电阻均匀平铺
Uniform tiling with electrical resistors
摘要：
得到了任意电阻无限点阵结构上任意两结点间的电阻，该结构是一个周期性的空间平铺。我们的一般方法是基于与网络相关联的拉普拉斯矩阵的格点格林函数。我们提出了几个非平凡的例子来展示我们的方法是多么有效。导出显式电阻公式，它表明，Kagomé，切割和装饰的晶格可以映射到三角形和正方形的电阻晶格。我们的工作可以推广到凝聚态物理中的随机行走问题或电子动力学。
英文摘要：
The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Green's function of the Laplacian matrix associated with the network. We present several non-trivial examples to show how efficient our method is. Deriving explicit resistance formulas it is shown that the Kagomé, the diced and the decorated lattice can be mapped to the triangular and square lattice of resistors. Our work can be extended to the random walk problem or to electron dynamics in condensed matter physics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
