ELECTRICAL RESPONSE MATRIX OF A REGULAR 2n-GON

被引：1

作者：

Blair-Stahn, Nathaniel D. ^{[1
]}

Wilson, David B. ^{[2
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Microsoft Res, Redmond, WA 98052 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 06期

关键词：

CRITICAL PERCOLATION;

D O I：

10.1090/S0002-9939-09-09734-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider a unit-resistive plate in the shape of a regular polygon with 2n sides, in which even-numbered sides are wired to electrodes and odd-numbered sides are insulated. The response matrix, or Dirichlet-to-Neumann map, allows one to compute the currents. owing through the electrodes when they are held at specified voltages. We show that the entries of the response matrix of the regular 2n-gon are given by the differences of cotangents of evenly spaced angles, and we describe some connections with the limiting distributions of certain random spanning forests.

引用

页码：2015 / 2025

页数：11