相关论文: Capacitance between Two Points in an Infinite Grid
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
As ASIC supply voltages approach one volt, the source-impedance goals for power distribution networks are driven ever lower as well. One approach to achieving these goals is to add decoupling capacitors of various values until the desired…
This paper introduces the covering path problem on a grid (CPPG) which finds the cost-minimizing path connecting a subset of points in a grid such that each point that needs to be covered is within a predetermined distance of a point from…
Capacitors are typically connected together in one of two configurations: either in series, or in parallel. Here we study a capacitor-within-capacitor (CWC). Simulations and experiments indicate that the overall capacitance of the…
Scattering off a potential is a fundamental problem in quantum physics. It has been studied extensively with amplitudes derived for various potentials. In this article, we explore a setting with no potentials, where scattering occurs off a…
Classical communication capacity of a channel can be enhanced either through a device called a 'quantum switch' or by putting the channel in a quantum superposition. The gains in the two cases, although different, have their origin in the…
We propose a non grid-based interpolation scheme based on the information from the data collected from the vicinity of the query point. As a non-grid-based interpolation, the data points can be distributed randomly in a small region, and…
In this paper we deal with the notion of the effective impedance of AC networks consisting of resistances, coils and capacitors. Mathematically such a network is a locally finite graph whose edges are endowed with complex-valued weights…
When inclusions with extreme conductivity (insulator or perfect conductor) are closely located, the gradient of the solution to the conductivity equation can be arbitrarily large. And computation of the gradient is extremely challenging due…
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
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…
An ill-posed problem of synthesis of the Pierce electrodes for a cylindrical beam with a polygonal cross-section is considered. It is assumed that a beam of charged particles is extracted from a space-charge-limited planar diode and the…
A behavior of a two qubit system coupled by the electric capacitance has been studied quantum mechanically. We found that the interaction is essentially the same as the one for the dipole-dipole interaction; i.e., qubit-qubit coupling of…
We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…
We present a simple algorithm to select multivariate interpolation stencil with a Cartesian grid. We show its applicability by using this algorithm in the embedded boundary method for solving the elliptic interface problem.
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…
We study the dissipativity of linear infinite-dimensional systems with respect to a prescribed quadratic supply rate functional. We characterize this property via an operator inequality that also yields the system's dissipation rate. We…
It is shown that the resistance between the origin and any lattice point (l,m,n) in an infinite perfect Simple Cubic (SC) is expressed rationally in terms of the known value of G0(0,0,0). The resistance between arbitrary sites in a SC is…
The capacitance of arbitrarily shaped objects is reformulated in terms of the Neumann-Poincar\'{e} operator. Capacitance is simply the dielectric permittivity of the surrounding medium multiplied by the area of the object and divided by the…
The behavior of the magnetic potential near a point charge (fluxon) located at a curved regular boundary surface is shown to be essentially different from that of a volume point charge. In addition to the usual inverse distance singularity,…