SGER: Pattern Formation in Chemical Systems with Nonstandard Diffusion

Southern Methodist University, Dallas TX

Investigators

Abstract

Werner Horsthemke of Southern Methodist University is supported by a Small Grant for Exploratory Research (SGER) from the Theoretical and Computational Chemistry program to begin a project aimed at developing theoretical methods to understand pattern formation in systems with nonstandard diffusion. The research is employing both analytical and numerical methods and is focusing on pattern formation in systems where Brownian motion is not an adequate model for transport. Two types of nonstandard transport are being investigated, anomalous diffusion and transport with inertia. Anomalous diffusion, where the mean square displacement of a particle does not grow linearly with time, occurs in a wide variety of media, such as porous or fractal media, turbulent flows, and living cells. Another type of deviation from standard diffusive motion occurs in systems of particles where inertial effects in the transport cannot be neglected, as for example in dilute gases, turbulent flows, and the motion of microorganisms. Such systems can be modelled by reaction-transport equations. The research is determining the conditions for pattern-forming instabilities and elucidating the mechanisms of pattern selection. The research will in particular seek to identify phenomena where the behavior of reaction-transport systems differs qualitatively from that of reaction/diffusion systems. Such phenomena will allow an unambiguous experimental assessment of the importance of inertia or anomalous diffusion in applications. The work is having a broader impact on other fields of science such as biology and geology where nonstandard diffusion occurs frequently.