

Khots, Boris 37

Khots, Dmitriy 37

Kim, Cha-kyum 37

Kisel, Nataliya N. 26

Klevchuk,Ivan 37

Kobayashi, Ryoya 38

Kobzev, Victor A. 40

Kolesnikov, Alexander A 38, 39

Kolesnikov, Anatoly A 39, 40

Kolesnikova, Tatiana A. 40

Komkhao, Maytiyanin 82

Korets, Anatoly 41

Korets, Anatoly 41

Koronovskii, Alexey A. 28, 29, 46,63

Kosem, Mustafa 41

Kostkin, Korniy 41

Kovalevska, Iryna 9

Kozlov, V.I. 27, 42

Krasnova, Svetlana A. 42

Kreerenko, Olga D. 43

Kretz, Johannes 43

Krishan, V. 69


99

Krot, Alexander M. 44

Krylov, Alexandr 41

Krylov, Alexandr 41

Kulinskii, V.L. 45

Kureychik,Victor M. 45

Kurkin, Semen A. 46

Kurovskaya, M.K. 29

Kusbeyzi, I. 10, 47

Kuzmenko, Andrew A. 48, 49, 59

Kuznetsov, A.P. 49

Kuznetsova, D. 49

Kyzyurov, Yurij 50

Lakeev, S.G. 90

Lambrou, George I. 51

Lan, Boon Leong 51

Landa, Emmanuel 19, 52, 87

Laureano, Fátima 52

Laureano, Rosário 52

Law, V J 53

Ławniczak, Michał 54

Lebo, A.I. 54

Lebo, I.G. 54

Leonov, Gennady A. 55

Lindkvist, Göran 1

Litak, G. 55

Loginov. N.A. 56

Lokshyn. B. 93

Lopez Vieyra, J.C. 52

Lubskiy, Anatoliy V. 56

Luca, Adrian 19

Lucarini, Valerio 56

Macek, Michal 87

Macek, Wieslaw M. 57

Maftei, Vlad 58

Magda, Igor I. 46

Maimone, Filippo 72

Marinov, M.B. 59

Markazi, Amirhossein Davaie 59

Martins Ferreira, Manuel A. 52

Maslov, V.P. 93

Matalliotakis, George 60

Materassi, Massimo 61

Mayorov, Oleg Yu. 61

Meesad, Phayung 82

Mendes, Diana A. 52

Meshkov, E.E. 62

Minasyan, Larisa A. 62

Mininni, Pablo 78

Mirabotalebi, Sedighe 80

Miranda, Eduardo 63

Mironov, Evgeny 41

Mironov, Evgeny 41

Mishra, Pankaj K. 95

Misurkin, P.I. 91

Mofidi, Alireza 67

Mohamadsalehi, F. 24

Mohammad Nouri, N. 67

Morales, I. 52

Moschovi, Maria 51

Moskalenko, Olga I. 29, 63

Mukhopadhyay, Banibrata 65

Munmuangsaen, Buncha 86

Musatenko, Iryna V. 65

Mushenko, Alexey S. 65

Mustafin, T.B. 66

Naanaa, Anis 66

Naimark, Oleg 23

Neishtadt, A.I. 4

Nemchina, Vera I. 66

Neri, Umberto 67

Nontapradit, Teera 86

Nowak, Andrzej 9

Nowicki, Tomasz 68

Nwankire, C.E. 53

Ohadi, Abdolreza 89

Onishi, Ryo 68

Orman, Gabriel V. 69

Oseloka Ezepue, P. 18, 28


100

Oshchepkov, A.S. 18

Ozerov, Vitaly V. 49, 59

Paillot, Jean-Marie 31

Pal, Pinaki 95

Pan, Jiaqing 69

Paniveni, U. 69

Pantelidis, Leonidas 70

Parekh, Nita 3

Pavlos, E.G. 72

Pavlos, G.P. 72

Pavluchenko, S. 8

Pegoraro, F. 9

Pelino, Vinicio 72

Pershin, Ivan M. 70

