Harmonic Measure Exponents for Two-Dimensional Percolation
Harmonic Measure Exponents for Two-Dimensional Percolation
复制标题
二维渗滤的谐波测量指数
DOI：
10.1103/physrevlett.82.3940
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发表时间：
1999
影响因子：
8.6
通讯作者：
B. Duplantier
中科院分区：
文献类型：
--
作者：
B. Duplantier
考虑二维渗流集团附近的调和测度（或扩散场或静电势）。它的力矩，在可接近的外部船体上求和，呈现出多重分形谱，我精确计算过。广义维数D（n）以及MF函数f（alpha）是由广义共形不变性导出的，并且证明了它们与二维随机游动或自回避游动上的调和测度的维数相同.给出了粗糙电极反常阻抗的一个精确应用。数字检查非常出色。另一组精确的和普遍的多重分形指数，获得了n个独立的自避免行走锚定在边界的渗流集群。这些指数描述的多重分形标度行为的平均n阶矩的概率SAW逃离的随机分形边界的渗流集团在两个维度。
The harmonic measure (or diffusion field or electrostatic potential) near a percolation cluster in two dimensions is considered. Its moments, summed over the accessible external hull, exhibit a multifractal spectrum, which I calculate exactly. The generalized dimensions D(n) as well as the MF function f(alpha) are derived from generalized conformal invariance, and are shown to be identical to those of the harmonic measure on 2D random walks or self-avoiding walks. An exact application to the anomalous impedance of a rough percolative electrode is given. The numerical checks are excellent. Another set of exact and universal multifractal exponents is obtained for n independent self-avoiding walks anchored at the boundary of a percolation cluster. These exponents describe the multifractal scaling behavior of the average nth moment of the probabity for a SAW to escape from the random fractal boundary of a percolation cluster in two dimensions.