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Programme & Abstract Book

DEPARTMENT OF MATHEMATICS

INDIAN INSTITUTE OF TECHNOLOGY MADRAS

CHENNAI-600 036

International Conference on

Mathematical Modeling and Computer Simulation

(ICMMCS)

December 8-10, 2014

in association with

Sponsored byby

Supported by

ICMMCS Program Schedule

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8th December 2014 (Day 1 – Monday)Venue: ICSR Hall 2

0850 – 0900 hrs Welcome

0900 – 0940 hrs Invited Talk 1 Prof. Dr. Oleg IlievFlow and Material Simulation DepartmentFraunhoferInstitute of Industrial MathematicsKaiserslautern, Germany“Water Treatment:Pore Scale Simulation ofFiltration and Separation Processes inMembranes (Osmosis, Ultra/NanoFiltration)”

0940 – 1020 hrs Invited Talk 2 Prof. KarmeshuSchool of Computer and Systems ScienceJawaharlal Nehru University, New Delhi“Stochastic Modeling of Spiking NeuronalActivity: Bimodality and Power-law BehaviorIn ISI Distribution”

1020 – 1040 hrs TEA BREAK

1040 – 1120 hrs Invited Talk 3 Dr. Ashok GopinathAerodynamics LabGE Global Research, Bangalore“Development and Validation of IntegratedDesign Framework for Compressor SystemModel”

1120 – 1200 hrs Invited Talk 4 Prof. Mohan K. KadalbajooDepartment of Mathematics and StatisticsIIT Kanpur“A Second Order Accurate IMEX Method fora Class of Parabolic PIDEs”

1200 – 1300 hrsPAPER

PRESENTATIONSHall 1: MM1 – MM4 on Mathematical Modeling AspectsHall 2: CS1 – CS4 on Computational and Simulation Aspects

1300 – 1400 hrs LUNCH BREAK


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Venue: ICSR Auditorium

1400 – 1440 hrs Invited Talk 5 Prof. B.V. Rathish KumarDepartment of Mathematics and StatisticsIIT Kanpur“On HPC of Convection in PorousEnclosures with Multiple Sources”

1440 – 1520 hrs Invited Talk 6 Prof. Neela NatarajDepartment of MathematicsIIT Bombay“Finite Element Method for the von KẚrmẚnEquations”


1540 – 1620 hrs Invited Talk 7 Dr. Sanjay SondhiMaterials Simulation LabGE Global Research, Bangalore“Materials Modeling: An IndustrialPerspective”


PRESENTATIONSHall 1: MM5 – MM8 on Mathematical Modeling AspectsAuditorium :CS5 – CS8 on Computational and Simulation Aspects

1720 – 1800 hrs Invited Talk 8 Dr. Sashikumaar GanesanSuper Computing Education and Research Centre

Indian Institute of Science, Bangalore“Finite Element Variational MultiscaleMethod for Simulation of Turbulent Flows”

1800 – 1840 hrs Invited Talk 9 Dr. C. V. KrishnamurthyDepartment of PhysicsIIT Madras“Microstructural Modeling of Materials”


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9th December 2014 (Day 2 –Tuesday)Venue: ICSR Hall 2

0900 – 0940 hrs Invited Talk 10 Prof. Dr. Joerg KuhnertTransport Processes DepartmentFraunhofer Institute of Industrial MathematicsKaiserslautern, Germany“Mesh free Numerical Scheme for TimeDependent Industrial Problems in Fluid andContinuum Mechanics”

0940 – 1020 hrs Invited Talk 11 Dr. David A. BlankCEO, HCRI Technologies InternationalUSA.“Role of Simulation in the Genesis of aRadical Chemistry Engine”


1040 – 1120 hrs Invited Talk 12 Prof.Dr.Thomas GoetzMathematik InstituetUniversitaet Koblenz, Germany“Optimization in Epidemiology, Biomechanicsand Medicine”

1120 – 1200 hrs Invited Talk 13 Prof. Raju K. GeorgeDepartment of MathematicsIndian Institute of Space TechnologyTrivandrum“Trajectory Controllability of Systems”


PRESENTATIONSHall 1: MM9 – MM12 Mathematical Modeling AspectsHall 2: CS9 – CS12 Computational and Simulation Aspects



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Venue: ICSR Hall 2

1400 – 1440 hrs Invited Talk 14 Dr.P.ShanmugamSundaram Fasteners Limited, Chennai“Forging Processes for Fasteners – AnOpportunity for Simulation”

1440 – 1520 hrs Invited Talk 15 Prof. S. V. Raghurama RaoDepartment of Aerospace EngineeringIndian Institute of Science, Bangalore“Lattice Boltzmann Relaxation Scheme forInviscid Compressible Flows”


1540 – 1620 hrs Invited Talk 16 Dr. Jitendra KumarDepartment of MathematicsIIT Kharagpur“Analysis, Modeling and Simulation ofParticulate Systems”


PRESENTATIONSHall 1: MM13 – MM16 Mathematical Modeling AspectsHall 2: CS13 – CS16 Computational and Simulation Aspects

1720 – 1800 hrs Invited Talk 17 Prof. Renuka Ravindran(formerly with) Department of MathematicsIndian Institute of Science, Bangalore“50 Years of Association with AppliedMathematics”

1800 – 1840 hrs Invited Talk 18 Dr. Satyananda PandaDepartment of MathematicsNIT Calicut“Process Parameter Identification in ThinFilm Flows”

1840 – 1920 hrs Invited Talk 19 Dr. Samir RoyRPM College, University of CalcuttaKolkata“Application of Asymptotic Analysis toInvestigate Heat Flow through Highly PorousInsulators”


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10th December 2014 (Day 3 – Wednesday)Venue: ICSR Hall 2

0900 – 0940 hrs Invited Talk 20 Prof. M. T. NairDepartment of MathematicsIIT Madras“An FEM-Based Discrete Regularization for aParameter Identification Problem in PDE”

0940 – 1020 hrs Invited Talk 21 Prof. J. B. Shukla(formerly with) Department of Mathematics andStatistics IIT Kanpur“Modeling of Climate Change: its impacts andresponses”


1040 – 1120 hrs Invited Talk 22 Prof. Kailash C. PatidarDepartment of MathematicsUniversity of the Western Cape, South Africa“Limitations of Spectral Methods for SolvingOption Pricing Problems”

1120 – 1200 hrs Invited Talk 23 Prof. J. C. MandalDepartment of Aerospace EngineeringIIT Bombay“Uncertainty in High Speed Compressible FlowComputations”

1200 – 1240 hrs Invited Talk 24 Dr. K. SelvanayagamLMS India Engineering Solutions,Chennai“Bond Graph Theory in Simulation Software”



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Venue: ICSR Hall 2

1400 – 1440 hrs Invited Talk 25 Prof. A. ArockiarajanDepartment of Applied MechanicsIIT Madras“Numerical Modeling on Time-DependentBehaviour of 1-3 Piezocomposites”

1440 – 1520 hrs Invited Talk 26 Prof. A. K. NandakumaranDepartment of MathematicsIndian Institute of Science, Bangalore“Unfolding Method in Homogenization”


1540 – 1620 hrs Invited Talk 27 Prof. V. SubramanianDepartment of PhysicsIIT Madras“Numerical Simulation of electromagnetic wavepropagation through bounded medium -Limitations and Challenges”

1620 – 1700 hrs Invited Talk 28 Dr.Vikash Kumar SharmaGENPACT, Bangalore“Obligor Idiosyncracy Sensitive Based PricingMechanism with Profit OptimizationInclusiveness”

1700 hrs Summary and Closing


PAPER PRESENTATIONS on Mathematical Modeling Aspects

Session 1: MM – 1 to MM – 48.12.2014

1200 – 1215 – 1230 – 1245 – 1300 hrs

1. Deepak Patil, Department of Mechanical Engineering, NIT Calicut“Thermal stress modeling of micro-electro discharge machining on titanium alloy”(with Basil Kuriachen and Jose Mathew)

2. S.Susmetha Kumari, Department of Chemical Engineering, IIT Madras“PID control of humidity system under model uncertainty” (with M. Chidambaram)

3. Saroj Kumar Sahani, Department of Mathematics, South Asian University, New Delhi“A delayed model for HIV infection incorporating intracellular delay”

4. E.S.V. Narayana Rao, Department of Statistics, Pondicherry University, Puducherry“Stochastic programming for optimal parametric estimation of infectious diseases”(with P.Tirupathi Rao)

Session 2: MM – 5 to MM – 88.12.2014

1620 – 1635 – 1650 – 1705 – 1720 hrs

5. Bikash Sahoo, Department of Mathematics, NIT Rourkela“Effects of suction and injection on swirling flow near a rough disk” (with SebastienPoncet and Fotini Labropulu)

6. C.Sankar Rao, Department of Chemical Engineering, IIT Madras“Experimental application of subspace model identification of an unstable system”(with M.Chidambaram)

7. Joseph Mathew, Computer Centre, North Eastern Hill University, Shillong“Long wavelength soliton solutions of KdV equation” (with Sanjib Malla Bujar Baruahand Tapas Kumar Sinha)

8. Poonam Redhu, Department of Mathematics, IIT Ropar“A new multi-phase lattice hydrodynamic model considering the effect of driver’santicipation” (with Arvind Kumar Gupta)


Session 3: MM – 9to MM – 129.12.2014

1200 – 1215 – 1230 – 1245 – 1300 hrs

9. Chandra Shekar Besta, Department of Chemical Engineering, IIT Madras“Modelling of multivariable systems for control” (with M.Chidambaram)

10. Subhas Khajanchi, Department of Mathematics, IIT Roorkee“Bifurcation analysis of a delayed mathematical model for tumor growth”

11. K. Krishnakumar, Department of Mathematics, Pondicherry University, Puducherry“A simple approach to find first integrals of certain nonlinear ordinary differentialequations” (with A.Annamalai and KM.Tamizhmani)

12. G.Nath, Department of Mathematics, Motilal Nehru National Institute of Technology,Allahabad“Non-similarity solution for shock waves in rotational axisymmetric perfect gas withmagnetic field and density varying exponentially” (with A.K.Sinha)

