Department ofDepartment of MathematicalMathematical

SciencesSciences

• 40 Faculty40 Faculty

• 41 Graduate• 41 Graduate Students

• Approximately 80 U d d tUndergraduate Students

Research Areas• Applied Mathematics

Research AreasApplied Mathematics

St ti ti• Statistics

• Combinatorics and Pure Math

• Mathematics Education

Applied MathematicsApplied Mathematics

– Computational Engine Research – F. Tanner– Simulation of Food Sprays – F. Tanner– Multiphase Fluid Systems – K. Feigl– Cardiac Dynamics – W. Ying– Computational Biology – L. Zhang

March 2008 Computing Initiative

• Computational Engine ResearchResearch

• Modeling of flow, g ,spray and combustion processes

Prof. Franz Tanner

• Motivation

Computational Engine Research

– Health and Environmental– Sustainability

• Main Objectives– Understand physical processes– Develop simulation tools

• Results– Strategy to minimize fuel consumption

and emissions– Multi-orifice asynchronous injection

Mass fraction of an evaporatingfuel spray

• Motivation

Modeling of Food Sprays

– Spray-drying and spray-freezing– Encapsulation of nutrients

• Main Objectives– Obtain desired drop size distributions– Maximize productionp

• Modeling Challenges/Research– Complex flows and materialsp– Phase changes Air-assisted atomization of a

nutriose liquid spray

• Simulation of flow of complex fluidscomplex fluids

• Collaborations with ETH-Zurich and University of Tennessee

Prof. Kathleen Feigl

Simulation of Fluid Systems

• Examples/ApplicationsEmulsions foams polymer blends

Simulation of Fluid Systems

– Emulsions, foams, polymer blends– Foods, plastics, pharmaceuticals

• GoalsGoals– Understand process-

microstructure- rheology relationshipD i t ti i– Design processes to optimize product properties

• Research Si l t d d f ti fResearch– Multidisciplinary approach– Combine modeling, simulation

and experiments

Simulated deformation of afluid droplet

March 2008 Computing Initiative

Simulation of Fluid SystemsSimulation of Fluid Systems

Droplet deforming in supercriticalshear flow

Droplet deforming in supercriticalelongational flow

• Ph.D. – Duke

• Joined MTU Fall 2008

• Research Interests– Scientific Computingp g– Modeling/Simulation– Mathematical Biology– CFD

Wenjun Ying, Asst. Prof.

Simulation of Cardiac DynamicsSimulation of Cardiac Dynamics

• Space-time adaptive mesh refinement

• Multi-scale adaptive modeling of electrical dynamics in the heart

Simulation of wave propagation in a virtual dog heart

Cartesian Grid Method

• Beating heart

Cartesian Grid Method

g

• Droplet deformation

• Multiphase flows

• Other free-boundary or moving interface problemsproblems

Grid lines not aligned with complex domain boundary

• Ph.D. – Louisiana Tech

• Post-doc – Harvard/MIT

J i d MTU F ll 2008• Joined MTU Fall 2008

• Research Interests– Computational biology–– Cluster and classification Cluster and classification

algorithmsalgorithmsgg–– Software application Software application

developmentdevelopment Le (Adam) Zhang, Asst. Prof.

Simulation of Brain CancerSimulation of Brain Cancer Progression

Brain Cancer Cell

• Performing multi-scale, multi-resolution hybrid

d llicancer modelling

• Regression analysis• Regression analysis, multivariate analysis

Simulation of Cancer Progression

Simulation of Hyperthermia in Skin Cancer Treatment

• Simulate bio-heat transfer Skin Cell Structure

by finite difference method

• Inverse heat convection problemp

Treatment Simulation

StatisticsStatistics

– Statistical Genetics – Q. Sha, R. Jiang, J. Dong, S. Zhang, H. Chen

– Wildlife Population Studies – T. Drummer

– Statistics , Probability, Optimization – I. Pinelis

– Statistical Methodolgy and Data Analysis – Y Munoz– Statistical Methodolgy and Data Analysis – Y. Munoz –Maldonado

March 2008 Computing Initiative

P l i di• Population studies for moose, wolves and sharp tailand sharp-tail grouse in U.P.

