Related papers: Resistance Calculation for an infinite Simple Cubi…
A review of the theoretical approach for calculating the resistance between two arbitrary lattice points in an infinite square lattice (perfect and perturbed cases)is carried out using the Lattice Green's Function. We show how to calculate…
We calculate the resistance between two arbitrary grid points of several infinite lattice structures of resistors by using lattice Green's functions. The resistance for $d$ dimensional hypercubic, rectangular, triangular and honeycomb…
We express the equivalent resistance between the origin and any other lattice site in an infinite Body Centered Cubic (BCC) network consisting of identical resistors each of resistance R rationally in terms of known values and . The…
The resistance between arbitrary nodes of infinite networks of resistors is studied when the network is perturbed by removing one bond from the perfect lattice. A connection is made between the resistance and the lattice Green's function of…
The equivalent resistance between the origin and the lattice site (2n,0,0), in an infinite Face Centered Cubic network consisting from identical resistors each of resistance R, has been expressed in terms of the complete elliptic integral…
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…
We calculate the effective resistance between two arbitrary lattice points on infinite strip of the triangular lattice (ladder network) in one dimension, and on infinite modified square and Union Jack lattices in two dimensions, and on…
The equivalent resistance between the origin and any other lattice site, in an infinite Face Centered Cubic network consisting from identical resistors, has been expressed rationally in terms of the known value and . The asymptotic behavior…
The capacitance between the origin and any other lattice site in an infinite square lattice of identical capacitors is studied. The method is generalized to infinite Simple Cubic (SC) lattice. We make use of the superposition principle and…
The capacitance between any two arbitrary lattice sites in an infinite square lattice is studied when one bond is removed (i.e. perturbed). A connection is made between the capacitance and the Lattice Green's Function of the perturbed…
The effective resistance between any two nodes in a perturbed resistor network is determined by removing multiple bonds from an infinite resistor lattice. We have developed an efficient method for calculating the Green operator of the…
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…
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…
We study infinite resistor networks perturbed by line defects, in which the resistances are periodically modified along a single line. Using the Sherman-Morrison identity applied to the reciprocal-space representation of the lattice Green's…
A mapping between random walk problems and resistor network problems is described and used to calculate the effective resistance between any two nodes on an infinite two-dimensional square lattice of unit resistors. The superposition…
A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence…
The resistance between arbitrary two nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulas for two-point resistances are deduced for…
We perfect the recursion-transform method to be a complete theory, which can derive the general exact resistance between any two nodes in a resistor network with several arbitrary boundaries. As application of the method, we give a profound…
An explicit formula for the resistance between two nodes in a network with a non-symmetric Laplacian matrix L is obtained. This is of great advantage e.g. in electronic circuit fault analysis, where non-linear systems have to be solved…
Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic…