ArticleProceedings of the National Academy of Sciences of the United States of America2013
A Huygens principle for diffusion and anomalous diffusion in spatially extended systems.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Limiting stochastic processes of shift-periodic dynamical systems.Royal Society open science · 2019Article
- Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.Proceedings. Mathematical, physical, and engineering sciences · 2017Article
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2 authors.
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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.
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