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25 Department of Mathematical Sciences

26 40 Faculty 41 Graduate Students Approximately 80 Undergraduate Students

27 Applied Mathematics Statistics Combinatorics and Pure Math Mathematics Education Research Areas

28 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 2008Computing Initiative

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

30 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

31 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

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

33 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 2008Computing Initiative

34 Droplet deforming in supercritical shear flow Droplet deforming in supercritical elongational flow Simulation of Fluid Systems

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

36 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

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

38 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.

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

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

41 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 2008Computing Initiative

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

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

44 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.

45 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

46 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

47 5 Faculty 2 Post – docs 9 PhD Students Support from NIH and NSF Statistical Genetics Group

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

49 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 Statistical Genetics Group

50 Statistical Genetics Prof. Quiying Sha PhD Student Elena Kasyanova

51 Development of new computational and statistical tools Primary focus is analysis and interpretation of genomic data

52 Concentration on complex human diseases Key activities –Functional gene mapping –Pedigree analysis –Genetic diversity

53 Combinatorics and Pure Math –Combinatorics – J. Bierbauer, D. Kreher, P. Merkey, V. Tonchev, M. Keranen –Commutative Algebra – F. Zanello March 2008Computing Initiative

54 ??? Members –? faculty –? post-docs –? PhD Students Supported by ???? Combinatorics Group

55 Ph.D. – Queen’s University Kingston Joined MTU Fall 2007 Commutative Algebra Fabrizio Zanello, Asst. Prof.

56 Identified in Codimension 3. h = (1, 3, 6, 10, 15, 21, 28, 27, 27, 28) Existence was long-standing open problem, and has led to several publications Non-Unimodal Level Hilbert Functions

57 Identified asymptotic lower bound for the least possible Degree 2 entry Socle degree 4 and codimension r Solved 1983 conjecture of Stanley, proved in collaboration with Juan Migliore (Notre Dame) and Uwe Nagel (U. Kentucky) f(r) ~ r (6r) 2/3 Gorenstein Hilbert Functions

58 Teaching and Instructional Resources

59 Prof. Allan Struthers Graduate Student Yejun Gong Excellent faculty accessibility

60 Dr. Ghan Bhatt teaches an introductory calculus course Typical calculus class size is ~ 50 students

61 Beth Reed uses document camera in statistics lecture Math classrooms renovated in 2006 Rooms equipped with latest audio-visual tools

62 Teaching Assistant Rachel Robertson works with a student in the Mathlab Calculus courses include laboratory component to reinforce lectures

63 Tutoring session in the Math Learning Center Walk-in assistance or appointments with regular tutors

64 Math Learning Center open 6 days per week Students teach students

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