Spatially Adaptive Stochastic Numerical Methods for Intrinsic Fluctuations in Reaction-Diffusion Systems

Professor Paul J. Atzberger
Department of Mathematics
University of California, Santa Barbara


We shall discuss reaction diffusion systems arising in the study of biological systems where concentration fluctuations play an important role. This includes the study of cell signaling, cell polarization, and directed cell motility through detection of shallow concentration gradients. To study these systems we shall formulate stochastic partial differential equations to model intrinsic fluctuations in the concentration fields associated with these processes. A number of challenges arise in approximating the solutions of such SPDE's. Further issues arise when considering non-periodic domains with complex geometries which arise naturally in modeling biological systems. We shall also discuss an approach to obtain spatially adaptive numerical discretization of SPDE's, which specifically address how to discretize stochastic terms at coarse-refined interfaces. In the spirit of the seminar we shall try to make the talk accessible to a wide audience with ample time for informal discussion.