无序电阻网络中的最大电流研究

本文证明,一个无序电阻网络中的平均最大电流可标度为(JnL)^α,这里L为网络的线度,而幂指数α不仅与维数和电导率之比有关,而且还与缺陷的端角β有关。这个结论是从分析含通道的漏斗形缺陷中的电位和电流分布得到的。文中还对Machta等人和DBL理论预言过的,当σ₂→0时幂指数α的差异,提出一个定性的解释。 关键词：

INVESTIGATION OF THE LARGEST CURRENT IN A RANDOM RESISTOR NETWORK

In this paper it is shown that the expected largest current in a random resistor network can be scaled as (InL)^α , where L is the size of the network and the exponent a not only depends on dimension and the ratio of two conductances in the network, but also depends on the value of vertex angle β of the defects remarkably. This result follows from an analysis of the funnel configuration with a channel in it. Here we have also suggested a qualitative explanation concerning the difference in the values of exponent α when σ₂→0 of Machta et al. and DEL theory.