Transcript Document

Department of
Mathematical
Sciences
• 40 Faculty
• 41 Graduate
Students
• Approximately 80
Undergraduate
Students
Research Areas
• 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
Computational Engine Research
• 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
Mass fraction of an evaporating
fuel spray
Modeling of Food Sprays
• 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
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
Simulation of Fluid Systems
•
Examples/Applications
– Emulsions, foams, polymer blends
– Foods, plastics, pharmaceuticals
•
Goals
– Understand processmicrostructure- rheology
relationship
– Design processes to optimize
product properties
•
Research
Simulated deformation of a
fluid droplet
– Multidisciplinary approach
– Combine modeling, simulation
March
Computing Initiative
and2008
experiments
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.
Simulation 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
• Droplet deformation
• Multiphase flows
• Other free-boundary or
moving interface
problems
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.
Simulation of Brain Cancer
Progression
Brain Cancer Cell
• Performing multi-scale,
multi-resolution hybrid
cancer modelling
• Regression analysis,
multivariate analysis
Simulation of Cancer
Progression
Simulation of Hyperthermia
in Skin Cancer Treatment
Skin Cell Structure
• Simulate bio-heat transfer
by finite difference
method
• Inverse heat convection
problem
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
Statistical Genetics Group
• 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
–
–
–
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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.
Non-Unimodal Level Hilbert Functions
• 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
Gorenstein 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
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