Diffusion in Heterogeneous Media with Stochastic Resetting and Pauses

Ervin K. Lenzi, Luciano R. da Silva and Marcelo K. Lenzi ()
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Ervin K. Lenzi: Departamento de Física, Universidade Estadual de Maringá, Av. Colombo 5790, Maringá 87020-900, PR, Brazil
Luciano R. da Silva: National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro 22290-180, RJ, Brazil
Marcelo K. Lenzi: Departamento de Engenharia Química, Universidade Federal do Paraná, Rua Coronel Francisco Heráclito dos Santos 100, Curitiba 81531-980, PR, Brazil

Mathematics, 2025, vol. 13, issue 21, 1-9

Abstract: Diffusion in heterogeneous environments is usually governed by unusual dynamics, exhibiting sub- or superdiffusive scaling depending on the structural complexity and memory effects. In many systems, diffusing particles may alternate between periods of motion and rest, or may undergo stochastic resetting to a preferred position. While each of these mechanisms has been studied independently, their combined effect in a heterogeneous medium has been insufficiently investigated. We formulate and solve a coupled set of one dimension diffusion equations for the probability densities of moving and resting particles, accounting for space-dependent diffusivity and stochastic resetting. We obtain expressions for the probability distribution and show the behavior of the survival probability, mean-square displacement, and first-passage time. The results reveal a diverse range of behaviors with distinct diffusion regimes. One of them is obtained for small times, which can be connected to the heterogeneity present in the system, and another for intermediate times related to the intermittent process produced by the moving and pauses before the system reaches the stationary state.

Keywords: anomalous diffusion; intermittent motion; first passage time (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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