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Description of diffusive and propagative behavior on fractals

The known properties of diffusion on fractals are reviewed in order to give a general outlook of these dynamic processes. After that, we propose a description developed in the context of the intrinsic metric of fractals, which leads us to a differential equation able to describe diffusion in real fractals in the asymptotic regime. We show that our approach has a stronger physical justification than previous works on this field. The most important result we present is the introduction of a dependence on time and space for the conductivity in fractals, which is deduced by scaling arguments and supported by computer simulations. Finally, the diffusion equation is used to introduce the possibility of reaction-diffusion processes on fractals and analyze their properties. Specifically, an analytic expression for the speed of the corresponding travelling fronts, which can be of great interest for application purposes, is derived

© Physical Review E, 2004, vol. 69, núm. 3, p. 031115

American Physical Society

Author: Campos, Daniel
Méndez López, Vicenç
Fort, Joaquim
Date: 2004
Abstract: The known properties of diffusion on fractals are reviewed in order to give a general outlook of these dynamic processes. After that, we propose a description developed in the context of the intrinsic metric of fractals, which leads us to a differential equation able to describe diffusion in real fractals in the asymptotic regime. We show that our approach has a stronger physical justification than previous works on this field. The most important result we present is the introduction of a dependence on time and space for the conductivity in fractals, which is deduced by scaling arguments and supported by computer simulations. Finally, the diffusion equation is used to introduce the possibility of reaction-diffusion processes on fractals and analyze their properties. Specifically, an analytic expression for the speed of the corresponding travelling fronts, which can be of great interest for application purposes, is derived
Format: application/pdf
ISSN: 1539-3755 (versió paper)
1550-2376 (versió electrònica)
Document access: http://hdl.handle.net/10256/7619
Language: eng
Publisher: American Physical Society
Collection: Reproducció digital del document publicat a: http://dx.doi.org/10.1103/PhysRevE.69.031115
Articles publicats (D-F)
Is part of: © Physical Review E, 2004, vol. 69, núm. 3, p. 031115
Rights: Tots els drets reservats
Subject: Fractals
Equacions de reacció-difusió
Reaction-diffusion equations
Title: Description of diffusive and propagative behavior on fractals
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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