Session 4: MM – 13 to MM – 169.12.2014

1620 – 1635 – 1650 – 1705 – 1720 hrs

13. Anindita Bhattacharjee, Department of Management Studies, Galgotia Institute ofManagement & Technology, Greater Noida, UP“Impact of connection topology on cooperative dynamics of FHN neurons withrandomly varying threshold” (with M.K.Das)

14. Nidhi Chaudhary, Department of Mathematics, BITS Pilani, Pilani Campus, Rajasthan“Dynamics of formation offoam cells from LDL cholesterol and the inhibitory effects oftherapeutic agents like statins” (with Padma Murali and Rajiv Kumar)

15. Ram Naresh, Department of Mathematics, H.B. Technological Institute, Kanpur“Modeling the effect of treatment on the spread of HIV/AIDS”

16. M.V.Jayanthi, Research Scholar, Department of Mathematics, B.S.Abdur RahmanUniversity, Chennai“An EOQ model with deteriorating items under inflation and time varying holdingcost” (with P.S.Sheik Uduman)


PAPER PRESENTATIONS on Computational and Simulation Aspects

Session 1: CS – 1 to CS – 48.12.2014

1200 – 1215 – 1230 – 1245 – 1300 hrs

1. Alpesh Kumar, Department of Mathematics, IIT Kanpur“A radial basis function based implicit explicit method for jump-diffusion modelarising in finance” (with Mohan.K.Kadalbajoo and LokPati Tripathi)

2. K.Venkateshwarlu, Department of Mathematics, IIT Roorkee“Numerical investigation of mixed convection in a ventilated enclosure withdifferentially heated side walls” (with V.K.Katiyar and A.K.Nayak)

3. Sudharkar Matle, School of Advanced Sciences, VIT University, Vellore“Anisotropy due to orientation study for a poly-crystalline copper using finite elementmethod”

4. N.H.Maruthi, Department of Aerospace Engineering, IISc Bangalore“An entropy stable central solver for Euler Equations” (with S.V.Raghurama Rao)

Session 2: CS – 5 to CS – 88.12.2014

1620 – 1635 – 1650 – 1705 – 1720 hrs

5. B. Mayur Prakash, Department of Mechanical Engineering, NIT Calicut“A numerical implementation of higher order time integration algorithm on unsteadyBurgers’ equation” (with Ashish Awasthi and S.Jayaraj)

6. Navnit Jha, Department of Mathematics, South Asian University, New Delhi“An arithmetic average geometric mesh discretization for semilinear elliptic equationsand estimate of first and second order partial derivatives”

7. Naveen Kumar Garg, IMI,Department of Mathematics, IISc Bangalore“Weak-Strong hyperbolic splitting for simulating conservation laws”(with M.Sekhar and S.V.Raghurama Rao)

8. Shuvam Sen, Department of Mathematics, Tezpur University“HOC schemes for 2D parabolic problems with mixed derivatives”


Session 3: CS – 9 to CS – 129.12.2014

1200– 1215 – 1230 – 1245 – 1300 hrs

9. Sundararajan Natarajan, Department of Mechanical Engineering, IIT Madras“Semi-analytical approach to treat singularities within the extended finite elementmethod” (with E.T.Ooi and C.Song)

10. Jugal Mohapatra, Department of Mathematics, NIT Rourkela“Uniform numerical method for a class of parameterized singularly perturbedproblems”

11. .Ameeya Kumar Nayak, Department of Mathematics, IIT Roorkee“Numerical study of mixed convection cooling of heat source mounted in lid-drivencavity filled with nanofluid” (with Sumit Malik)

12. Swapan K. Pandit, Integrated Science Education and Research Centre (ISERC), Visva-Bharati, Santiniketan, West Bengal“An efficient Navier-Stokes solver using stream function-velocity formulation oncompact nonuniform space grids”

Session 4: CS – 13 to CS – 169.12.2014

1620 – 1635 – 1650 – 1705 – 1720 hrs

13. Ameya D. Jagtap, Department of Aerospace Engineering, IISc Bangalore“Maxwellian distribution based finite element method for hyperbolic PDEs”(with S.V.Raghurama Rao)

14. Ankit Ruhi, IMI,Department of Mathematics, IISc Bangalore“A computational approach to Kinetic Theory based turbulence model”(with Mohammed Lemou, Nicolas Crouseilles and S.V.Raghurama Rao)

15. Chithra Ayappan, B.S.Abdur Rahman University, Chennai“MATLAB Simulink – mathematical modeling of chaotic oscillator system for securecommunication” (with I. Raja Mohamed)

16. S.Sheela, Department of Mathematics, Gojan School of Business and Technology“A method for solving balanced and unbalanced trapezoidal intuitionistic fuzzyassignment problem” (with M.Joseph Robinson and A. Sudha Rani)

ICMMCS Abstracts of Invited Talks

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Invited Talk 1 Pore Scale Simulation of Filtration Processes in Membranes (Osmosis,Ultra/Nano Filtration)Prof. Dr. Oleg IlievFraunhofer Institute for Industrial Mathematics (ITWM)[email protected]

Clean water is fundamental for human life and health. The increasing worldpopulation is fueling increased requirements for safe water [1]. Research intomethods for purifying water is therefore imperative. The use of functionalizedmembrane for the capturing of specific contaminants for the purification of water isone method that has great promise [2]. Given the expense and difficulty of designingefficient membranes, mathematical modeling and numerical simulation has anessential role to play in aiding the design process of efficient membranes andinforming membrane producers of optimal operational conditions.The water desalination is another promising technology, able to improve the accessto fresh water to many people. Being still a very expensive and energy consumingtechnology, it provides great challenges to the researchers for developingmembranes and regimes reducing the energy consumption and increasing theproductivity.Due to the large disparity of spatial scales involved in a typical nan filtration setup,with contaminants of the spatial several Angstrom in size, a typical pore size on thespatial scale of microns, and the total module size on the scale of cm, we employ aMultiscale model. Such a model allows us to capture the effects at the micro scalewhile simulating the efficiency of the membrane under consideration at the modulescale. Once the model has been validated, it may be used to optimize experimentalprotocols, such as the flow rate, surface concentration and positioning of thefunctional groups, and inflow concentration of contaminants. Furthermore, theinformation gained from the numerical simulation effort can aid membraneproducers in their generation of membranes, allowing efficient membranes suitablefor the specific purpose of interest to be designed.In this presentation, first we will discuss general issues in pore scale modeling andsimulation of filtration and osmosis processes, and after that will shortly discuss thefiltration of separate drugs: Vancomycin, Metoprolol and Diclofenac, and theiradsorption to a polyvinylidene fluoride (PVDF) membrane with Carboxylicfunctional groups [3].References:[1] P Hunter et al, PLoS Medicine, 7(11):e1000361, (2010)[2] J Theron et al, Critical Review in Microbiology, 34, p.43, (2008)[3] V. Dick et al, JCIS, 434, p.70, (2014)


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Invited Talk 2 Stochastic Modeling of Spiking Neuronal Activity: Bimodality and Power-lawBehavior In ISI DistributionProf.KarmeshuSchool of Computer and Systems ScienceJawaharlal Nehru UniversityNew [email protected]

The purpose of modeling of the neuronal dynamics is to capture the mechanisms which cangenerate empirically observed inter spike interval (ISI) patterns. The time interval betweenspikes gives ISI distribution which requires solution of the first passage time problem whenthe underlying stochastic dynamics of the membrane potential reaches the threshold valuefor the first time. An important aspect is to elucidate the statistical distribution of the spikingpattern and the information transfer from the sensory input to the output response. Thewidely used neuronal models are referred to as Integrate-Fire (IF) model and LeakyIntegrate-Fire (LIF) model. These models are known to exhibit unimodal ISI distribution.A challenging problem is to develop a model which is capable of generating both unimodaland bimodal distributions. An important issue is to identify the mechanisms which mayexplain the empirically observed rich behaviour of spiking pattern of a single neuron. Aneuronal model with distributed delay has been proposed by Karmeshu, Varun, Kadambari[1] with gamma distributed memory kernel. Two types of memory kernels viz. weak delayand strong delay have been considered. The weak delay yields unimodal ISI distributionwhile strong delay leads to emergence of bimodal behaviour when mean time delay reachesa critical value. Further, an interesting feature in the context of neuronal spiking pattern isfound to display long-range dependence exhibiting power law behaviour. A theoreticalframework based on super statistics is employed to provide a rationale for emergence ofpower law when an ensemble of neurons group together and fire together. Investigating thisframework in relation to IF and LIF models, it is found that in the presence of randomlyfluctuating rates of the underlying models, ISI distribution of the ensemble of neuronsasymptotically yields power law. These findings are in agreement with the empirical studywhere Suprachiasmatic nucleus (SCN) neurons display power law behaviour. The lecture isbased on our following published research articles:

1. Karmeshu, Varun Gupta, K. V. Kadambari, Neuronal model with distributed delay:Analysis and simulation study for gamma distribution memory kernel, BiologicalCybernetics, vol. 104, 2011.

2. Sharma S. K., Karmeshu, Power law behaviour in IF model with random excitatoryand inhibitory rates, IEEE transactions on Nanobioscience, vol. 10, 2011.

3. Sharma S. K., Karmeshu, Neuronal model with distributed delay: Emergence ofunimodal and bimodal ISI distributions, IEEE transactions on Nanobioscience, vol.12, 2013.

4. Karmeshu and Sharma S. K., Ensemble of LIF neurons with random membranedecay constant: Emergence of Power-law behaviour on ISI distribution, IEEEtransactions on Nanobioscience, vol. 13, 2014.


