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Department of Mathematical Sciences

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Department of Mathematical Sciences

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Department of Mathematical Sciences

- 40 Faculty
- 41 Graduate Students
- Approximately 80 Undergraduate Students

Applied Mathematics

Statistics

Combinatorics and Pure Math

Mathematics Education

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

- Computational Engine Research
- Modeling of flow, spray and combustion processes

Prof. Franz Tanner

- 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

- 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

- Simulation of flow of complex fluids
- Collaborations with ETH-Zurich and University of Tennessee

Prof. Kathleen Feigl

- 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

Simulation of Fluid Systems

Droplet deforming in supercritical

shear flow

Droplet deforming in supercritical

elongational flow

- Ph.D. – Duke
- Joined MTU Fall 2008
- Research Interests
- Scientific Computing
- Modeling/Simulation
- Mathematical Biology
- CFD

Wenjun Ying, Asst. Prof.

- 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

Beating heart

Droplet deformation

Multiphase flows

Other free-boundary or moving interface problems

Cartesian Grid Method

Grid lines not aligned with complex domain boundary

- 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.

- Performing multi-scale, multi-resolution hybrid cancer modelling
- Regression analysis, multivariate analysis

Simulation of Brain Cancer Progression

Brain Cancer Cell

Simulation of Cancer Progression

Simulate bio-heat transfer by finite difference method

Inverse heat convection problem

Simulation of Hyperthermia in Skin Cancer Treatment

Skin Cell Structure

Treatment Simulation

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

- Population studies for moose, wolves and 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 of sighting animals

- 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.

- 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

- 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

- 5 Faculty
- 2 Post – docs
- 9 PhD Students
- Support from NIH and NSF

Statistical Genetics Group

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

- Supported by 4 NIH Grants
- Total funding of over $1 million

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

- Statistical Genetics
- Prof. Quiying Sha
- PhD Student Elena Kasyanova

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

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

Combinatorics and Pure Math

Combinatorics – J. Bierbauer, D. Kreher, P. Merkey, V. Tonchev, M. Keranen

Commutative Algebra – F. Zanello

March 2008

Computing Initiative

Combinatorics Group

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

- Supported by ????

- Ph.D. – Queen’s University Kingston
- Joined MTU Fall 2007
- Commutative Algebra

Fabrizio Zanello, Asst. Prof.

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

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

Teaching and Instructional Resources

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

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

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

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

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

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