Results for Nonlinear Diffusion Equations with Stochastic Resetting.

Autor: Lenzi EK; Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil.; National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro 22290-180, RJ, Brazil., Zola RS; Departamento de Física, Universidade Tecnológica Federal do Paraná, Apucarana 86812-460, PR, Brazil., Rosseto MP; Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil., Mendes RS; Departamento de Física, Universidade Estadual de Maringá, Maringa 87020-900, PR, Brazil., Ribeiro HV; Departamento de Física, Universidade Estadual de Maringá, Maringa 87020-900, PR, Brazil., Silva LRD; National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro 22290-180, RJ, Brazil.; Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil., Evangelista LR; Departamento de Física, Universidade Estadual de Maringá, Maringa 87020-900, PR, Brazil.; Istituto dei Sistemi Complessi (ISC-CNR), Via dei Taurini, 19, 00185 Rome, Italy.
Jazyk: angličtina
Zdroj: Entropy (Basel, Switzerland) [Entropy (Basel)] 2023 Dec 12; Vol. 25 (12). Date of Electronic Publication: 2023 Dec 12.
DOI: 10.3390/e25121647
Abstrakt: 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.
Databáze: MEDLINE
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