个人简介

About Me: I am a Professor at Institute of Natural Sciences and School of Mathematics, Shanghai Jiaotong University. I am an applied mathematician working on mathematical biology and numerical methods. In mathematical biology, I am mainly interested in mathematical models of chemotaxis and cancer evolution. For numerical methods, my main focus is on various kinds of kinetic and diffusion equations. Chemotaxis Chemotaxis is the central mechanism for bacteria/microorganism to find their favorite environment. In multicellular organisms, chemotaxis is critical for development and health. Along with the understanding of more biological details of chemotaxis, its mathematical models become more and more complete and complex. There exist classical chemotaxis models at different scales: the Keller-Segel model proposed in the 70’s last century, the velocity jump model given in the 90s, and the pathway-based kinetic model proposed at the beginning of this century. I wrote a review paper (in Chinese) about different mathematical aspects of chemotaxis models [36]. I try to mathematically understand chemotaxis models at different scales. More Cancer modeling Cancer modeling I mainly work on two kinds of cancer modeling. One is continuous models of solid cancerous cells multiplication, the other is for white blood cell production. Continuous models consider the population level ’geometric’ motion of tumor, in which interesting mathematical problems arise. For example, strong nonlinearity, traveling wave solutions, front instability, etc. My recent interest is to apply these mechanical models to radiation oncology. Blood cancer is a typical stem cell-driven cancer. Mathematical models help to understand how blood cell formation is regulated. A quantitative understanding of stem cell self-renewal and differentiation provides insights into the mechanisms of cancerogenesis and cancer therapy. More Asymptotic preserving methods Asymptotic preserving methods Asymptotic preserving (AP) schemes can use unresolved meshes to capture the right solutions. They have been successfully applied to many applications. I mainly focus on AP schemes for linear radiative transport equations, nonlinear radiation magnetohydrodynamics systems and their associated diffusion equations. Topics include problems with boundary and interface layers, schemes that are not only AP in space but also in time and frequency, strongly anisotropic diffusion equations and all-mach number flows. More Other numerical methods Other numerical methods Designing other numerical methods is motivated in my course of studying biological systems or radiation magnetohydrodynamics systems. For example, traveling waves or periodic traveling waves can be observed in a lot of biological systems. It is important to get the right traveling wave speed and the traveling profile. This motivates the relaxation method for traveling wave and periodic traveling wave simulations. When I looked at the tumor growth model, I found it is difficult to get the right front propagation speed of diffusion equation with strong nonlinearity, which motivates the study of numerical methods for nonlinear degenerate diffusion equation.