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Invited Talk 3 Development and Validation of Integrated Design Framework forCompressor System ModelDr.Ashok GopinathAerodynamics LabGE Global Research ,[email protected]

The performance of a refrigerator is largely guided by the efficiency of its drive unit,namely, the compressor and understanding the compressor behavior requires adetailed study of its dynamics, flow-thermals, electrical and controls aspects.Having a simulation model which captures these physics reasonably well is a criticalpart of the design and performance prediction of a compressor. The current paperdescribes a systematic approach of making a system level simulation framework byfirst developing individual models and then integrating them into a single frameworkto capture the multi-physics interaction of the different sub-components. Thisframework, developed in MATLAB/SIMULINK contains five modules, namely,Dynamics, Thermal, Motor, Controls and Post-processor. Piston Dynamics ismodeled as a spring-mass system with adjustable static equilibrium and head-crashprevention algorithm. The thermodynamics model essentially captures the valvephysics. The valves in a reciprocating compressor contribute to pressure losses(pressure profile deviation from ideal suction and discharge processes, valvedynamics, leakages, pressure pulsations) and thermal losses (refrigerant back-flowcaused by incorrect valve timing). The starting point of simulating these details isconsidering the gas dynamics and coupling it to the valve motion. The prediction ofthis model is validated against test data of a baseline compressor. As part of theintegrated design framework, a permanent magnet linear motor is simulated as aresistance-inductance network with a series, velocity dependent voltage. To controlthe desired operating conditions (capacity, stroke, clearance etc.) upon the integratedsystem model, a set of controllers were designed to control the motor.

Invited Talk 4 A Second Order Accurate IMEX Method for a Class of Parabolic PIDEsProf. Mohan K. KadalbajooDepartment of Mathematics and StatisticsIIT [email protected]

We develop time semi-discrete second order implicit-explicit (IMEX-BDF1 &IMEX-BDF2) methods for solving parabolic partial integro-differential equations(PIDEs) governing option pricing when the underlying asset follows a jumpdiffusion process. The resulting semi discrete problem is solved by cubic B-splinecollocation method. Some theoretical results including Stability estimates andconvergence analysis of the proposed methods are discussed. Numerical results withrespect to Merton and Kou jump diffusion models are presented to corroborate thetheory.


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Invited Talk 5 On HPC of Convection in Porous Enclosures with Multiple SourcesProf.B.V.Rathish KumarDepartment of Mathematics and StatisticsIIT [email protected]

In this study, a parallel finite element scheme for the three-dimensional analysis offree and mixed convection in fluid saturated isotropic porous enclosures has beenproposed based on a flow modelling vector potential and temperature as fieldvariables. In view of the large size of the linear systems resulting from the 3D finiteelement analysis, the scheme is evolved in a de-coupled framework. Further tohandle the resulting large scale systems, suitable data structures have been designedand global stiffness matrices are assembled in sparse matrix format. Following thenotion of Domain Decomposition the 3-D FEM code has been parallelized under themaster-slave paradigm for implementation on Linux-Cluster. Computations arecarried out to analyse the free and mixed convection process in few of the fluidsaturated porous enclosures with multiples sources.

Invited Talk 6 Finite Element Method for the von Kẚrmẚn EquationsProf. Neela NatarajDepartment of Mathematics,IIT [email protected]

In this talk, we consider the von Kẚrmẚn equations which describe bending of thinelastic plates governed by a coupled non-linear fourth order partial differentialequations. The well-known non-conforming Morley element has been used to obtainapproximate solution. Optimal order error estimates in energy norm and H1norm arederived and numerical results that justify the theoretical results are presented.Results obtained using the Bogner Fox Schmidt conforming finite element methodsare also discussed. This is a joint work with Gouranga Mallik.


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Invited Talk 7 Materials Modeling: An Industrial PerspectiveDr.Sanjay SondhiMaterials Simulation LabGE Global [email protected]

Realizing full potential of ICME for industrial applications requires not only robustmaterials modeling capabilities, but also multiple additional enablers. A startingpoint is to link materials models and relevant statistical methods into a Tool that can(a) examine the effect of material and processing variability, and (b) carry outsensitivity analysis to identify the most critical material/process parameters. Anotherkey step is to develop the requisite hardware/software infrastructure that allows adiverse set of end users to access a combination of in-house and commerciallyavailable Tools/Software/Data. This talk will share our experiences of implementingthe same at GE.

Examples will be provided of materials modeling efforts that span multiple length-scales, and leverage a wide range of modeling approaches. In some cases, the modelsare stitched-together, and share information in a seamless fashion; while in othersthe information is passed discretely. The eventual emphasis is on predicting themicrostructure and resulting properties of engineering alloys, based on alloychemistry and processing conditions.

Invited Talk 8 Variational Multiscale Method for Simulation of Turbulent FlowsDr. Sashikumaar GanesanNumerical Mathematics and Scientific ComputingSERC, Indian Institute of [email protected]

Simulations of turbulent fluid flows are highly demanded in many applications forvery many reasons. Turbulent flows are highly unsteady flows, which containseveral flow scales.Despite several advances made in computational fluid dynamics(CFD), accurate modeling of turbulent flows is still very challenging. Thenumerical simulation of turbulent flows are performed using either the directnumerical simulation (DNS) or turbulent models such as Reynolds-averagedNavier-Stokes equations (RANS) or Large Eddy Simulations (LES). The Navier-Stokes equations are solved by resolving all flow scales in DNS. The scales inturbulent flows varies in size and a very fine mesh is needed to resolve small flowscales, which makes DNS computationally unfeasible for most of the practicalapplications. LES is one of the popular approaches for turbulence modeling. In


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LES, the large flow scales are resolved by the computational mesh and the effect ofthe small flow scales are incorporated into the large scale using turbulent models.A filter function has to be used for scale separation, and it induces commutationerror in LES. Moreover an appropriate choice of filter function is very challenging.Variational Multiscale method (VMS) is relatively a new approach, which separatethe flow scales into two or three different scales, for e.g., resolved large scale,resolved small scale and unresolved small scale. The flow scale separation enablesto treat different flows scales with tailor-made numerical schemes. Two importantaspects that characterize the VMS method are: (i) Variational projection is usedto separate flow scales that avoids the use of filter function as in traditional LESthereby doing away with the commutation errors involved, and (ii) theinfluence/effect of the unresolved scale is incorporated into the resolved smallscales which is coupled with the large scales, thus the unresolved small scales’effect is indirectly induced on the large scales. In this talk, the finite elementVMS method for time-dependent incompressible Navier-Stokes equations forhigh Reynolds number will be presented. After a brief discussion on the DNSand the LES, the development of a two-scale and three-scale VMS schemes will bediscussed in detail. Further a projection based numerical scheme in the context ofVMS will be presented. Numerical experiments of turbulent flows with obstacleswill be presented.

Invited Talk 9 Microstructural modelling of materialsDr. C.V. KrishnamurthyDepartment of PhysicsIIT Madrascvkm @ iitm.ac.in

The response of polycrystalline materials and multi-phase materials to externalstimuli is determined by the material characteristics at several length scales. Modelshave been evolving from coarse length scales down to atomistic length scales fuelledby the desire to engineer structures on the one hand and by the desire to understandand predict complex structures through increasingly powerful computationalresources on the other. We present an overview of the various 2D and3D numericalmodels developed to define the microstructure and understand the manner by whichthe various physical properties are deduced. Models dealing with voronoi cells thatdescribe the elastic and plastic behaviour of polycrystalline materials such as metalswould be discussed. Schemes to homogenize and generate averaged physicalproperties would be described. Models that describe multiphase materials will bepresented and the efforts to reconstruct the structure using experimental data will bediscussed. Directions in which modelling efforts are moving and the challenges thatexist would be indicated.


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Invited Talk 10 Mesh free Numerical Scheme for Time Dependent Industrial Problems inFluid and Continuum MechanicsProf. Dr. Joerg KuhnertTransport Processes DepartmentFraunhofer Institute of Industrial MathematicsKaiserslautern ,[email protected]

The Finite Point set Method (FPM) is a mesh free approach to numerically solvepartial differential equations (PDE).The method uses a cloud of numerical points,each of which carrying necessary numerical data. In order to solve a PDE, FPMneeds to establish approximations of derivatives, which are provided by aspecialized least squares algorithm. The least squares idea turns the whole methodinto a generalized finite difference procedure. Even though the main field ofapplication of FPM has been computational fluid dynamics (CFD), FPM is alsoextended to solve plastic and visco-plastic material behavior or heat transfer.In this presentation, industrial applications of FPM will be demonstrated. Thisincludes classical fluid mechanics such as industrial filling, sloshing, water drain,and water crossing applications. However, also non-Newtonian industrial cases willbe presented, including the dynamics of sand, the chip formation in metal cuttingprocesses, or freezing of water in injection units.

Invited Talk 11 Role of Simulation in the Genesis of a Radical Chemistry EngineDr. David A. BlankHCRI Technologies [email protected]


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In the field of internal combustion engines (ICEs) the role of computer simulationhas been focused primarily on the improving of, on the testing of and on the gainingof better understandings of: previously existing technologies. However, as in otherselect fields, simulation has potential for also generating novel technologies for usein the field of ICEs. This presentation is concerned with one example of such, nowreferred to as the HCRI (Homogeneous Combustion Radical Ignition) engine. Thediscovery and initial application confirmations of the HCRI technology were all bysimulation. An extensive series of computer simulations were conducted longbefore the first major physical test of the HCRI technology at the Argonne NationalLaboratory (NL) using an SI (spark ignition) variant of the technology. Thesesimulations addressed three major engine types and were conducted with a varietyof fuels. A comparison and analysis of these studies revealed a novel generalchemistry that is universal to most hydrocarbon fuels. The results of seven of thesestudies were published and presented two years prior to both the Argonne tests andto the first physical test of a compression ignited prototype. While using only thesecond design iteration of a simplified version of the technology with CNG, theproof of concept test at Argonne NL generated break-through results. Simulationhas since also played a major role in most all of the evolution steps of thistechnology. Thus, with a view to motivating development of tailored numericalsolutions for relevant real world applications, this presentation discusses the overallsimulation strategy and several of the many novel numerical techniques developedand employed in the evolution of the HCRI engine and its new chemistry.

