Results for Nonlinear Diffusion Equations with Stochastic Resetting-Reference-Cited by-同舟云学术

Results for Nonlinear Diffusion Equations with Stochastic Resetting

Published:2023-12-12 Issue:12 Volume:25 Page:1647
ISSN:1099-4300
Container-title:Entropy
language:en
Short-container-title:Entropy

Author:

Lenzi Ervin K.¹²^ORCID,Zola Rafael S.³^ORCID,Rosseto Michely P.¹^ORCID,Mendes Renio S.⁴^ORCID,Ribeiro Haroldo V.⁴^ORCID,Silva Luciano R. da²⁵^ORCID,Evangelista Luiz R.⁴⁶^ORCID

Affiliation:

1. Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil

2. National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro 22290-180, RJ, Brazil

3. Departamento de Física, Universidade Tecnológica Federal do Paraná, Apucarana 86812-460, PR, Brazil

4. Departamento de Física, Universidade Estadual de Maringá, Maringa 87020-900, PR, Brazil

5. Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil

6. Istituto dei Sistemi Complessi (ISC–CNR), Via dei Taurini, 19, 00185 Rome, Italy

Abstract

In this study, we investigate a nonlinear diffusion process in which particles stochastically reset to their initial positions at a constant rate. The nonlinear diffusion process is modeled using the porous media equation and its extensions, which are nonlinear diffusion equations. We use analytical and numerical calculations to obtain and interpret the probability distribution of the position of the particles and the mean square displacement. These results are further compared and shown to agree with the results of numerical simulations. Our findings show that a system of this kind exhibits non-Gaussian distributions, transient anomalous diffusion (subdiffusion and superdiffusion), and stationary states that simultaneously depend on the nonlinearity and resetting rate.

Funder

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brasil

CNPq

National Council for Scientific and Technological Development, CNPq

National Institute of Science and Technology Complex Fluids

Publisher

MDPI AG

Subject

General Physics and Astronomy

Link

https://www.mdpi.com/1099-4300/25/12/1647/pdf

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