Hopping Conduction and Bacteria: Transport in Hostile Reaction-Diffusion Systems

Andrew Missel, Department of Physics, University of Illinois at Urbana-Champaign

The growth of microbial populations near sea floor vents, the spread of disease in corals, and the seasonal variation of the distribution of phytoplankton populations in the oceans are difficult biological problems to model because spatial heterogeneity is of fundamental significance to transport and reaction kinetics. The purpose of this project is to study a generalization of a simple model for how genes spread in a population, when reproduction may only occur in small patches ("oases"), and where organisms die and compete for resources everywhere else. We present a calculation of the average time taken for a population to traverse such an environment, and the fluctuations about this average time. The problem turns out to be related to hopping conduction in doped semiconductors.