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Applied Mathematics Colloquium

Friday, October 19, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Differential and Cross-Diffusion Effects on Pattern Formation in Reaction-Diffusion Systems

Irving Epstein

Chemistry Department

Brandeis University

Waltham, MA

Abstract

A reverse microemulsion consisting of nanometer diameter droplets of water containing the reactants of the Belousov-Zhabotinsky oscillating chemical reaction dispersed in oil displays a remarkable variety of stationary and moving patterns, including Turing structures, ordinary and antispirals, segmented waves and spatiotemporal chaos. These observations raise a number of interesting physical, chemical and mathematical questions. I will show examples of patterns and discuss two alternative mechanisms by which they may arise, one involving diffusion of different species at very different rates, the other via cross-diffusion, whereby gradients in the concentration of one species influence the rate of diffusion of another species. Possible links to pattern formation in biological, and even social, systems will be noted.