• Aerial Observation

Prof. Tom Drummer

• Moose survey conducted at 500 ft altitude over 1600 sq. mile area

• Model developed to yield probability ofyield probability of sighting animals

• Ph.D. – Texas A&M U i itUniversity

• Statistical MethodologyStatistical Methodology and Analysis of Data– Functional Data Analysis

N t i M th d– Non parametric Methods– Linear and Mixed Models– Multivariate Analysis

Yolanda Munoz-Maldonado, Asst. Prof.

• Ganglioside Profiles• Ganglioside Profiles Analysis

D t t diff i• Detect differences in brains of young and old rats

• Differences found in locus coeruleus of young rats y gwhich may affect sleep regulation

• Study of effect of chronic• Study of effect of chronic exposure to particulate matter on mortality

• Temporal analysis of PM10 in El Paso, TX

• Study suggests use a principal component p p panalysis

Statistical Genetics Group

5 F lt

Statistical Genetics Group

• 5 Faculty

• 2 Post docs• 2 Post – docs

• 9 PhD Students• 9 PhD Students

• Support from NIHSupport from NIH and NSF

Statistical Genetics Group

• Sixteen Members• Sixteen Members– 5 faculty– 2 post-docs– 9 PhD Students

• Supported by 4 NIHSupported by 4 NIH Grants

T t l f di f• Total funding of over $1 million

Statistical Genetics Group

Group Aims

Statistical Genetics Group

– Develop new tools for analysis of genomic data

– Use innovative models and methods in human genetic studies

Key Research Areas– Functional gene mapping– Pedigree analysis– Gene interactions– Computational methodologies– Microarray analysis

• Statistical Genetics

• Prof. Quiying Sha

• PhD Student Elena KasyanovaKasyanova

• Development of new computational and statistical tools

P i f i• Primary focus is analysis and interpretation ofinterpretation of genomic data

• Concentration on complex human diseases

K ti iti• Key activities– Functional gene

mappingmapping– Pedigree analysis– Genetic diversityy

Combinatorics and Pure MathCombinatorics and Pure Math

C bi t i J Bi b D K h P M k– Combinatorics – J. Bierbauer, D. Kreher, P. Merkey, V. Tonchev, M. Keranen

– Commutative Algebra – F. Zanello

March 2008 Computing Initiative

Combinatorics Group

• ??? Members• ??? Members– ? faculty– ? post-docs– ? PhD Students

• Supported by ????Supported by ????

• Ph.D. – Queen’s University KingstonUniversity Kingston

• Joined MTU Fall 2007

• Commutative Algebra g

Fabrizio Zanello, Asst. Prof.

Non-Unimodal Level Hilbert Functions

• Identified in Codimension 3.

Non-Unimodal Level Hilbert Functions

• h = (1, 3, 6, 10, 15, 21, 28, 27, 27, 28)

• Existence was long-standing open problem, and has led to several publicationsp

Gorenstein Hilbert Functions

• Identified asymptotic lower bound for the

Gorenstein Hilbert Functions

y pleast possible Degree 2 entry

• Socle degree 4 and codimension r• Socle degree 4 and codimension r

• Solved 1983 conjecture of Stanley, proved in j y, pcollaboration with Juan Migliore (Notre Dame) and Uwe Nagel (U. Kentucky)

• f(r) ~r (6r)2/3

T hi dTeaching and I t ti lInstructional ResourcesResources

• Prof. Allan Struthers

• Graduate Student Yejun Gong

• Excellent faculty ibiliaccessibility

• Dr. Ghan Bhatt teaches anteaches an introductory calculus course

• Typical calculus class size is ~ 50 students

B th R d• Beth Reed uses document camera in statistics lecture

• Math classrooms t d i 2006renovated in 2006

• Rooms equipped with• Rooms equipped with latest audio-visual tools

• Teaching Assistant Rachel Robertson works with a studentworks with a student in the Mathlab

• Calculus courses include laboratoryinclude laboratory component to reinforce lectures

• Tutoring session in the Math Learning Center

W lk i i t• Walk-in assistance or appointments with regular tutorsregular tutors

• Math Learning Center open 6 days per week

St d t t h• Students teach students