Brownian dynamic simulation by reticular mapping matrix method

TL;DR

This paper introduces a novel reticular mapping matrix method for simulating two-dimensional Brownian motion of particles in restricted fluids, validated by comparing displacement and velocity with theoretical diffusion values.

Contribution

The paper presents a simple, matrix-based numerical approach for simulating Brownian particles, incorporating statistical rules for movement and validation against theoretical diffusion coefficients.

Findings

Root mean square displacement matches theoretical diffusion.

Simulation results align with expected Brownian velocities.

Model effectively captures particle behavior in restricted environments.

Abstract

This work proposes a method for the two-dimensional simulation of Brownian particles in a fluid with restrictions. The method is based on simple numerical rules between two matrices. One of the matrix represent the identification of all particles over which are adapted statistics rules for particles movement, the results are mapped over other matrix which represent the particles positions. The rules for the movement are established by a statistic mechanism allowing assign random or non-random movement direction. The same probably of movement for each direction for each time step is assumed, in order to be agreed with the physics conditions of Brownian movement in a two dimensional network. The root mean square displacement of all particles was calculated in a large number of simulations, together with the translational velocity of particles in order to compare with theoretical values of diffusion coefficient and the validation of model. Also, the time duration for some simulations vs. the number of particles and concentration was calculated.