论文标题
二维电阻网络的有效电阻
Effective resistances of two dimensional resistor networks
论文作者
论文摘要
我们研究了两个维电阻网络的行为，该网络具有有限尺寸和不同种类的晶格几何形状（矩形，六边形和三角形）的行为。我们通过让网络元件重复$ l_x $ times $ x $ - 方向和$ y $ $ $ $ $ times来构建网络。我们研究网络上的有效电阻（$ r_ \ mathrm {eff} $）$ l_x $和$ l_y $之间的关系。对于具有矩形几何形状的网络而言，该行为是简单而直观的，但是，对于其他几何形状而言，它变得不平凡。我们发现$ r_ \ mathrm {eff} $取决于所有三个研究网络中的比率$ l_x/l_y $。我们还通过实验检查了小型网络大小的数值结果的一致性。
We investigate the behavior of two dimensional resistor networks, with finite sizes and different kinds (rectangular, hexagonal, and triangular) of lattice geometry. We construct the network by having a network-element repeat itself $L_x$ times in $x$-direction and $L_y$ times in the $y$-direction. We study the relationship between the effective resistance ($R_\mathrm{eff}$) of the network on dimensions $L_x$ and $L_y$. The behavior is simple and intuitive for a network with rectangular geometry, however, it becomes non-trivial for other geometries which are solved numerically. We find that $R_\mathrm{eff}$ depends on the ratio $L_x/L_y$ in all the three studied networks. We also check the consistency of our numerical results experimentally for small network sizes.
