Stochastic Analysis of Reaction-diffusion Processes

Thursday, May 16, 2013 - 3:15pm - 4:05pm
Keller 3-180
Hans Othmer (University of Minnesota, Twin Cities)
Reaction and diffusion processes are used to model chemical and biological
processes over a wide range of spatial and temporal scales. Several routes to
the diffusion process at various levels of description in time and space are
discussed and the master equation for spatially-discretized systems involving
reaction and diffusion is developed. We discuss an estimator for the appropriate
compartment size for simulating reaction-diffusion systems and introduce a
measure of fluctuations in a discretized system. We then describe a new
computational algorithm for implementing a modified Gillespie method for
compartmental systems in which reactions are aggregated into equivalence classes
and computational cells are searched via an optimized tree structure. Finally,
we discuss several examples that illustrate the issues that have to be addressed
in general systems.
MSC Code: