相关论文: Capacitance between Two Points in an Infinite Grid

In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface. Second order accuracy for the first derivative is obtained as well. The method is…

Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the conductivity is indeed…

The exterior solution for an arbitrary charged, massive source, is studied as a static deviation from the Reissner-Nordstr\o m metric. This is reduced to two coupled ordinary differential equations for the gravitational and electrostatic…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

Motivated by the problem of finding resistances among vertices in a hypercube, we derive exact expressions, generating functions, and asymptotic expansions for these resistances, then study the combinatorial interpretations of the…

Output impedances are inherent elements of power sources in the electrical grids. In this paper, we give an answer to the following question: What is the effect of output impedances on the inductivity of the power network? To address this…

A closed form of the electrostatic potential of a homogeneously charged cube is derived by integration. The exact result is compared with multipole expansions for the exterior and interior of the cube. The electrostatic potential of a…

A symmetric variant of Shannon capacity is defined and computed.

In this paper we study the problem of generation of dependent random variables, known as the "coordination capacity" [4,5], in multiterminal networks. In this model $m$ nodes of the network are observing i.i.d. repetitions of $X^{(1)}$,…

A certain two-dimensional supersymmetric gauge theory is argued to satisfy a relation that promotes the Zamolodchikov tetrahedron equation to an infrared duality between two quantum field theories. Solutions of the tetrahedron equation with…

Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum…

We develop bounds on the capacity of wireless networks when the traffic is non-uniform, i.e., not all nodes are required to receive and send similar volumes of traffic. Our results are asymptotic, i.e., they hold with probability going to…

We present a generalized algorithm based on a spherical harmonics expansion method for efficient computation of the three-dimensional gravitational potential on a multi-patch grid in spherical geometry. Instead of solving for the…

This paper considers a two-hop interference network, where two users transmit independent messages to their respective receivers with the help of two relay nodes. The transmitters do not have direct links to the receivers; instead, two…

We present a sharp collocated projection method for solving the immiscible, two-phase Navier-Stokes equations in two- and three-dimensions. Our method is built using non-graded adaptive quadtree and octree grids, where all of the fluid…

This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators…

The deformed supersymmetric sine-Gordon model, obtained through known deformation of the corresponding potential, is found to be quasi-integrable, like its non-supersymmetric counterpart, which was observed earlier. The system expectedly…

The problem of measuring similarity of graphs and their nodes is important in a range of practical problems. There is a number of proposed measures, some of them being based on iterative calculation of similarity between two graphs and the…

We consider two laminar incompressible flows coupled by the continuous law at a fixed interface. We approach the system by one that satisfies a friction Navier law, and we show that when the friction coefficient goes to infinity, the…

Combinatorial characterisations are obtained of symmetric and anti-symmetric infinitesimal rigidity for two-dimensional frameworks with reflectional symmetry in the case of norms where the unit ball is a quadrilateral and where the…