Related papers: Resistance Calculation for an infinite Simple Cubi…
We study a model of random electric networks with Bernoulli resistances. In the case of the lattice Z^2, we show that the point-to-point effective resistance between 0 and a vertex v has a variance of order at most (log |v|)^(2/3) whereas…
Antilattices $(S;\lor, \land)$ for which the Green's equivalences $\mathcal L_{(\lor)}$, $\mathcal R_{(\lor)}$, $\mathcal L_{(\land)}$ and $\mathcal R_{(\land)}$ are all congruences of the entire antilattice are studied and enumerated.
We show how to use the lattice Green function to calculate capacitances in two dimensions with boundary conditions at infinity. It is shown how to calculate coefficients of capacitance and induction from the lattice Green function. A…
An analytical approach is developed to obtain the exact expressions for the two-point resistance, and the total effective resistance of the complete graph minus $N$ edges of the opposite vertices. These expressions are written in terms of…
A parameter free calculation of the resistivity is applied to liquid metals near the melting point ranging from weak to strong scattering limit. The method is based on length dependent resistance calculations for quasi-one dimensional…
An analytic approach is presented to developing exact expressions for the two-point resistance between arbitrary nodes on certain non-regular resistor networks. This generalises previous approaches, which only deliver results for networks…
It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.
The exact expression for the effective resistance between any two vertices of the $N$-cycle graph with four nearest neighbors $C_{N}(1,2)$, is given. It turns out that this expression is written in terms of the effective resistance of the…
In this paper we derive general relations for the band-structure of an array of quantum dots and compute its transport properties when connected to two perfect leads. The exact lattice Green's functions for the perfect array and with an…
We analyze random resistor networks through a study of lattice Green's functions in arbitrary dimensions. We develop a systematic disorder perturbation expansion to describe the weak disorder regime of such a system. We use this formulation…
We present a formulation of the determination of the impedance between any two nodes in an impedance network. An impedance network is described by its Laplacian matrix L which has generally complex matrix elements. We show that by solving…
A square lattice of mesoscopic resistors is considered. Each bond is modeled as a narrow waveguide, while junctions are sources of elastic scattering given by a scattering matrix \mathbf{S}. Symmetry and unitarity constraints are used in a…
We calculate the zero-temperature resistivity of model 3-dimensional disordered metals described by tight-binding Hamiltonians. Two different mechanisms of disorder are considered: diagonal and off-diagonal. The non-equilibrium Green…
An exact solution is presented for the resistance of an orifice in a 2D membrane separating two infinitely large conductive reservoirs and obstructed by an infinitely long cylinder. The solution is obtained by constructing a curvilinear…
We examine the formation of bound states on a generalized nonlinear impurity located at or near the beginning (surface) of a linear, tight-binding semi-infinite lattice. Using the formalism of lattice Green functions, we obtain in closed…
An expression for the Green's function (GF) of anisotropic face centered cubic lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are…
We prove undecidability and pinpoint the place in the arithmetical hierarchy for commutative action logic, that is, the equational theory of commutative residuated Kleene lattices (action lattices), and infinitary commutative action logic,…
In this paper we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent role not only in circuit theory and chemistry, but also in…
We reconsider the problem of discretising the worldsheet for the gauge-fixed Green-Schwarz superstring on a null cusp background, and present a setup which fully preserves its global $U(1)\times SU(4)$ symmetry. We discuss divergences by…
The congruence lattices of all algebras defined on a fixed finite set $A$ ordered by inclusion form a finite atomistic lattice $\mathcal E$. We describe the atoms and coatoms. Each meet-irreducible element of $\mathcal E$ being determined…