A Huygens principle for diffusion and anomalous diffusion in spatially extended systems.
basic_science · Level V
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- Record sourced from PubMed, PMID 23653481.
- Also identified by DOI 10.1073/pnas.1217926110 and PMC identifier 3666731.
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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.