Invited Talk 12 Optimization in Epidemiology, Biomechanics and MedicineProf. Dr.Thomas GoetzMathematik InstituetUniversitaet Koblenz,Germanygoetz @uni-koblenz.de

Mathematical simulations are of increasing relevance for applications in engineeringand the life sciences. Disciplines like epidemiology, biomechanics, medical imageprocessing, just to name a few, are subject of academic research since decades. Withmodern numerical methods and the ever increasing computing power not justsimulations of biological systems are within reach, but also questions of optimizingthe systems to aim at a certain goal can be addressed. In this talk, we will discusssome fist examples from classical disease dynamics as well as biomechanicalmodels for muscles and the human skeleton with application in surgery planning.All these examples have in common, that the models are based on a set of differentialequations. Defining a suitable cost functional to measure the distance to the goal ofour optimization, mathematical tools from constrained optimization can be appliedto solve optimization problems and to derive suitable numerical algorithms.


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Invited Talk 13 Trajectory Controllability of SystemsProf. Raju K. GeorgeDepartment of MathematicsIndian Institute of Space [email protected]

In this talk we consider control systems of the form

where, are an matrices and

function. For each is the state; u(t) 2 IR nis the control. The above system is said to be Trajectory controllable if there existsa control function u(t), sufficiently smooth, such that the states of the system can besteered along a given trajectory. We provide conditions to ensure trajectorycontrollability of the system. Further, we compute the steering controller which doesthese teeing. We then extend this idea to infinite-dimensional systems. In particularwe consider thepartial differential equation:

where u is the distributed control and f is a nonlinear function. Results are obtainedby imposing Lipschitz continuity assumptions on f. We illustrate the results withnumerical examples.References:

(1) E.D. Sontag: Mathematical Control Theory: Deterministic Finite dimensionalsystems, Springer1998.

(2) R.F.Curtain, A.J. Prichard: Infinite Dimensional Systems, 1978.

(3) D.N. Chalishajar, R.K. Georgeetal: Trajectory Controllability of nonlinearintegro-differential systems, Journal of the Franklin Institute, 347, 1065-1075.(2010)


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Invited Talk 14 Forging Processes For Fasteners – An Opportunity For SimulationDr. P. ShanmugamSundaram Fastners [email protected]

In present scenario, metal forming industries employ a range of technologies inmanufacturing fasteners. We, TVS Sundaram Fastners Limited based in many partsof South India and catering to various esteemed National and InternationalCustomers. Our products range includes M6 to M48 sized Bolts, Nuts, Socket headfasteners, Studs, Washers which applies to different sectors such as Automotive,Marine, Construction, Aerospace, Wind Energy and Space applications. ProgressiveHeaders and Hot Nut Formers are being used in the manufacture of Bolts and Nutsrespectively.In a cold forging industry, it is well known that deformation mechanism of billet andforming tools plays a vital role in designing the dies and to estimate the tool life.Simulation plays an important role in developing process flow for manufacturing.For geometrically complex shapes, 3D Process simulation is being used forunderstanding the metal flow, material behaviour which helps us in robust design ofprocess and products.

Invited Talk 15 Lattice Boltzmann Relaxation Scheme for Inviscid Compressible FlowsProf. S. V. Raghurama RaoDepartment of Aerospace EngineeringIndian Institute of [email protected]

Lattice Boltzmann Method (LBM) has been quite successful for incompressibleflows. The traditional LBM, due to an inherent low Mach number expansion, islimited for incompressible flows. In this research work, a new Lattice BoltzmannMethod is introduced for simulating compressible flows, by using the concept ofa relaxation system, which is traditionally used as a semi-linear alternative fornon-linear hyperbolic systems in CFD. In the relaxation system originallyintroduced by Jin and Xin (1995), the non-linear flux in a hyperbolic conservationlaw is replaced by a new variable, together with a relaxation equation for this newvariable augmented by a relaxation term in which it relaxes to the originalnonlinear flux, in the limit of a vanishing relaxation parameter. The advantage isthat instead of one non-linear hyperbolic equation, two linear hyperbolicequations need to be solved, together with a non-linear relaxation term. Basedon the interpretation of Natalini (1998) of a relaxation system as a discretevelocity Boltzmann equation, with a new isotropic relaxation system as the basicbuilding block, a Lattice Boltzmann Method is introduced for solving the


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equations of inviscid compressible flows. Since the associated equilibriumdistribution functions of the relaxation system are not based on a low Machnumber expansion, this method is not restricted to the incompressible limit. Freeslip boundary condition is introduced with this new relaxation system basedLattice Boltzmann method framework. This new Lattice Boltzmann RelaxationScheme is successfully tested on various bench-mark test cases for solving theEuler equations of gas dynamics, demonstrating its efficiency is capturing flowfeatures like shock waves and expansion fans, typical of inviscid compressibleflows.

Invited Talk 16 Analysis, Modeling and Simulation of Particulate SystemsDr. Jitendra KumarDepartment of MathematicsIIT Kharagpurjkumar @ maths.iitkgp.ernet.in

The process by which particles undergo changes in its physical properties iscalled the particulate process. The dynamics of the particulate process arecaptured by an integro-partial differential equation known as the populationbalance equation (PBE). The various process conditions are modelled in the formof the aggregation and breakage kernels of the equations. In this talk, threeaspects of the PBE, mainly analysis, modelling and simulation, are discussed.The first part of the talk is devoted to the global existence and uniqueness of themass conserving solution of the PBE. The proof is based on strong convergencemethods applied to suitably chosen unbounded aggregation kernels havingsingularities in both the coordinate axes and satisfying linear growth conditionsat infinity and the fragmentation kernel covers a very large class of unboundedfunctions. Furthermore, an efficient and accurate discretization method based ona finite volume approach for solving PBE is presented. The principal of themethod lies in the introduction of an extra feature that is beyond the essentialrequirement of mass conservation. The extra feature controls more precisely thebehavior of a chosen integral property of the particle size distribution that doesnot remain constant like mass, but changes with time. The new scheme isvalidated and compared with an existing method against several test cases.Finally, some applications of the population balance model are simulated. Inparticular, a general population balance model for simulating spray fluidized bedgranulation of non-porous particles is introduced. The model takes into accountthe particle size enlargement by aggregation and simultaneous drying as well aswetting of particles. In contrary to the existing models available in the literature,it captures variations of several process conditions in its results with almost nodata fitting. Further, synthesis of Titanium dioxide nanoparticles is also simulatedusing an appropriate population balance model.


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Invited Talk 17 50 Years of Association with Applied MathematicsProf. Renuka Ravindran(formerly with) Department of MathematicsIndian Institute of [email protected]

A leisurely walk with me through the last fifty years of Applied Mathematics asI knew it. This is an account of topics I worked on, people I met and centers Iworked in.

Invited Talk 18 Process Parameter Identification in Thin Film FlowsDr. Satyananda PandaDepartment of MathematicsNIT [email protected]

We will consider the flow of a thin liquid film over a heated stretching surface.Due to a potential non-uniform temperature distribution on the stretching sheet,a temperature gradient occurs in the fluid which produces surface tension gradientat the free surface of the thin film. As a result, the free surface deforms and thesedeformations are adverted by the flow in the stretching direction. This talkfocuses on the inverse problem of reconstructing the sheet temperaturedistribution and the sheet stretch rate from observed free surface variations.

Invited Talk 19 Application of Asymptotic Analysis to Investigate Heat Flow through HighlyPorous InsulatorsDr.Samir RoyRPM College, University of [email protected]

We consider a conduction-convection based model to describe the heat flowthrough heat insulators based on materials with a high air content like glass-fibresheets, cellular glass, or extruded polystyrene (XPS) foams. The geometry of themodel consists of regularly shaped air pockets which are separated from eachother by thin rims of solid material. To avoid computational difficulties, theequations on the thin solid part are treated analytically using methods ofasymptotic analysis. The result of the asymptotic expansion is verifiednumerically.


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Invited Talk 20 An FEM-Based Discrete Regularization for a Parameter IdentificationProblem in PDEProf.M.T.NairDepartment of MathematicsIIT [email protected]

An FEM-based discrete regularization method has been considered foridentifying the spatially varying diffusion coefficients in second order ellipticboundary value problems. The problem is first discretized and then the ill-conditioned discrete problem is regularized using Tikhnov regularization. Thedata measurement error is also taken into account. Error estimates are derivedand numerical experiments are performed to validate the results. The resultspresented are based on a recently communicated paper co-authored by NeelaNataraj and Divya Venkataraman.

Invited Talk 21 Modeling of Climate Change, its impacts and responsesProf.J.B.Shukla(formerly with) Department of Mathematics and StatisticsIIT [email protected]

In this lecture, some mathematical models on climate change, its impact andresponses would proposed and analyzed. (See science and environment,www.mathmodsim.com).

Invited Talk 22 Limitations of Spectral Methods for Solving Option Pricing ProblemsProf. Kailash C. PatidarDepartment of MathematicsUniversity of the Western CapeSouth [email protected]

Spectral methods are widely used in fields such a fluid dynamics (see, e.g., C.Canuto, M.Y. Hussaini, A.Quarteroni, and T.A. Zang, Spectral Methods in FluidDynamics, Springer Series in Computational Physics, Springer-Verlag, NewYork, 1988). However, their uses for option pricing problems have been veryrare. The main drawback in their direct applications to option pricing problemsis that the payoff functions or the initial conditions for some of the associatedPDEs that are used in pricing typical options are non-smooth. Thus thecollocation approximations give lower order accuracy and hence make them lesscompetitive than even the finite difference methods. In this talk, we will discusshow to resolve these issues by considering a class of option pricing models.


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Invited Talk 23 Uncertainty in High Speed Compressible Flow ComputationsProf. J. C. MandalDepartment of Aerospace EngineeringIIT [email protected]

High speed compressible flows are characterised by the appearance ofdiscontinuous surfaces like shock wave, contact wave and slip line in the flowfield. Appearance of these discontinuities poses serious challenge in thedevelopment of numerical methods for high speed compressible flowcomputations. Many stringent criteria like conservation, up winding,monotonicity, positivity and entropy conditions are imposed in order to developrobust numerical methods for high speed compressible flows. In spite of all thecare, almost all the advanced numerical methods capable of capturing veryaccurate flow features fail catastrophically under certain situations due tonumerical shock instabilities. The numerical shock instabilities producephysically unrealistic solutions like carbuncle phenomenon, odd even decouplingand kinked Mach stem, spurious expansion shock and oscillations in slow movingshock. The cause for numerical shock instability is not yet understood clearly. Sofar, several attempts to overcome the numerical shock instability are not fullysuccessful.In the present talk, development of a novel approach [1] to avoidnumerical shock instability will be discussed. A set of test examples will bepresented in order to demonstrate the efficacy of the present method.

