Asymptotic expansion for the resistance between two maximally separated nodes on an M by N resistor network
Asymptotic expansion for the resistance between two maximally separated nodes on an M by N resistor network
复制标题
DOI：
10.1103/physreve.82.011125
复制
发表时间：
2010-07-19
影响因子：
2.4
通讯作者：
Huang, Ming-Chang
中科院分区：
文献类型：
--
作者：
Izmailian, N. Sh.;Huang, Ming-Chang
本文分析了Wu [J.]在自由、周期和圆柱边界条件下得到的矩形电阻网络中任意音符间电阻的精确公式。理论物理。[j].中国农业科学，2004,17(4)。在此基础上，应用Ivashkevich、Izmailian和Hu [J]的算法。理论物理。[A 35, 5543(2002)]推导出M x N电阻矩形网络上两个最大分离节点之间电阻的精确渐近展开式，其中电阻r和s在两个空间方向上。我们的结果是1/s r -M x N(r,s) = c(rho)ln s + c(0)(rho,xi) + Sigma(∞)(p=1)c(2p)(rho,xi)/ s -p，其中s = MN, rho = r/s,xi = M/N。展开式中的所有系数都用解析函数表示。在自由和周期边界条件下引入有效纵横比xi(eff) =根rho xi，在圆柱边界条件下引入有效纵横比xi(eff) =根rho xi/2，并证明在变换xi(eff)-> 1/xi（eff）下，所有有限大小的校正项都是不变的。
We analyze the exact formulas for the resistance between two arbitrary notes in a rectangular network of resistors under free, periodic and cylindrical boundary conditions obtained by Wu [J. Phys. A 37, 6653 (2004)]. Based on such expression, we then apply the algorithm of Ivashkevich, Izmailian, and Hu [J. Phys. A 35, 5543 (2002)] to derive the exact asymptotic expansions of the resistance between two maximally separated nodes on an M x N rectangular network of resistors with resistors r and s in the two spatial directions. Our results is 1/s R-M x N(r,s) = c(rho)ln S + c(0)(rho,xi) + Sigma(infinity)(p=1)c(2p)(rho,xi)/S-p with S = MN, rho = r/s and xi = M/N. The all coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio xi(eff) = root rho xi for free and periodic boundary conditions and xi(eff) = root rho xi/2 for cylindrical boundary condition and show that all finite-size correction terms are invariant under transformation xi(eff)-> 1/xi(eff).