Infinite Simple 3D Cubic Lattice of Identical Resistors (Two Missing Bonds)

TL;DR

This paper investigates the electrical resistance between two points in an infinite 3D resistor lattice with two missing bonds, analyzing different cases and their asymptotic behavior for large distances.

Contribution

It provides a detailed analysis of the equivalent resistance in a 3D resistor network with missing bonds, including numerical calculations and asymptotic behavior insights.

Findings

Equivalent resistance varies with bond removal cases

Numerical values for specific configurations are provided

Asymptotic resistance behavior is characterized for large distances

Abstract

An infinite regular three-dimensional network is composed of identical resistors each of resistance joining adjacent nodes. What is the equivalent resistance between the lattice site and the lattice site, when two bonds are removed from the perfect network? Three cases are considered here, and some numerical values are calculated. Finally, the asymptotic behavior of the equivalent resistance is studied for large distances between the two sites.