Multifractal properties of the harmonic measure on Koch boundaries in two and three dimensions

被引：23
|
作者：
Grebenkov, DS [1 ]
Lebedev, AA
Filoche, M
Sapoval, B
机构：
[1] Ecole Polytech, CNRS, Phys Mat Condensee Lab, F-91128 Palaiseau, France
[2] Ecole Normale Super, CNRS, Ctr Math & Leurs Applicat, F-94140 Cachan, France
来源：
PHYSICAL REVIEW E | 2005年 / 71卷 / 05期
关键词：
D O I：
10.1103/PhysRevE.71.056121
中图分类号：
O35 [流体力学]; O53 [等离子体物理学];
学科分类号：
070204 ; 080103 ; 080704 ;
摘要：
The multifractal properties of the harmonic measure on quadratic and cubic Koch boundaries are studied with the help of a new fast random walk algorithm adapted to these fractal geometries. The conjectural logarithmic development of local multifractal exponents is guessed for regular fractals and checked by extensive numerical simulations. This development allows one to compute the multifractal exponents of the harmonic measure with high accuracy, even with the first generations of the fractal. In particular, the information dimension in the case of the concave cubic Koch surface embedded in three dimensions is found to be slightly higher than its value D-1=2 for a smooth boundary.
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页数：11
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