Fractional Diffusion and Medium Heterogeneity

Autor(en)

Vittoria Sposini, Silvia Vitali, Paolo Paradisi, Gianni Pagnini

Abstrakt

In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a power-law heterogeneity. Within the framework of the continuous time random walk, the heterogeneity of the medium is represented by the selection, at any jump, of a different time-scale for an exponential survival probability. The resulting process is a non-Markovian non-Gaussian random walk. In particular, for a power-law distribution of the time-scales, the resulting random walk corresponds to a time-fractional diffusion process. We relates the power-law of the medium heterogeneity to the fractional order of the diffusion. This relation provides an interpretation and an estimation of the fractional order of derivation in terms of environment heterogeneity. The results are supported by simulations.

Organisation(en)

Computergestützte Physik und Physik der Weichen Materie

Externe Organisation(en)

Consiglio Nazionale delle Ricerche, Universität Potsdam, Basque Center for Applied Mathematics, Ikerbasque Basque Foundation for Science

Seiten

275-286

Anzahl der Seiten

12

DOI

https://doi.org/10.1007/978-3-030-69236-0_14

Publikationsdatum

2021

Peer-reviewed

Ja

ÖFOS 2012

103029 Statistische Physik, 101019 Stochastik

Schlagwörter

ASJC Scopus Sachgebiete

Computational Mechanics, Numerical Analysis, Agricultural and Biological Sciences (miscellaneous), Physics and Astronomy (miscellaneous), Fluid Flow and Transfer Processes, Computational Mathematics, Industrial and Manufacturing Engineering, Applied Mathematics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/449960cc-4f55-4b22-8d90-2688717a9fdf