Brownian Dynamics Simulation by Reticular Mapping Matrix Method

Abstract

In this chapter, we present a method for the two-dimensional simulation of Brownian particles in a fluid with restrictions. The method combines characteristics of the cellular automata and Monte Carlo approaches, and is based on simple numerical rules that use two matrices for controlling the movement of the particles. One matrix serves to identify all particles on which statistical rules are adopted for their motion. This information is then mapped onto another matrix representing the positions of particles. The motion of the particles is governed by a statistical assignation mechanism, which allows to define either a random or non-random movement direction. The same probability of movement in each direction is assumed at each time step and for each particle to simulate the physical behaviour of Brownian movement in a two-dimensional network. For model validation, the predicted root-mean-square displacement of all particles along with their translational velocities are compared to theoretical values of the diffusion coefficient. The dependence of the computational time on the number of particles and concentration is calculated for the models.