Bidimensional Deterministic Model for Diffusion and Settling of Particles

Stephanie Esmeralda Velázquez Pérez; Eric Campos-Cantón; Guillermo Huerta Cuellar; Héctor Eduardo Gilardi Velázquez

doi:10.3390/axioms12020191

Bidimensional Deterministic Model for Diffusion and Settling of Particles

Journal

Axioms

ISSN

2075-1680

Date Issued

2023

Author(s)

Stephanie Esmeralda Velázquez Pérez

Eric Campos-Cantón

Guillermo Huerta Cuellar

Héctor Eduardo Gilardi Velázquez

Facultad de Ingeniería - CampAGS

Type

text::journal::journal article

DOI

10.3390/axioms12020191

URL

https://scripta.up.edu.mx/handle/20.500.12552/3671

Abstract

In this paper, we present a study of the diffusion properties of a deterministic model for settling particles in two displacement dimensions. The particularities of the novel deterministic model include the generation of Brownian motion and a two-dimensional displacement model without stochastic processes, which are governed by a set of six differential equations. This model is a piecewise system consisting of subsystems governed by jerk equations. With this model, we can consider different conditions of diffusion in both the dimensions and size of the space where the particles are dispersed. The settling time versus the dispersion medium and its size, as well as the average settling time and its probability distributions, are analyzed. Furthermore, the probability distributions for the settling location are presented for the changes in the diffusion parameters and space size. Finally, the basins of attraction for the settling positions are shown as a function of each dimensional diffusion parameter and for the medium size.