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Department of Mathematical Sciences

Department of Mathematical Sciences. 40 Faculty 41 Graduate Students Approximately 80 Undergraduate Students. Applied Mathematics Statistics Combinatorics and Pure Math Mathematics Education. Research Areas. Applied Mathematics Computational Engine Research – F. Tanner

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Department of Mathematical Sciences

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  1. Department of Mathematical Sciences

  2. 40 Faculty • 41 Graduate Students • Approximately 80 Undergraduate Students

  3. Applied Mathematics Statistics Combinatorics and Pure Math Mathematics Education Research Areas

  4. Applied 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

  5. Computational Engine Research • Modeling of flow, spray and combustion processes Prof. Franz Tanner

  6. Motivation • Health and Environmental • Sustainability • Main Objectives • Understand physical processes • Develop simulation tools • Results • Strategy to minimize fuel consumption and emissions • Multi-orifice asynchronous injection Computational Engine Research Mass fraction of an evaporating fuel spray

  7. Motivation • Spray-drying and spray-freezing • Encapsulation of nutrients • Main Objectives • Obtain desired drop size distributions • Maximize production • Modeling Challenges/Research • Complex flows and materials • Phase changes Modeling of Food Sprays Air-assisted atomization of a nutriose liquid spray

  8. Simulation of flow of complex fluids • Collaborations with ETH-Zurich and University of Tennessee Prof. Kathleen Feigl

  9. Examples/Applications • Emulsions, foams, polymer blends • Foods, plastics, pharmaceuticals • Goals • Understand process-microstructure- rheology relationship • Design processes to optimize product properties • Research • Multidisciplinary approach • Combine modeling, simulation and experiments Simulation of Fluid Systems Simulated deformation of a fluid droplet March 2008 Computing Initiative

  10. Simulation of Fluid Systems Droplet deforming in supercritical shear flow Droplet deforming in supercritical elongational flow

  11. Ph.D. – Duke • Joined MTU Fall 2008 • Research Interests • Scientific Computing • Modeling/Simulation • Mathematical Biology • CFD Wenjun Ying, Asst. Prof.

  12. Space-time adaptive mesh refinement • Multi-scale adaptive modeling of electrical dynamics in the heart Simulation of Cardiac Dynamics Simulation of wave propagation in a virtual dog heart

  13. Beating heart Droplet deformation Multiphase flows Other free-boundary or moving interface problems Cartesian Grid Method Grid lines not aligned with complex domain boundary

  14. Ph.D. – Louisiana Tech • Post-doc – Harvard/MIT • Joined MTU Fall 2008 • Research Interests • Computational biology • Cluster and classification algorithms • Software application development Le (Adam) Zhang, Asst. Prof.

  15. Performing multi-scale, multi-resolution hybrid cancer modelling • Regression analysis, multivariate analysis Simulation of Brain Cancer Progression Brain Cancer Cell Simulation of Cancer Progression

  16. Simulate bio-heat transfer by finite difference method Inverse heat convection problem Simulation of Hyperthermia in Skin Cancer Treatment Skin Cell Structure Treatment Simulation

  17. Statistics 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 –Maldonado March 2008 Computing Initiative

  18. Population studies for moose, wolves and sharp-tail grouse in U.P. • Aerial Observation Prof. Tom Drummer

  19. Moose survey conducted at 500 ft altitude over 1600 sq. mile area • Model developed to yield probability of sighting animals

  20. Ph.D. – Texas A&M University • Statistical Methodology and Analysis of Data • Functional Data Analysis • Non parametric Methods • Linear and Mixed Models • Multivariate Analysis Yolanda Munoz-Maldonado, Asst. Prof.

  21. Ganglioside Profiles Analysis • Detect differences in brains of young and old rats • Differences found in locus coeruleus of young rats which may affect sleep regulation

  22. 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 analysis

  23. Statistical Genetics Group • 5 Faculty • 2 Post – docs • 9 PhD Students • Support from NIH and NSF

  24. Statistical Genetics Group • Sixteen Members • 5 faculty • 2 post-docs • 9 PhD Students • Supported by 4 NIH Grants • Total funding of over $1 million

  25. Statistical Genetics Group Group Aims • 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

  26. Statistical Genetics • Prof. Quiying Sha • PhD Student Elena Kasyanova

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