Related papers: Infinite circuits are easy. How about long ones?
Finding the equivalent resistance of an infinite ladder circuit is a classical problem in physics. We expand this well-known challenge to new classes of network topologies, in which the unit cells are much more entangled together. The exact…
In a recent article, we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance, inductive…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
From the theory of quantum $LC$ circuits with discrete charge, and {\em semiclassical} considerations, we obtain approximate energy eigenvalues, depending on the parameter $q_e^2/h$. Next, we include electrical resistance for the quantum…
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…
In this paper we introduce the notion of nonlinear resistance forms. We define a $1$-parameter family of nonlinear resistance metrics and show their additivity over serial circuits. Moreover, we prove that resistance forms and…
This is a reminder that an infinite series can be defined other than as the limit of a sequence of finite series. An example is provided in which a circuit element comprised of an infinite series of resistors has negative resistance.
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…
In this paper, we study the computational complexity of the commutative determinant polynomial computed by a class of set-multilinear circuits which we call regular set-multilinear circuits. Regular set-multilinear circuits are commutative…
Except for Koshy who devotes seven pages to applications of Fibonacci Numbers to electric circuits, most books and the Fibonacci Quarterly have been relatively silent on applications of graphs and electric circuits to Fibonacci numbers.…
The theme of this article is a "reciprocity" between bounded up-down paths and bounded alternating sequences. Roughly speaking, this ``reciprocity" manifests itself by the fact that the extension of the sequence of numbers of paths of…
In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This…
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…
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…
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…
Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…
Circuits and extended formulations are classical concepts in linear programming theory. The circuits of a polyhedron are the elementary difference vectors between feasible points and include all edge directions. We study the connection…
The motivation for this paper is to study the complexity of constant-width arithmetic circuits. Our main results are the following. 1. For every k > 1, we provide an explicit polynomial that can be computed by a linear-sized monotone…
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 structural analysis, i.e., the investigation of the differential-algebraic nature, of circuits containing simple elements, i.e., resistances, inductances and capacitances is well established. However, nowadays circuits contain all sorts…