Related papers: Current distribution in an infinite plate
We consider the class of integer rectifiable currents without boundary satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.
This paper proposes a new analysis of graph using the concept of electric potential, and also proposes a graph simplification method based on this analysis. Suppose that each node in the weighted-graph has its respective potential value.…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
We examine electrolyte systems confined between two parallel, grounded metal plates using a field-theoretic approach truncated at one-loop order. For symmetric electrolytes, the density distribution of the ions is non-uniform, with a…
Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…
Several applications require spatial distributions of the incident electric field that maximize the electric field at a focal point for a given input power. The field distributions are derived for various optical systems in a direct way…
We consider free electrons in rectangular quantum dots, with either hard wall boundary conditions or anharmonic confinement. In both cases, due to finite size effects, a homogeneous electric field applied along one of the rectangular axis…
Many methods for computing electronic correlation effects at finite temperature are related to many-body perturbation theory in the grand-canonical ensemble. In most applications, however, the average number of electrons is known rather…
We study the statistics of level widths of a quantum dot with extended contacts in the absence of time-reversal symmetry. The widths are determined by the amplitude of the wavefunction averaged over the contact area. The distribution…
We address a class of systems for which the solution to an H-infinity optimal control problem can be given on a very simple closed form. In fact, both the control law and optimal performance value are explicitly given. The class of systems…
We study the distribution of the $n$-th energy level for two different one-dimensional random potentials. This distribution is shown to be related to the distribution of the distance between two consecutive nodes of the wave function. We…
The classical electromagnetic friction of a charged particle moving with prescribed constant velocity parallel to a planar imperfectly conducting surface is reinvestigated. As a concrete example, the Drude model is used to describe the…
We use covariance and dimensional analysis to find expressions for the discontinuity of the potential and normal electric field across a flat surface with multipolar charge surface density in vacuum.
The problem of a conducting checkerboard has recently been solved via an elliptic function whose argument is another elliptic function. The behavior of the fields and currents near a vertex of the checkerboard pattern can be discussed by…
We report results of a numerical study of noninteracting electrons moving in two dimensions, in the presence of a random potential and a random magnetic field for a sequence of finite sizes, using topological properties of the wave…
We consider the stability in the inverse problem consisting in the determination of an electric potential $q$, appearing in a Dirichlet initial-boundary value problem for the wave equation $\partial_t^2u-\Delta u+q(x)u=0$ in an unbounded…
We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures.…
We study long range propagation of electromagnetic waves in random waveguides with rectangular cross-section and perfectly conducting boundaries. The waveguide is filled with an isotropic linear dielectric material, with randomly…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic…