I am currently working on transport in disordered reaction-diffusion systems. I am studying a system which consists of diffusing particles which can compete with each other for resources (2A→A), give birth (A→2A), and die (A→0). Systems such as these have been studied extensively, and, with minor modifications, have been used to model everything from animal coat patterns to the distribution of plankton populations. However, most studies have not dealt with the case in which the reaction rates for the various processes vary with position. In our model, most of space is hostile to growth--that is, the A→0 process occurs there--and there are only a few patches--or oases--in this desert which admit growth. We want know how a population traverses this landscape, and to do so we have had to employ tools from the theory of hopping conduction and first passage percolation.
A. Missel and K. Dahmen, "Hopping conduction and bacteria: Transport in disordered reaction-diffusion systems," Phys. Rev. Lett. 100, 058301 (2007)