Infinite simple 3D cubic lattice of identical resistors (two missing bonds)

Abstract

An infinite regular three-dimensional network is composed of identical resistors each of resistance R joining adjacent nodes. What is the equivalent resistance between the lattice site i r r and the lattice j r r 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.

Design and analysis of two layers RLC network of rectangular topology by wave concept iterative process method

“…The implementation of the iterative process consists in establishing a recurrence relationship between Equations (17) and (24). These equations sum up the boundary conditions and the topology of the lattice in the spatial domain and the periodicity properties in the spectral domain.…”

The two-point capacitance of infinite triangular and honeycomb networks

“…Using equations (1), (3), (5), (7) and (9), writing r 2 − r 1 = a + mb and changing the variables k • a = θ 1 , k • b = θ 2 , the Green's function for the triangular lattice and the capacitance between the origin and node ( , m) can be obtained as:…”

“…Several techniques have been developed to study this problem, such as superposition of current distribution [1,2], random walks [3,4], lattice Green's function [5]. The later is the most suitable approach because it can be employed for any infinite perfect lattice structure of resistors [6,7] and perturbed lattices cases [8][9][10][11][12][13].…”

Remarks on the Lattice Green Function for the Anisotropic Face Centered Cubic Lattice

“…Nowadays, GF is one of the most important concepts in many branches of physics, as many quantities in solid state physics can be expressed in terms of the LGF. In the following there are some examples: statistical model of ferromagnetism such as the Ising model [5], the Heisenberg model [6], spherical model [7], random walk theory [8,9], diffusion [10], band structure [11], and in recent * corresponding author; e-mail: drjasad@yahoo.com years it becomes an important tool in analyzing infinite electric networks [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”