ENEA National Laboratory, Centro Ricerche Frascati, I-00044 Frascati, Rome, Italy.
Space Research Institute, Russian Academy of Sciences, 117997 Moscow, Russia.
Phys Rev E. 2018 Aug;98(2-1):022208. doi: 10.1103/PhysRevE.98.022208.
We formulate the problem of confined Lévy flight on a comb. The comb represents a sawtoothlike potential field V(x), with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law dependence V(x)∝|Δx|^{n} within the sawtooth period, followed by an abrupt drop-off to zero, after which the initial power-law dependence is reset. It is found that the Lévy flights will be confined in the sense of generalized central limit theorem if (i) the spacing between the teeth is sufficiently broad, and (ii) n>4-μ, where μ is the fractal dimension of the flights. In particular, for the Cauchy flights (μ=1), n>3. The study is motivated by recent observations of localization-delocalization of transport avalanches in banded flows in the Tore Supra tokamak and is intended to devise a theory basis to explain the observed phenomenology.
我们提出了在梳齿上受限 Lévy 飞行的问题。梳齿代表了锯齿状的势场 V(x)，其中不对称的齿有利于在优先方向上的净输运。形状效应被建模为锯齿周期内的幂律依赖 V(x)∝|Δx|^{n}，之后急剧下降到零，之后初始幂律依赖被重置。如果 (i) 齿之间的间距足够宽，以及 (ii) n>4-μ，其中 μ 是飞行的分形维数，则发现 Lévy 飞行将在广义中心极限定理的意义上受到限制。特别是，对于 Cauchy 飞行 (μ=1)，n>3。这项研究的动机是最近在 Tore Supra 托卡马克中的带状流中观察到的输运雪崩的局部化-去局部化现象，并旨在设计一种理论基础来解释观察到的现象。
