Theory of resistor networks: the two-point resistance
Theory of resistor networks: the two-point resistance
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DOI：
10.1088/0305-4470/37/26/004
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发表时间：
2004-07-02
期刊：
影响因子：
--
通讯作者：
Wu, FY
中科院分区：
文献类型：
--
作者：
Wu, FY
电阻网络中任意两节点间的电阻可由网络的拉普拉斯矩阵的特征值和特征函数求得。本文推导了一维、二维和三维规则晶格在各种边界条件下的两点电阻的显式公式，包括莫比乌斯带和克莱因瓶的边界条件。重点是有限大小的格。我们还推导出求和和产品的身份，可用于分析在两个和更高的维度大尺寸的扩展。
The resistance between two arbitrary nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulae for two-point resistances are deduced for regular lattices in one, two and three dimensions under various boundary conditions including that of a Mobius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyse large-size expansions in two and higher dimensions.