Analytic Solutions for Some Reaction-Diffusion Scenarios

Motivated currently by the problem of coalescence of receptor clusters in mast cells in the general subject of immune reactions, and formerly by the investigation of exciton trapping and sensitized luminescence in molecular systems and aggregates, we present analytic expressions for survival probabilities of moving entities undergoing diffusion and reaction on encounter. Results we provide cover several novel situations in simple 1-d systems as well as higher-dimensional counterparts along with a useful compendium of such expressions in chemical physics and allied fields. We also emphasize the importance of the relationship of discrete sink term analysis to continuum boundary condition studies.