Dr. Dai’s research interests lie in nonlinear partial differential equations, applied analysis, and numerical analysis, with applications in physical, biological and materials sciences. Specific areas include:
- Network formation in amphiphilic mixtures with applications to lipid bilayer evolution and morphology in polymer electrolyte materials
- Domain coarsening and self similarity in materials science, phase transitions and thin films
- Free boundary problems
Dr. Hadji’s research focuses on modeling physical phenomena in fluid mechanics and solidification.
Dr. Halpern’s research interests are in applied mathematics, fluid dynamics and scientific computing. He is particularly interested in developing theoretical models to simulate and analyze nonlinear physical phenomena primarily with applications in the biomedical sciences. Examples include the closure and reopening of the lung’s airways.
Dr. Rasoulzadeh’s main area of research is flow and transport modeling in highly heterogeneous subsurface formations. She is interested in analytical solutions and numerical simulation of coupled hydro-mechanical-chemical processes in porous media, such as sinkhole formation and evolution, flow and deformation in fractured/vuggy carbonate reservoirs, groundwater flow modeling in karst aquifers, particle adhesion and removal over rough surfaces.
Dr. Sidje’s research focuses on numerical methods for linear algebra and computational biology, with particular focus on numerical methods for solving the chemical master equation. Dr. Sidje is also the Associate Dean for Graduate Studies for the College of Arts and Sciences.
See Dr. Sidje’s publications on MathSciNet.
Dr. Chuntian Wang’s research focuses on:
- Nonlinear partial differential equations (PDEs) and applications. In particular, Dr. Wang’s research focuses on (1) the deterministic and stochastic Zakharov-Kuznetsov (ZK) equations and establishment of basic mathematical theorems for the initial-boundary value problem; and (2) numerical analysis for stochastic geophysical fluid models, specifically the construction of a time discrete approximation for the stochastic primitive equations of the atmosphere and oceans.
- Mathematical modeling, computation and applied analysis. Dr. Wang is currently working on projects regarding: Stochastic-statistical models of criminal behavior. Statistical agent-based residential Burglary models are improved and analyzed with the application of probability, PDE, and stochastic analysis.
Dr. Shan Zhao specializes in scientific computing and mathematical biology. He has a solid track record in developing computational tools for various interdisciplinary fields. Dr Zhao’s recent research focuses on high-order methods for solving PDEs, high-order interface and boundary treatments, protein modelling, computational biophysics, fast biomolecular simulation, and computational electromagnetics and optics. Dr. Zhao has published more than 50 journal articles, which have been cited more than 1500 times according to the Google Scholar.
Dr. Zhu’s research mainly focuses on proposing a variety of variational models for typical imaging problems as well as developing fast algorithms for those models by using augmented Lagrangian methods. Dr. Zhu’s research also investigates the application of these techniques in mathematical imaging to deal with big data problems.