Download This PaperStochastic Simulation of Diffusion with Absorbing and Reflecting Boundary Conditions
16 Pages Posted: 5 May 2020
Date Written: January 4, 1995
Abstract
We present an algorithm for simulating diffusion of particles in the presence of absorbing or reflecting boundaries. The algorithm is based up on the exact solution of the first passage time problem for a particle to arrive at the surface of a sphere (for d=3) or disc (for d=2) after having been started in its center. The simulation steps are taken to be diffusion jumps within maximal spheres (discs) which are centered in the particle's present position and touch the nearest boundary. The use of the exact solution of the first passage time problem enables us to evaluate all kinds of probability densities without approximations or systematic errors up to any desired accuracy. The algorithm is applied to absorbing spheres (discs) in d=3 and d=2 and to reflecting discs in d=2 for regular and random positions of the spheres (discs).
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