Spatially Adaptive Stochastic Numerical Methods for Intrinsic Fluctuations in Reaction-Diffusion Systems
Professor
Paul J. Atzberger
Department of Mathematics
University of California, Santa Barbara
Abstract
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.