Infinite Network of Identical Capacitors by Green's Function

Abstract

The capacitance between arbitrary nodes in perfect infinite networks of identical capacitors is studied. We calculate the capacitance between the origin and the lattice site (l, m) for an infinite linear chain, and for an infinite square network consisting of identical capacitors using the Lattice Green's Function. The asymptotic behavior of the capacitance for an infinite square lattice is investigated for infinite separation between the origin and the site (l, m). We point out the relation between the capacitance of the lattice and the van Hove singularity of the tight-binding Hamiltonian. This method can be applied directly to other lattice structures.

On the perturbation of a uniform tiling with resistors

“…Applying the Ohm's and Kirchhoff's law's one can write the current at each lattice point in one unit cell as   12 (0, 0, 0) R = 0.334, 11 (1, 0, 0) R = 0.2128, 12 (1, 0, 0) R = 0.4167, 11 (1,1, 0) R = 0.2465, 11 (1,1,1) R = 0.2739, 22 (1, 0, 0) R = 0.5414…”

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].…”

Resistance calculation of the decorated centered cubic networks: Applications of the Green's function

“…18 Based on this approach, several interesting applications were presented. [9][10][11][12][13][14][15][16][17][18] The problem of computing the two-node resistance on finite resistor networks was considered by Wu. 19 He obtained a general expression for the resistance of a finite resistor graph in terms of the eigenvalues and the eigenvectors of the Kirchhoff matrix.…”