Reference:

[1] Mandal, J.C., Panwar, V., “Robust HLL-type Riemann solver capable ofresolving contact discontinuity”, Computers and Fluids, v.63, pp.148-164

Invited Talk 24 Bond Graph Theory in Simulation SoftwareDr. K. SelvanayagamLMS India Engineering [email protected]

Bond graphs are useful to unify the approach of system dynamics. This techniqueoffers the unique capability of explicitly describing both power and energytransfers between the physical structures of the system under study. It is acceptedthat bond graphs are not only graphical representations of mathematicalexpressions, but a conceptual framework offering a highly-structured languageand based on considerations derived from physics. The improvement of computersystems, numerical procedures and simulation programs are closely related to theextended application of the bond graph theory.


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Invited Talk 25 Numerical Modeling on Time-Dependent Behaviour of 1-3 PiezocompositesProf. A. ArockiarajanDepartment of Applied MechanicsIIT [email protected]

The temperature-dependent viscoelastic behaviour of 1-3 piezo composites andbulk piezo ceramics under electromechanical loading are studied experimentallyand theoretically. The resonance based measurement technique is used tomeasure the temperature-dependent effective properties. Experiments are alsopreformed to evaluate the time-dependent electromechanical behaviour of 1-3piezo composites under constant compressive prestress and cyclic electric fieldat elevated temperatures to understand the time-dependent behaviour for variousfiber volume fractions. The experimental results show that the viscoelasticbehaviour has a significant influence on the electromechanical responses of 1-3piezo composites. Hence the time-dependent effective properties of 1-3 piezocomposites are obtained using a viscoelastic based numerical model (unit cellapproach). The evaluated effective properties are incorporated into a finiteelement based 3-D micromechanical model to predict the time-dependent thermoelectro-mechanical behaviour of 1-3 piezo composites. The simulated results arecompared with the experimental observations.Key words: Viscoelastic behaviour, Electromechanical loading, Temperatureeffects, Micro-mechanical model

Invited Talk 26 Unfolding Method in HomogenizationProf. A. K. NandakumaranDepartment of MathematicsIndian Institute of Science, [email protected]

Homogenization is a branch of science where we try to understand microscopicstructures via a macroscopic medium. Hence, it has applications in variousbranches of science and engineering. This study is basically developed frommaterial science in the creation of composite materials though the presentapplication is much far and wide. It is a process of understanding the microscopicbehaviour of an in-homogeneous medium via a homogenized medium.Mathematically, it is a kind of asymptotic analysis .here are various methodsdeveloped in the last 40 years to understand the homogenization theory and some


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them are; Asymptotic Expansion, Energy Method, Two-scale convergence,Gamma Convergence, Bloch Wave Analysis, Unfolding Method etc. In this talk,we plan to introduce a relatively recent method known as Unfolding method.Unfolding also gives a better understanding of the in homogenized problem.Further it translates the known two-scale convergence to the weak convergenceof course by paying a penalty that it doubles The dimension of the space understudy. We introduce the notion of unfolding operator and some related results andthen we apply it to the well-known standard oscillatory homogenization problem.We also apply this method to our study of optimal control problems in anOscillatory domain.

Invited Talk 27 Numerical Simulation of electromagnetic wave propagation throughbounded medium - Limitations and ChallengesProf. V. SubramanianDepartment of PhysicsIIT [email protected]

It is well known that electromagnetic waves play an important role in our day today life. In order to effectively use the electromagnetic radiation, one has tounderstand the flow of radiation through medium. Though the analytical methodsare easy to use in homogeneous and isotropic medium, the numerical simulationis preferred as it is employable for all types of media. In this talk, a specific useof electromagnetic radiation useful for energy generation is explained. In thiscontext, the limitations and challenges while using numerical simulations arepresented.


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Invited Talk 28 Obligor Idiosyncracy Sensitive Based Pricing Mechanism with ProfitOptimization InclusivenessDr. Vikash Kumar SharmaGENPACT, [email protected]

In today’s environment, banks and financial institutions are challenged to growand remain profitable in the face of stricter regulation, changing customerbehavior and increasing competition in a highly saturated credit market. Price ofcredit is undoubtedly the ultimate competitive differentiator helping lendingorganizations build sustainable competitive advantage. Optimizing pricingdecisions enable lenders to maximize loan lifetime value and realize the fullpotential for growth and profitability. Price optimization is also a key lever inbuilding sustainable profitable relationships with customers through differentialstrategy to reward clients for loyalty and value. The most common approach usedby lenders for consumer credit is risk based pricing where the interest rate offeredto customers differs by risk idiosyncrasy. Approved loan applicants aresegmented into risk bands based on unwillingness to pay and each band is thenoffered a homogenous interest rate. This interest rate in each risk band is astandard mark-up on costs where costs include the expected loss from customersin the given risk band. While a more risky customer (in a higher risk band) paysa higher price to compensate for the higher probability of unwillingness to payassociated with that risk band, this increased interest rate itself may lead to ahigher rate of default amongst these customers. Also low risk customers (in alower risk band) are increasingly price sensitive and may respond unfavourablyto any non-competitive interest rate. Choosing the optimal price thus becomes allthe more imperative given this complex interplay of price and risk. There isempirical evidence of high risk customers being relatively less sensitive to priceincreases as compared to low risk customers. Increase in price however lowersloan volumes and makes a lender uncompetitive. Lender needs to acknowledgethis price elasticity of consumers’ demand for credit to arrive at the optimal pricethat would maximize its profitability. This is something that a simple risk basedpricing framework fail to take into account.

ICMMCS Abstracts of Paper Presentation[MM]

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Paper Presentation on Mathematical Modeling Aspects [MM]

MM-1 Thermal Stress Modeling of Micro-Electro discharge Machining on TitaniumAlloyDeepak Patil, Department of Mechanical Engineering, NIT Calicutwith Basil Kuriachen and Jose Mathew

Micro electrical discharge machining is known for its unique feature to produce microcomponents in any electricaly conductive difficult to machine materials irrespective ofits mechanical properties. In this study, an attempt has been made to develop amathematical model based on heat transfer principle for the simulation of thermalstresses developed due to micro electric discharge machining. The developed modelutilises various factors like latent heat of fusion, latent heat of vaporization, Gaussiandistribution of heat ux and temperature dependent material properties. Initially 3Dtemperature distribution in the Ti-6Al-4V work piece has been analyzed with Finitevolume method .Later, the thermal stress developed on the work piece due to the rapidtemperature rise were calculated. The results of the simulation were compared withalready published results and found that it is in good agreement and follows the similartrend.

MM-2 Pid Control of Humidity System Under Model uncertaintyS.Susmitha Kumari, Department of Chemical Engineering, IIT Madraswith M.Chidambaram

In this work, a comparison of the controllers designed based on local model, averagemodel and worst case model is carried out for a system which shows model uncertainty.For this, identification of an experimental air humidity system is carried out using openloop identification technique. The uncertainties in model parameters are determined byperturbing the system input with positive and negative step change from the nominalvalue. Designing of the PID controller settings using some of the recent techniques arecarried out based on worst case model. A comparison of the same is made with thatusing a local model and an average model. The same is implemented on theexperimental air humidity control system using simulation .PID controllers by ZieglerNichols (ZN), SIMC and Improved SIMC (ISIMC) methods based on the worst casemodel, average model and local model are evaluated using simulation studies. Fromtotal IAE value, the suitability of the controller is verified. The controllers designedusing Improved SIMC and ZN tuning rules based on worst case model areexperimentally validated

ICMMCS Abstracts of Paper Presentation [MM]

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MM-3 A Delayed Model for HIV Infection Incorporating Intracellular DelaySaroj Kumar Sahani, Department of Mathematics, South Asian University, New Delhi

This article introduces a delayed HIV model arising out of incorporating theintracellular delay. It has been assumed that intracellular delay τ is constant and someof the infected T cell actually dies out due to infection and only a portion ofinfected T cell which remain alive a time lag of τ after infection will producenewly HIV particles. The mathematical analysis on the present model suggests thatinfection free equilibrium is still always possible. The endemic equilibrium point existsif number of virus particle produced is greater than eδ2 τ and δ2 < δ∗ where δ2 is thedeath rate of infected T cell. The local stability analysis and Hopf Bifurcationanalysis have been carried out on the proposed model and same supported bynumerical simulation. The proposed model exhibit some interesting dynamicalbehaviour of the HIV infection. At last, the comparisons of the proposed model havebeen made with the existing models

MM-4 Stochastic Programming for Optimal Parametric Estimation of InfectiousDiseasesE.S.V. Narayana Rao, Department of Statistics, Pondicherry University, Puducherrywith P.Tirupathi Rao

Infectious Diseases cause mortality and morbidity in the infected individuals and haveimmense social and economic consequences. Understanding the dynamical behaviourof an infectious disease will greatly help the healthcare organizations in designing theeffective treatment protocols and intervention methods. In this paper a stochastic non-linear programming problem is developed with the objective of minimizing theexpected number of individuals in the groups of infected with disease and acquired withdisease. Optimal decision parameters like rates of new additions due to (i). Immigrationfrom source region (ii). Growth within the group (iii). Emigration to disease free zone(iv).loss within the group (v). Intermediate transition from one stage to other etc., areexplored by formulating suitable objective functions and respective constraints.

MM-5 Effects of suction and injection on swirling flow near a rough diskBikash Sahoo, Department of Mathematics, NIT Rourkelawith Sebastien Poncet and Fotini Labropulu

The flow due to uniform rotation of a viscous fluid at a larger distance from a roughstationary disk is investigated numerically. A uniform suction or injection is applied atthe surface of the disk. The system of fully coupled, nonlinear similarity equations isintegrated accurately for full range of flow parameters. Effects of wall roughness,suction and injection on the boundary layer are discussed with relevant physicalinterpretations


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MM-6 Experimental application of subspace model identification of an unstable systemC. Sankar Rao, Department of Chemical Engineering, IIT Madraswith M.Chidambaram

In this paper, experimental application of subspace identification on an unstableinverted pendulum is considered. The work presents the controller design for the cart-inverted pendulum system. Modeling of an inverted pendulum system is discussed.Models are identified from the data obtained from both simulation and experiment.From the identified model, PID controllers are designed by the pole placement method.The controllers are implemented on the experimental system to study the performanceof the proposed method.

