Applied Mathematics

1
Department of Mathematical Sciences

• Applied Mathematics
• Computational Engine Research F. Tanner
• Simulation of Food Sprays F. Tanner
• Multiphase Fluid Systems K. Feigl
• Cardiac Dynamics W. Ying
• Statistical Genetics Group
• Q. Sha, R. Jiang, J. Dong, S. Zhang, H. Chen

March 2008
Computing Initiative
2
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
March 2008
Computing Initiative
3
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
March 2008
Computing Initiative
4
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
5
Simulation of Fluid Systems
Droplet deforming in supercritical shear flow
Droplet deforming in supercritical elongational
flow
March 2008
Computing Initiative
6
Simulation of Cardiac Dynamics

• Wenjun Ying
• Ph.D. Math Duke University
• Post-doc Biomedical Eng. Duke University
• Modeling electrical dynamics in the heart using
  adaptive meshes

Simulation of Dog Heart
March 2008
Computing Initiative
7
Statistical Genetics Group

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

March 2008
Computing Initiative
8
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

March 2008
Computing Initiative