{"title":"Universal superdiffusion of random walks in media with embedded fractal networks of low diffusivity","authors":"Fábio D. A. Aarão Reis, Vaughan R. Voller","doi":"10.1103/physreve.110.l022102","DOIUrl":null,"url":null,"abstract":"Diffusion in composite media with high contrasts between diffusion coefficients in fractal sets of inclusions and in their embedding matrices is modeled by lattice random walks (RWs) with probabilities <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>p</mi><mo><</mo><mn>1</mn></mrow></math> of hops from fractal sites and 1 from matrix sites. Superdiffusion is predicted in time intervals that depend on <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi></math> and with diffusion exponents that depend on the dimensions of matrix <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>(</mo><mi>E</mi><mo>)</mo></math> and fractal <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>(</mo><msub><mi>D</mi><mi>F</mi></msub><mo>)</mo></math> as <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>ν</mi><mo>=</mo><mn>1</mn><mo>/</mo><mo>(</mo><mn>2</mn><mo>+</mo><msub><mi>D</mi><mi>F</mi></msub><mo>−</mo><mi>E</mi><mo>)</mo></mrow></math>. This contrasts with the nonuniversal subdiffusion of RWs confined to fractal media. Simulations with four fractals show the anomaly at several time decades for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>p</mi><mo>≲</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> and the crossover to the asymptotic normal diffusion. These results show that superdiffusion can be observed in isotropic RWs with finite moments of hop length distributions and allow the estimation of the dimension of the inclusion set from the diffusion exponent. However, displacements within single trajectories have normal scaling, which shows transient ergodicity breaking.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physreve.110.l022102","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Diffusion in composite media with high contrasts between diffusion coefficients in fractal sets of inclusions and in their embedding matrices is modeled by lattice random walks (RWs) with probabilities of hops from fractal sites and 1 from matrix sites. Superdiffusion is predicted in time intervals that depend on and with diffusion exponents that depend on the dimensions of matrix and fractal as . This contrasts with the nonuniversal subdiffusion of RWs confined to fractal media. Simulations with four fractals show the anomaly at several time decades for and the crossover to the asymptotic normal diffusion. These results show that superdiffusion can be observed in isotropic RWs with finite moments of hop length distributions and allow the estimation of the dimension of the inclusion set from the diffusion exponent. However, displacements within single trajectories have normal scaling, which shows transient ergodicity breaking.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.