MM-7 Long wavelength Soliton Solutions of KdV EquationJoseph Mathew ,Computer Centre, North Eastern Hill University, Shillongwith Sanjib Malla Bujar Baruah and Tapas Kumar Sinha

We have extended the technique of Sakaguchi and Malomed to obtain the longwavelength Soliton solutions of the KdV equation. In the long wavelength limit theeffective potential is a double well which admits both tanh Soliton solutions as wellsinusoidal solutions.

MM-8 A new multi-phase lattice hydrodynamic model considering the effect of driver’santicipationPoonam Redhu, Department of Mathematics, IIT Roparwith Arvind Kumar Gupta

In this work, we study multi-phase lattice hydrodynamic model by considering theeffect of driver’s anticipation in sensing the relative flux. We consider the new optimalvelocity function which incorporates the stepwise acceleration effect. We examined thephase transition and critical phenomena both analytically and numerically. The stabilitycondition is derived from linear stability analysis and the neutral stability curves areplotted. Phase diagrams are presented for multiple jamming transitions and found thatthe stability of traffic flow increases with the increase of the sensitivity. At a givensensitivity, the phase transition behaviour is different for different densities and tri-stable states occur. From numerical results, we showed the effect of driver’santicipation on traffic flow and obtained that traffic jam suppressed efficiently byincreasing the sensitivity.


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MM-9 Modelling of Multivariable Systems for ControlChandra Shekar Besta, Department of Chemical Engineering, IIT Madraswith M.Chidambaram

Higher order transfer function models are approximated by a three parameters modelssuch as critical damped SOPTD and FOPTD. A method is proposed to designdecentralized PID controllers using Skogestad (SIMC) approach for identified criticaldamped Second order plus time delay (SOPTD). Decentralized PI controllers are alsodesigned by the SIMC method from identified First order plus time delay (FOPTD).Thedecentralized SOPTD-PID control system give improved main responses anddecreased interactions. This improvement is shown particularly for TITO systemshaving the relative gain element, λij< 1 and λij> 1. The robustness of these controllersis evaluated by the Inverse Maximum Singular Value versus Frequency plot for boththe input and output multiplicative uncertainties. Simulation results are given for oneTITO systems having λij< 1, one TITO system having λ ij> 1. The present decentralizedSOPTD-PID controller gives improved performances over the decentralized FOPTD-PID/PI controllers.

MM-10 Bifurcation analysis of a delayed mathematical model for tumor growthSubhas Khajanchi, Department of Mathematics, IIT Roorkee

In this study, we represent a modified mathematical model of tumor growth byintroducing discrete time delay in the interaction terms. The model describes theinteraction between tumor cells, healthy tissue cells (normal cells) and immune effectorcells. The goal of this study is to obtain a better compatibility with reality for whichwe introduce the discrete time delay in the interaction between tumor calls and normalcells. We investigate the local stability of the non-negative equilibria and the existenceof Hopf-bifurcation by considering the discrete time delay as a bifurcation parameter.We estimate the length of delay to preserve the stability of bifurcating periodicsolutions, which gives an idea about the mode of action for controlling oscillations inthe tumor growth. The numerical simulations of the model confirm the analyticalfindings.


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MM-11 Simple Approach to Find First Integrals of Certain Nonlinear OrdinaryDifferential EquationsK. Krishna kumar ,Department of Mathematics, Pondicherry University, Puducherrywith A.Annamalai and KM.Tamizhmani

We propose a novel and simple method to derive first integrals of a given nonlinearFinite-dimensional system. The idea is based up on adivision process of polynomialsby monomials. We apply this method to several second-order equations and also to athird-order equation.

MM-12 Non-similarity solution for shock waves in a rotational axisymmetric perfect gaswith magnetic Field and density varying exponentiallyG.Nath ,Department of Mathematics,Motilal Nehru National Institute of TechnologyAllahabadwith A.K.Sinha

The propagation of a cylindrical shock wave in an ideal gas in the presence of a constantazimuthal magnetic field, with axisymmetric rotational effects is investigated. Theambient medium is assumed to have radial, axial and azimuthal components of uidvelocities. The uid velocities, the initial density of the ambient medium are assumed tobe varying and obeying an exponential law. Non-similar solutions are obtained for one-dimensional adiabatic ow behind a magneto gas dynamic cylindrical shock wave bytaking into account the vorticity vector and its components. In order to obtain thesolutions the angular velocity of the ambient medium is assumed to be decreasingexponentially as the distance from the axis increases. The shock wave moves withvariable velocity, and the total energy of the wave is non-constant and varies with time.The effects of variation of Alfven-Mach number and time are obtained. It is shown thatthe presence of magnetic field has decaying effect on the shock wave. The pressure anddensity with magnetic field vanish at the inner surface (piston) and hence a vacuum isform at the line of symmetry. The shock waves in conducting perfect gas can beimportant for description of shocks in supernova explosions, in the study of central partof star burst galaxies, nuclear explosion, rupture of a pressurized vessel and explosionin the ionosphere. Other potential applications of this study include analysis of datafrom exploding wire experiments and cylindrically symmetric hypersonic ow problemsassociated with meteors or re-entry vehicles etc. The obtained solutions are applicablefor arbitrary values of time.


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MM-13 Impact of Connection Topology on Cooperative Dynamics Of FHN NeuronsWith Randomly Varying ThresholdAnindita Bhattacharjee, Department of Management Studies, Galgotia Institute ofManagement & Technology, Greater Noida.with M. K .Das

Emergence of behavioural and cognitive processes takes place due to the structural andfunctional complexities of neurons. Collective dynamics of coupled neurons has arelevant role for various physiological processes. The structure of the network is veryimportant in view of its cooperative dynamics. Connection topology reveals thepossible communication pathways. Investigation of complex patterns reveals theunderlying mechanism of various neuronal activities i.e., loss of consciousness,emergence of epileptic seizure etc. In the present work, we consider randomly varyingfiring threshold of the coupled FHN neurons to mimic the dynamics of real biologicalneurons .Further, numerical simulations have been carried out to understand thecooperative dynamics in terms of the coefficient of variation parameter,

of neurons under different connection topologies with couplingstrength D and S-the standard deviation of the threshold. Here< T> refers to the inter-spike interval of the average membrane potential V (t). The present work suggests that,the threshold fluctuation has an important hole in firing coherence. Raster plots fordifferent settings clearly indicate that the neurons fire less coherently if the fluctuationof the firing threshold, S, is increased. This may be attributed to neurons internalphysiological conditions. However increasing the coupling strength, D, the rhythm canbe retrieved as shown in various contour plots. Besides the fluctuation, S, and thecoupling strength, D, the topological order of the network also play a significant role inmaking the neurons fire regularly. A particular topological arrangement has also beenidentified showing the possibility of maximum coherence.

MM-14 Dynamics of formation offoam cells from LDL cholesterol and the inhibitoryeffects of therapeutic agents like statinsNidhi Chaudhary,Department of Mathematics,BITS Pilani, Pilani Campus, Rajasthanwith Padma Murali and Rajiv Kumar

Cardiovascular disease (CVD) refers to coronary artery, cerebrovascular, andperipheral vascular disease. India has among the highest rates of cardiovascular disease(CVD) globally. Atherosclerotic CVD is an inflammatory disease and is the leadingcause of morbidity and mortality in human populations. Low density lipoprotein (LDL)concentration is a major risk factor for Atheros clerosi and the disease is characterisedby arterial fatty-streak lesions that contain T cells and lipid-laden macrophages, or foamcells. The aim of this work is to model the dynamics of LDL and foam cell formationin the presence of a therapeutic drug using mathematical modelling and thereby providesolutions to control the disease. According to this model, the biological processes of


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conversion of LDL to foam cells and the inhibitory effects of the drug on LDLconcentration and foam cells can be described by a system of ordinary differentialequations. The equilibrium points of the model are computed and their stability isstudied. We give a numerical simulation of the model and we find that the disease freestate can be achieved in the presence of a therapeutic drug. The duration of the diseasefree state is found to increase with the concentration of the drug injected into the systemand the optimum concentration of the therapeutic agent was derived.

MM-15 Modeling the effect of treatment on the spread of HIV/AIDSRam Naresh, Department of Mathematics, H.B. Technological Institute, Kanpur

A nonlinear mathematical model to study the effect of treatment on the spread ofHIV/AIDS in a population with variable size structure is proposed and analyzed. Thepopulation, under consideration, is divided into four subclasses i.e. susceptibles,asymptomatic infectives, symptomatic infectives and AIDS patients. The modelexhibits two equilibria namely, the disease-free and the endemic equilibrium. Modelis analyzed using stability theory of differential equations and the global dynamics ofthe spread of the HIV/AIDS is found to be completely determined by the basicreproduction number R0. If R0 1, the endemic equilibrium is globally asymptotically

stable under certain conditions showing that the disease becomes endemic. It has alsobeen found that with increase in the treatment rate, the symptomatic infectives decreasewhich ultimately reduces AIDS population. Numerical analysis of the model is alsoperformed to investigate the influence of certain key parameters on the spread of thedisease and to support the analytical results.

MM-16 An EOQ model with deteriorating items under inflation and time varyingholding costM.V.Jayanthi, Department of Mathematics, B. S. Abdur Rahman University, Chennaiwith P.S.Sheik Uduman

The items that incur a gradual loss in quality or quantity over time while in inventoryare usually called deteriorating items. In this paper, an effort has been made toincorporate physical characteristics of stored items into inventory model. We developmodels for deteriorating items with linear time dependent demand pattern over a finiteplanning horizon, taking into account the effect of inflation. The traditional parameterssuch as unit cost and ordering cost are kept constant whereas the holding cost isconsidered to be varying. Two possibilities of variations in the holding cost namely;constant holding cost and time varying holding cost are considered. The approximateoptimal solution of the total cost is studied for both the cases with the help of anumerical example and a sensitivity analysis of the optimal solution with respect to theparameters of the system is carried out.

