Hailiang's  Research Computational  & Applied  Math

Applied partial diff. eqns.  structure  & dynamics  Computational methods,   accuracy  & stability  Numerical simulation,       efficiency & applications

In recent years PDE based modeling has become an important research area in applied mathematics. In our group, we develop and analyze new PDE models and numerical techniques with cutting edge research problems in physical sciences. Our main research interests are kinetic modeling of small scale phenomena, analysis of macro-micro models and high resolution numerical methods.

Research Interests

a. Modeling--kinetic description of small scale phenomena

Ø Polymers

Ø Fluid-particle flows

Ø Collective behavior of biological agents

b. Analysis -- well-posedness and solution behavior for mathematical models

Ø Analysis of macro-micro models for complex fluids

Ø Critical thresholds in hyperbolic balance laws

c. Computation-- development of high resolution numerical methods

Ø Level set methods for capturing statistics in high-frequency waves

Ø The Direct Discontinuous Galerkin (DDG) methods for higher order PDEs 

Ø The alternating evolution (AE) methods for quasilinear and nonlinear PDEs

Research grants

• 2013-2017, NSF-DMS (PI): Recovery of high frequency wave fields, kinetic theory of photons and entropy satisfying methods.

• 2009-2013, NSF-DMS (PI): Geometrically based kinetic approach to multi-scale problems

• 2008-2011, NSF-DMS (PI), FRG (Focused Research Group) Collaborative Research: Kinetic Description of Multi-scale Phenomena: Modeling, Theory And Computation

• 2005-2008, NSF-DMS (PI), Multi-scale Wave Dynamics in Nonlinear Balance Laws

• 2005-2006, Ames Lab of DOE (PI), High Frequency Wave Propagation and Geometric Motion

• 2003-2005, PSI Grant (Co-PI), System Biology: Genome, Genetic Network, and Evolution

• 2001-2004, NSF-DMS (Co-PI), Critical Threshold Phenomena in Nonlinear Balance Laws

Publications

• Listed by years of publication
• Google Scholar
• Refereed  via Math Reviews

Research Projects:

• Hyperbolic Conservation Laws,  Stability of Discrete and Viscous Shock Profiles
• Relaxation Dynamics, Scaling Limits and Convergence of Relaxation Schemes,
• Critical Threshold Phenomena  in Nonlinear Balance Laws,
• High Frequency Wave Propagation and Geometric Motion, 
• Orientation,  Dynamics  of  Crystalline Polymers  and Phase Transition Phenomena 
• Multi-scale Wave Dynamics

Funding Agencies

• NSF

• DOE

Last Revision: April 20, 2010.