Pestana, Dinis D. 73, 77

Petritsch, R. 74

Phuong, Nguyen 40

Pietsch, S.A. 74

Pikulin, Dmitry 74

Pipin, V.V. 76

Pisarenko, Veronika I. 45

Polyakov, Yu.S. 90

Poonia, Anup 58

Popov, Andrey N. 71

Potbhare, V. 13

Pound, Eleri A. 71

Prants, S.V. 75

Prokopev, E.P. 75

Radu, Matei 60

Ragulskaya, M.V. 76

Rajaei, Leila 80

Rakesh , Mahla 58

Ramm, Alexander G. 77

Reddy, Sandeep 70

Rocha, J. Leonel 12, 73,77

Rodriguez Imazio, Paola 78

Rupak, Kharel 34

Rusinek, R. 55

Ryabov, Vladimir B. 21, 38, 78

Rybaczuk, Marek 2

Ryzhkov, А.В. 18

Salloum, Zaynab 79

Samadzadeh, H. 79

Sarkar, Amartya 6

Schep, T.J. 9

Schweitzer, J.S. 32

Selvam, A.M. 80

Semenov, A. V. 22

Sengor, Serap N. 41

Serquera, Jaime 63

Shokri, Babak 80

Shrimali, Manish 58

Shurygina, Svetlana A. 63

Shvets, A.Yu. 81

Sibgatullin, I. 49

Singhm, Jagdev 69

Sirenko, V.A. 81

Siriburanon, Teerachot 86

Sirko, Leszek 54

Skiadas, Christos H. 4, 81,82

Skiadas, Harilaos 82

Smith, Nathan 61

Sodsee, Sunantha 82

Sokolov, Valentin V. 82

Solovieva, A.B. 91

Son, E.E. 5,56

Sotiropoulos, Anastasios D. 83

Sotiropoulos, Dimitrios A. 84, 85

Sotiropoulos, Vaggelis D. 85

Srikanth, R. 69

Srisuchinwong, Banlue 86

Stankevich, N.V. 49

Stasiewicz, K. 86

Statsenko, V.P. 27

Stine, P. 32

Stransky, Pavel 52, 87

Strumik, M. 86

Supriyo, Paul 70


101

Szuba, Tadeusz (Ted) 87

Tae Lee, Jong 37

Taghavi Zenouz, Reza 88

Takahashi, Keiko 68

Talagaev, Yuri V. 88

Tarakanov, Andrey F. 88

Tardu, Sedat 89

Tayefi, Siavash 89

Teodorescu, Horia-Nicolai 90

Thidè, B. 86

Timashev, S.F. 90, 91

Timofeeva, V.A. 91

Timoshenko, Dmitry V. 91

Tkachova, Polina P. 92

Toporensky, A. 8

Tsolakis, Cristos 22

Tsoutsouras, V.G. 72

Tsyplakov, V.V. 34, 35, 36

U’Ren, Alfred 19

Uangpairoj, Pichitra 92

Urminsky, David 93

Utkin, Anton V. 42

Utkin, Victor A. 42

Vannitsem, Stephane 12

Vardoulaki, Maria 60

Vaskov, Maksim A. 92

Velazquez, Victor 19, 52

Venger, E. F. 93

Venturi, Beatrice 67

Verbovšek, T. 96

Vereshchagina, Anna 93

Verma, Mahendra K. 70, 95

Veselov, Gennady E. 94

Virnina, Natalia A. 94

Vlad, Adriana 14, 20

Vlahopoulos, Spiros 51

Volkov, Yuri G. 95

Vyklyuk, Yaroslav 27, 95

Wahi, Pankaj 70, 95

Wojtylak, M. 17

Xaplanteris, C. L. 96

Yanilkin, Yu.V. 42

Zakovorotny, Vilor L 96

Zelenyi, L.M. 4

Zhirov, Oleg V. 82

Zhong, Li 82

Žibret, G. 96


102

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