ICMMCS Abstracts of Paper Presentation[CS]

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Paper Presentation on Computational and Simulation Aspects [CS]

CS-1 A radial basis function based implicit explicit method or jump diffusionmodel arising in financeAlpesh Kumar, Department of Mathematics and Statistics, IIT Kanpurwith Mohan .K. Kadalbajoo and Lok Pati Tripathi

In this article, we present a radial basis function based implicit explicit numericalmethod to solve the partial integro-differential equation which describe the natureof the option price under jump diffusion model. The governing equation is time issemi discretised by using the Crank-Nicolson Leap-Frog scheme followed byradial basis function based finite difference method. Numerical results for putoption under Merton model are given to illustrate the efficiency and accuracy ofthe present method.

CS-2 Numerical Study of Mixed Convection Cooling of Heat Source Mounted inLid-Driven Cavity Filled with NanouidA. K. Nayak, Department of Mathematics, IIT Roorkeewith Sumit Malik

This work is focussed on the numerical modelling of steady mixed convection ow,in a square lid-driven cavity filled with a copper-water nanouid mounted with theheat source at different walls. The right vertical wall is always kept at the constanttemperature, while the other walls are insulated. A finite volume based numericalapproach is used for the solution of governing equations. Extensive results fort wodimensions ow field is obtained over a wide range of physical parameters, namelyReynolds number, Rayleigh number and solid volume fraction. The effective heattransfer variation is analyzed by placing the mounted block along the left and rightwall. The changes in main characteristics of the ow due to variation of Reynoldsnumber and Rayleigh number are elaborated.


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CS-3 Anisotropy due to orientation study for a poly-crystalline copper using finiteelement methodSudhakar Matle, School of Advanced Sciences, VIT University, Vellore

The present paper addresses the numerical investigation on the anisotropy of thepoly-crystalline material using finite element method. The parameters studied hereare the cell size and random orientation of the cell. A 2D plane stain analysis isconducted on the poly-crystal of size 50_50 (in mill-meters) using Hanning 3-cylcewindow. The boundary conditions at the interfaces of any two cells of the crystalare welded in contact. The polycrystalline material is modeled as a 2Dcomputational do-main in which each crystallite or grain cell represents onerandomly generated Voronoi cell. The basic idea in deriving this model is that thescattering of the wave is independent of the shape when the cell size is much lessthan the wave length. The scattering of the wave due to orientation (anisotropy)and scattering of the wave without orientation of the cell for a poly-crystallinecopper are compared at the various frequencies. It is concluded that thedisplacement profile at the probe of the poly-crystalline copper approximates thedisplacement profile of the Isotropic case (a single crystal) when the ratio of thewavelength to the cell size much greater than one.

CS-4 An Entropy Stable Central Solver for Euler EquationsN.H Maruthi, Department of Aerospace Engineering, IISc, Bengaluruwith S.V.Raghurama Rao

An exact discontinuity capturing central solver developed recently, namedMOVERS (Method of Optimal Viscosity for Enhanced Resolution of Shocks) (S.Jaisankar and S.V. Raghurama Rao, Journal of Computational Physics, 220, 770-798, 2009), is analyzed and improved further to make it entropy stable. MOVERS,which is designed to capture steady shocks and contact discontinuities exactly byenforcing the Rankine-Hugoniot jump condition directly in the discretizationprocess, is a low diffusive algorithm in a simple central discretization framework,free of complicated Riemann solvers and flux splitting. However, this algorithmneeds an entropy fix to avoid non smoothness in the expansion regions. Theentropy conservation equation is used as a guideline to introduce an optimalnumerical diffusion in the smooth regions and a limiter based switchover isintroduced for numerical diffusion based on jump conditions at the large gradients.The resulting new scheme is entropy stable, accurate and captures steadydiscontinuities exactly while avoiding an entropy fix.


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CS-5 A Numerical Implementation of Higher Order Time Integration Algorithmon Unsteady Burgers' EquationB. Mayur Prakash, Department of Mechanical Engineering, NIT Calicutwith Ashish Awasthi and S.Jayaraj

In this paper, method-of-lines (MOL) in conjunction with optimal four-stage, orderthree strong stability-preserving time-stepping Runge-Kutta (SSP-RK43) schemeis proposed to find the approximate solution of the unsteady Burgers' equation. TheMOL is used in space, and the SSP-RK43 scheme is used in time for solving theresulting system of ordinary differential equations. To check the efficiency andaccuracy of the method, two test examples of Burgers' equation are included withtheir numerical solutions, L2 and L1 errors and comparison is done with the exactsolution for modest values of Reynold numbers (Re). The numerical solutionsobtained typically does not exhibit nonlinear instabilities. It is also observed that,the proposed method yields satisfactory results for all the cases considered. Theproposed method is found to be robust for low and high Re therefore the proposedmethod also be useful for general models involving the solution of advection-diffusion equations or other transport equations with similar stability requirements.

CS-6 An Arithmetic Average Geometric Mesh Discretization For Semi linearElliptic Equations And Estimate Of First And Second Order PartialDerivativesNavnit Jha, Department of Mathematics, South Asian University, New Delhi

A new third order accurate variable mesh compact finite difference technique isproposed for the numerical solution of two dimensional semi linear elliptic partialdifferential equations. The method is also used to obtain third and second order ofaccuracy for the first and second order partial derivatives respectively on geometricmeshes. The essence of the method lies in the fact that it is applicable to thesingular problems as well. The consideration of geometricity of the meshes in boththe spatial directions enables the grid concentration adaptively, which leads tosignificant improvement in the numerical accuracy compared to the higher ordermethod on the uniform meshes. The convergence analysis of the method has beendescribed with monotonic and irreducible property of the iteration matrix.Numerical illustrations with stationary Schrodinger equation, Helmholtz equationand singular problems show the reliability and accuracy of the new technique interms of maximum absolute errors and computational order of convergence ofsolution values and their partial order derivatives.


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CS-7 Weak-Strong Hyperbolic Splitting for Simulating Conservation LawsNaveen Kumar Garg IMI, Department of Mathematics, IISc Bangalorewith M.Sekhar and S.V.Raghurama Rao

A simple and accurate central scheme in finite volume framework is developed forsystems of hyperbolic conservation laws, using a splitting of strongly hyperbolicand weakly hyperbolic parts. This leads to the flux function of 1D inviscid Eulercompressible system being split into convection and pressure parts and 1D inviscidshallow water system into convection and celerity parts. The numerical diffusionis fixed based on flux equivalence principle, which leads to the satisfaction of thejump conditions. The numerical scheme is tested on various shock tube problemsof gas dynamics for 1D Euler equations and on dam breaking problems for shallowwater equations. Comparison is done with an approximate Riemann solver todemonstrate the efficiency of the numerical method.

CS-8 HOC schemes for 2D parabolic problems with mixed derivativesShuvam Sen, Department of Mathematical Sciences, Tezpur Universitywith E.T.Ooi and C.Song

In this article, we discuss a higher order compact numerical method for 2Dparabolic problems with mixed derivatives. The finite difference scheme is basedon fourth order spatial discretization and second order Crank-Nicolson type timediscretization. The method has been extended to solve incompressible Navier-Stokes (N-S) equations in irregular domains. To verify the proposed method, threeproblems with exact and benchmark solutions has been investigated. The proposedcompact discretization has been extended to tackle flows governed by the two-dimensional unsteady N-S equations in domain beyond rectangular. The resultsshow good agreement for all the problems considered.


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CS-9 Semi-analytical approach to treat singularities within the extended finiteelement methodS. Natarajan, Department of Mechanical Engineering, IIT Madras

The classical finite element method (FEM) requires a conforming mesh to modelphysical boundaries. Within this framework, the discontinuities cannot cross themesh topology and evolving discontinuities are aided with constant re-meshing. Inspite of the success of the FEM, mesh generation in three-dimensions for evolvingdiscontinuities in still a major challenge. The introduction of implicit boundarydefinition-based method, viz., the extended/generalized FEM (XFEM/GFEM),alleviates shortcomings associated with the meshing of discontinuity surfacesprevalent in existing approaches. Crack modeling within the framework ofXFEM/GFEM requires a priori knowledge of the functional behavior of the solutionfield, which, in some cases does not exist in closed form or are very complex.Independently, Wolf and Song developed a semi-analytical method coined as thescaled boundary finite element method (SBFEM). The most distinct feature of theSBFEM that makes it very efficient for fracture analyses is that its semi-analyticalsolutions naturally conforms any type of singularity that may result from cracks,notches or material junctions. A unified definition of these singularities can berealized in the form of generalized stress intensity factors (GSIF). Fracture analysescan be solved efficiently without a very dense mesh at the crack tip or introducingenrichment functions. It is noted that the SBFEM relaxes the need to conform tostandard simplex shapes. Hence, the SBFEM has emerged as an attractive alternateto model problems with singularities in homogeneous and/or heterogeneousmaterials. This paper discusses the recently proposed extended SBFEM (xSBFEM), a semi-analytical approach to treat crack tip singularities and multi-materialjunctions within the XFEM framework. The spirit of the approach proposed hereshares some similarities with the work on using polygonal elements, the SpiderXFEM [4] and the methods with numerically determined enrichment functions. Theproposed method is validated by various numerical examples.

CS-10 Uniform numerical method for a class of parameterized singularly perturbedproblemsJugal Mohapatra, Department of Mathematics, NIT Rourkela

In this paper, we consider a quasilinear first order singularly perturbed boundaryvalue problem depending on a parameter. The problem is discretized by a backwardEuler finite difference scheme on an appropriate non uniform mesh constructedadaptively by equidistributing a positive monitor function based on the solution. Weshow that the proposed method is first order convergent whose error constants areshown to be independent of the singular perturbation parameter. Numericalexperiment illustrates in practice the result of convergence proved theoretically.


