Department of Mathematical Sciences

1
(No Transcript)
2
(No Transcript)
3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
Department of Mathematical Sciences
26

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

27
Research Areas

• Applied Mathematics
• Statistics
• Combinatorics and Pure Math
• Mathematics Education

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 2008
Computing Initiative
29

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

Prof. Franz Tanner
30
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
31
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
32

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

Prof. Kathleen Feigl
33
Simulation of Fluid Systems

• 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

Simulated deformation of a fluid droplet
March 2008
Computing Initiative
34
Simulation of Fluid Systems
Droplet deforming in supercritical shear flow
Droplet deforming in supercritical elongational
flow
35

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

Wenjun Ying, Asst. Prof.
36
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
37
Cartesian Grid Method

• Beating heart
• Droplet deformation
• Multiphase flows
• Other free-boundary or moving interface problems

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
Brain Cancer Cell

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

Simulation of Cancer Progression
40
Simulation of Hyperthermia in Skin Cancer
Treatment
Skin Cell Structure

• Simulate bio-heat transfer by finite difference
  method
• Inverse heat convection problem

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 2008
Computing 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 AM 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
Statistical Genetics Group

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

48
Statistical Genetics Group

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

49
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

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 2008
Computing Initiative
54
Combinatorics Group

• ??? Members
• ? faculty
• ? post-docs
• ? PhD Students
• Supported by ????

55

• Ph.D. Queens University Kingston
• Joined MTU Fall 2007
• Commutative Algebra

Fabrizio Zanello, Asst. Prof.
56
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

57
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

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