Random walks on finite lattices with traps

We consider dissipative processes involving both chemical reaction and physical diffusion in systems for which the influence of boundaries and system size on the dynamics cannot be neglected. We report the results of Monte Carlo simulations on an irreversible reaction in a confined system subject to two sorts of finite boundary conditions. The problem is posed in such a way as to take maximal advantage of two earlier studies: Montroll's work on random walks on $d$-dimensional periodic lattices with traps, and the work of Sanders, Ruijgrok, and ten Bosch on random walks on two-dimensional finite lattices with traps. Our results are used to discuss the concept of reduction of dimensionality as introduced by Adam and Delbrück in their study of biological diffusion processes.