Fractional Diffusion and Medium Heterogeneity
- Author(s)
- Vittoria Sposini, Silvia Vitali, Paolo Paradisi, Gianni Pagnini
- Abstract
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(s)
- Computational and Soft Matter Physics
- External organisation(s)
- Institute of Genetics and Biophysics "Adriano Buzzati-Traverso", CNR, Universität Potsdam, Basque Center for Applied Mathematics, Ikerbasque Basque Foundation for Science
- Pages
- 275-286
- No. of pages
- 12
- DOI
- https://doi.org/10.1007/978-3-030-69236-0_14
- Publication date
- 2021
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103029 Statistical physics, 101019 Stochastics
- Keywords
- ASJC Scopus subject areas
- 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
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/449960cc-4f55-4b22-8d90-2688717a9fdf