A Huygens principle for diffusion and anomalous diffusion in spatially extended systems
A Huygens principle for diffusion and anomalous diffusion in spatially extended systems
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DOI：
10.1073/pnas.1217926110
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发表时间：
2013-05-21
影响因子：
11.1
通讯作者：
Melbourne, Ian
中科院分区：
文献类型：
--
作者：
Gottwald, Georg A.;Melbourne, Ian
我们提出了关于各向异性和各向同性介质的混沌空间扩展系统中扩散行为的普遍观点。对于各向异性系统，强混沌会导致扩散行为（带漂移的布朗运动），弱混沌会导致超扩散行为（带漂移的 Levy 过程）。对于各向同性系统，漂移项消失，强混沌再次导致布朗运动。我们建立了各向同性介质中弱混沌系统的非线性惠更斯原理的存在性，其中动力学在偶数空间维度中表现出扩散行为，并在奇数空间维度中表现出超扩散行为。
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 (Levy 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.