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CS-11 Numerical investigation of mixed convection in a ventilatedenclosure with differentially heated side wallsK.Venkateshwarlu, Department of Mathematics, IIT Roorkeewith V.K.Katiyar and A.K.Nayak

This paper presents an investigation of fluid flow, effect of differentially heated sidewalls, and air inlet and outlet locations on the mechanically ventilated enclosureusing a numerical simulation. Thermally activated fluid was supplied throughvarious locations of a left vertical wall and flush-out through a right vertical wall ofthe enclosure. The horizontal walls were assumed to be impermeable and adiabatic.Steady, laminar, and incompressible flow under Boussinesq’s approximation wasconsidered and numerical results for Navier-Stokes equation and energy equationwere obtained using finite volume method based on Semi-Implicit Method forPressure Linked Equations (SIMPLE) algorithm. The validated model was then usedto investigate effects of Reynolds number and room aspect ratio on flow velocityand thermal characteristics within the room. The flow structures and thermalactivities were studied for Richardson’s number, (Ri), in the range of 0 ≤ Ri ≤10.Variation of convection co-efficient along the wall for cold and hot fluid at differentlocations has been investigated and cooling efficiency was found to be the maximumwhen the inlet and the outlet were placed at middle and lower parts respectively ofthe hot and the cold wall.

CS-12 An efficient Navier-Stokes solver using stream function-velocity formulationon compact non uniform space gridsSwapan K. Pandit, Integrated Science Education and Research CentreVisva-Bharati, Santiniketan, West Bengal.

In this study, we propose an implicit compact Finite difference scheme based onstream function-velocity formulation, with an averaged time discretization, forsolving the two-dimensional (2D) unsteady Navier-Stokes (N-S) equationsrepresenting incompressible viscous fluid flows on non-uniform grids. Theimportant advantage of this formulation is not only to overcome the difficultiesexisting in the velocity-pressure and stream function-vorticity formulations, but alsofor being applicable to complex geometries beyond rectangular. The robustness ofour proposed scheme is illustrated through its application to the three benchmarkproblems, viz., famous lid-driven cavity flow, natural convection in a squareenclosure and an external flow over a backward-facing step. Numerical results arepresented and compared with the benchmark solutions whenever available in theliterature, and they clearly demonstrate that the proposed compact scheme is stableand produces accurate results with superior scale resolution.


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CS-13 Maxwellian Distribution Based Finite Element Method for Hyperblic PDEsAmeya D. Jagtap, Department of Aerospace Engineering, IISc, Bangalorewith S.V.Raghurama Rao

A Maxwellian distribution function based finite element method is presented forhyperbolic partial differential equations. The proposed scheme performs better thanthe original SUPG stabilized method in multi-dimensions. Numerical experimentsare carried out for 1D and 2D (using Q4 and T3 elements) Burgers equation as wellas for 1D Euler equations of gas dynamics. Finally, the spectral stability analysisis done for the explicit 2D formulation.

CS-14 A computational approach to Kinetic Theory based Turbulence ModelAnkit Ruhi,IMI, Department of Mathematics, IISc Bangalorewith Mohammed Lemou, Nicolas Crouseilles and S.V.Raghurama Rao

In this research work, a k-epsilon type turbulence model based on kinetic theorydeveloped by Degond & Lemou (Journal of Mathematical Fluid Mechanics, 4, 257-284, 2002) is considered for analysis and numerical simulation. The governingequation for this turbulence model is similar to Boltzmann equation with a relaxationtype collision term. The modelling of collision term restricts the use of turbulencemodel for isotropic turbulence. The dependency of relaxation time on turbulentenergy at kinetic level makes it difficult in constructing efficient numerical methods.To investigate this problem, we focus here on a prototype one-dimensional model andfirst propose an appropriate change of frame that makes the numerical study simpler.Further a numerical strategy to tackle the stiff relaxation source term is introduced inthe spirit of Asymptotic Preserving Schemes.

CS-15 MATLAB Simulink-Mathematical Modeling of Chaotic Oscillator System forSecure CommunicationA.Chithra,, B.S.Abdur Rahman University, Chennaiwith I. Raja Mohamed

In this paper, a method of modeling a coupled Duffing oscillator chaotic system usingMATLAB Simulink technique is described. One way coupling is considered here dueto its simplicity in coupling. The method is to considering two identical duffingoscillator systems, one system to synchronize with other system with a one waycoupling element. As time progress, systems achieve a perfect synchronization. Theresult shows that based on coupling strength, the response system synchronize withthe drive system completely or partially (lag or lead). Under complete synchronizationstate, if the message signal is incorporated with this, it can be transmitted in a secureway Simulation results using MATLAB Simulink are provided to show theperformance and the level of synchronization achieved in this method.


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CS-16 A Method For Solving Balanced And Unbalanced Trapezoidal IntuitionisticFuzzy Assignment ProblemS. Sheela, Dept. of Mathematics, Gojan School of Business and Technology.with M.Joseph Robinson and A. Sudha Ran

In this paper, we examine an assignment problem in which cost coefficients aretrapezoidal intuitionistic fuzzy numbers. In conventional assignment problem, costis always certain. This paper develops an approach to solve an intuitionistic fuzzyassignment problem where cost is not deterministic numbers but imprecise ones.Here, the elements of the costs (profits) matrix of the assignment problem aretrapezoidal intuitionistic fuzzy numbers. Then it strapezoidal membership and non-membership functions are defined. A new proposed ranking procedure which befound in [1] and is used to compare the intuitionistic fuzzy numbers so that anIntuitionistic Fuzzy Hungarian method may be applied to solve the intuitionisticfuzzy assignment problem. Numerical examples show that an intuitionistic fuzzyranking method offers an effective tool for handling an intuitionistic fuzzyassignment problem.References[1]Annie Varghese and Sunny Kuriakose, Notes on Intuitionistic Fuzzy SetsVol. 18, 2012, No. 1, 19-24.

ICMMCS List of Participants

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Mr. Alpesh KumarDepartment of Mathematics andStatistics, IIT Kanpur

Dr. M. ChidambaramDepartment of Chemical EngineeringIIT Madras

Dr. Ameeya Kumar NayakDepartment of MathematicsIIT Roorkee

Ms. Chithra AyappanB. S. Abdur Rahman UniversityChennai

Mr. Ameya D. JagtapDepartment of Aerospace EngineeringIISc Bangalore

Ms. J. Christy RojaResearch ScholarDepartment of MathematicsBharathidasan UniversityTrichy

Mr. Anindita BhattacharjeeDepartment of Management StudiesGalgotia Institute of Management &TechnologyGreater Noida

Mr. Deepak PatilDepartment of Mechanical EngineeringNIT Calicut

Ms. Ankit RuhiIMI,Department of MathematicsIISc Bangalore

Mr. Ghanshyam PrasadResearch ScholarDepartment of MathematicsIIT BHU Varanasi

Ms. P. Avudai SelviResearch ScholarDepartment of MathematicsBharathidasan UniversityTrichy

Ms. N. GeethaResearch ScholarDepartment of MathematicsBharathidasan UniversityTrichy

Dr. Bikash SahooDepartment of MathematicsNIT Rourkela

Ms. Gurmeet KaurDepartment of MathematicsIIT Kharagpur

Mr. Chandra Shekar BestaDepartment of Chemical EngineeringIIT Madras

Ms. M. V. JayanthiResearch ScholarDepartment of MathematicsB.S.Abdur Rahman UniversityChennai


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Mr. Joseph MathewComputer CentreNorth Eastern Hill UniversityShillong

Mr. B. Mayur PrakashDepartment of Mechanical EngineeringNIT Calicut

Dr. Jugal MohapatraDepartment of MathematicsNIT Rourkela

Mr. Mitiku Daba FirdiResearch ScholarDepartment of MathematicsAnna UniversityChennai

Mr. T. KannanAssistant ProfessorK.S.Rangasamy College of TechnologyTiruchengode

Dr. E. S. V. Narayana RaoDepartment of StatisticsPondicherry UniversityPuducherry

Mr. K. Krishna kumarDepartment of MathematicsPondicherry UniversityPuducherry

Dr. G. NathDepartment of MathematicsMotilal Nehru National Institute ofTechnologyAllahabad.

Ms. Meenu SelvarajanM.Tech. StudentNIT Karnataka, Surathkal

Mr. Naveen Kumar GargIMI, Department of MathematicsIISc Bangalore

Ms. V. MalarvizhiLecturer – MathematicsJerusalem Engineering CollegePallikaranai,Chennai

Dr. Navnit JhaDepartment of MathematicsSouth Asian UniversityNew Delhi

Mr. N. H. MaruthiDepartment of Aerospace EngineeringIISc Bangalore

Ms. Nidhi ChaudharyDepartment of MathematicsBITS Pilani, Rajasthan


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Ms. Poonam RedhuDepartment of MathematicsIIT Ropar

Ms. Sudha RaniDepartment of MathematicsGojan School of Business andTechnology,Chennai

Dr. Ram NareshDepartment of MathematicsH.B. Technological InstituteKanpur

Mr. Subhas KhajanchiDepartment of MathematicsIIT Roorkee

Mr. N. RajaLecturer in MathematicsBasic Engineering DepartmentVPT-SRM ,Chennai

Dr. Sudharkar MatleSchool of Advanced SciencesVIT UniversityVellore

Mr. C. Sankar RaoDepartment of Chemical EngineeringIIT Madras

Dr. Sundararajan NatarajanDepartment of Mechanical EngineeringIIT Madras

Mr. Saroj Kumar SahaniDepartment of MathematicsSouth Asian University,New Delhi

Ms. S. Susmitha KumariDepartment of Chemical EngineeringIIT Madras

Ms. S. SheelaDepartment of MathematicsGojan School of Business andTechnology,Chennai

Dr. Swapan K. PanditIntegrated Science Education andResearch Centre, Visva-BharatiSantiniketan ,West Bengal

Mr. Shivam ShreevastavaResearch ScholarDepartment of Mathematical SciencesIIT (BHU) Varanasi

Mr. K. VenkateshwarluDepartment of MathematicsIIT Roorkee

Dr. Shuvam SenDepartment of MathematicsTezpur University

Ms. Joseph RobinsonDepartment of MathematicsGojan School of Business andTechnology,Chennai

Prof. S. Sundar, Organizing Secretary, ICMMCS

Thank

for their Generous Support and Sponsorship

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