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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. Research Areas. Applied Mathematics Computational Engine Research – F. Tanner

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Presentation Transcript
slide26
40 Faculty
  • 41 Graduate Students
  • Approximately 80 Undergraduate Students
research areas
Applied Mathematics

Statistics

Combinatorics and Pure Math

Mathematics Education

Research Areas
slide28
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

slide29
Computational Engine Research
  • Modeling of flow, spray and combustion processes

Prof. Franz Tanner

slide30
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

slide31
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

slide32
Simulation of flow of complex fluids
  • Collaborations with ETH-Zurich and University of Tennessee

Prof. Kathleen Feigl

slide33
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

slide34

Simulation of Fluid Systems

Droplet deforming in supercritical

shear flow

Droplet deforming in supercritical

elongational flow

slide35
Ph.D. – Duke
  • Joined MTU Fall 2008
  • Research Interests
    • Scientific Computing
    • Modeling/Simulation
    • Mathematical Biology
    • CFD

Wenjun Ying, Asst. Prof.

slide36
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

slide37
Beating heart

Droplet deformation

Multiphase flows

Other free-boundary or moving interface problems

Cartesian Grid Method

Grid lines not aligned with complex domain boundary

slide38
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.

slide39
Performing multi-scale, multi-resolution hybrid cancer modelling
  • Regression analysis, multivariate analysis

Simulation of Brain Cancer Progression

Brain Cancer Cell

Simulation of Cancer Progression

slide40
Simulate bio-heat transfer by finite difference method

Inverse heat convection problem

Simulation of Hyperthermia in Skin Cancer Treatment

Skin Cell Structure

Treatment Simulation

slide41
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

slide42
Population studies for moose, wolves and sharp-tail grouse in U.P.
  • Aerial Observation

Prof. Tom Drummer

slide43
Moose survey conducted at 500 ft altitude over 1600 sq. mile area
  • Model developed to yield probability of sighting animals
slide44
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.

slide45
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
slide46
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
statistical genetics group
Statistical Genetics Group
  • 5 Faculty
  • 2 Post – docs
  • 9 PhD Students
  • Support from NIH and NSF
slide48

Statistical Genetics Group

  • Sixteen Members
    • 5 faculty
    • 2 post-docs
    • 9 PhD Students
  • Supported by 4 NIH Grants
  • Total funding of over $1 million
slide49

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
slide50
Statistical Genetics
  • Prof. Quiying Sha
  • PhD Student Elena Kasyanova
slide51
Development of new computational and statistical tools
  • Primary focus is analysis and interpretation of genomic data
slide52
Concentration on complex human diseases
  • Key activities
    • Functional gene mapping
    • Pedigree analysis
    • Genetic diversity
slide53
Combinatorics and Pure Math

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

Commutative Algebra – F. Zanello

March 2008

Computing Initiative

slide54

Combinatorics Group

  • ??? Members
    • ? faculty
    • ? post-docs
    • ? PhD Students
  • Supported by ????
slide55
Ph.D. – Queen’s University Kingston
  • Joined MTU Fall 2007
  • Commutative Algebra

Fabrizio Zanello, Asst. Prof.

slide56
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

slide57
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

slide59
Prof. Allan Struthers
  • Graduate Student Yejun Gong
  • Excellent faculty accessibility
slide60
Dr. Ghan Bhatt teaches an introductory calculus course
  • Typical calculus class size is ~ 50 students
slide61
Beth Reed uses document camera in statistics lecture
  • Math classrooms renovated in 2006
  • Rooms equipped with latest audio-visual tools
slide62
Teaching Assistant Rachel Robertson works with a student in the Mathlab
  • Calculus courses include laboratory component to reinforce lectures
slide63
Tutoring session in the Math Learning Center
  • Walk-in assistance or appointments with regular tutors
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