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A Huygens principle for diffusion and anomalous diffusion in spatially extended systems.

ABSTRACT: We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behavior in odd space dimensions.

SUBMITTER: Gottwald GA

PROVIDER: S-EPMC3666731 | biostudies-literature | 2013 May

REPOSITORIES: biostudies-literature

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A Huygens principle for diffusion and anomalous diffusion in spatially extended systems.

Gottwald Georg A GA Melbourne Ian I

Proceedings of the National Academy of Sciences of the United States of America 20130507 21

We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media w ...[more]

PMID: 23653481

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