Two discrete models for diffusion-controlled reactions

C.A. CONDAT; Y. POSADA

San Juan, Puerto Rico

Conferencia; Third Intenational Conference on Stochastic Structural Dynamics; 1995

Two related models for diffusion-controlled reactions were formulated and solved using random walk methods on partially absorbing lattices. Model I describes how an intervening reaction caused by a contaminant modifies the reaction rate of interest by taking out the mobile reactant before it reaches the main reaction site. This intervening reaction is modeled with an absorption constant assigned to every interior site. Model II, the “sliding door” model, describes the fluctuations in the ionic currents flowing through cell membranes using a random walk representation for the channel wall motion. While in model I the long-time form of the reaction rates is exponential (absorption-dominated), in the sliding-door model it follows a t-3/2 power law indicating the asymptotic predominance of long-path walks inside a non-absorbing region.