Related papers: On the electrical current distributions for the ge…
A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
The L\'evy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas, for example in economics it is used to model financial market…
Kirchhoff's laws offer a general, straightforward approach to circuit analysis. Unfortunately, use of the laws becomes impractical for all but the simplest of circuits. This work presents a novel method of analyzing direct current resistor…
We extract local current distributions from interatomic currents calculated using a fully relativistic quantum mechanical scattering formalism by interpolation onto a three-dimensional grid. The method is illustrated with calculations for…
Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier…
A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that…
Electron conductivity is an important material property that can provide a wealth of information about the underlying system. Especially, the response of the conductivity with respect to electromagnetic fields corresponds to various…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
We develop a semiclassical density functional theory in the context of quantum dots. Coulomb blockade conductance oscillations have been measured in several experiments using nanostructured quantum dots. The statistical properties of these…
Using a TE/TM decomposition for an angular plane-wave spectrum of free random electromagnetic waves and matched boundary conditions, we derive the probability density function for the energy density of the vector electric field in the…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
A fourth-order Schr\"{o}dinger equation for the description of charge transport in semiconductors in the ballistic regime is proposed with the inclusion of non-parabolic effects in the dispersion relation in order to go beyond the simple…
Using the transfer matrix technique, we investigate the propagation of electron through a two dimensional disordered sample. We find that the spatial distribution of electrons is homogeneous only in the limit of weak disorder (diffusive…
In this paper, we investigate the analyticity of a class of exponential Dirichlet series. We then explicitly determine the coefficients of their power series decomposition and provide an estimate for the remainder. As an application, we…
An alternative method to the density matrix formalism for the derivation of general expressions of the interaction of polarized atoms with polarized photons and electrons is presented. The expression for the cross-section describing the…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
Power-law noises abound in nature and have been observed extensively in both time series and spatially varying environmental parameters. Although, recent years have seen the extension of traditional stochastic partial differential equations…
Fluctuation theorems have a very special place in the study of non equilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen Fluctuation Theorem which is in terms of the distribution of…
In this paper we study the distributions of the number of real solutions to the power flow equations over varying electrical parameters. We introduce a new monodromy and parameter homotopy continuation method for quickly finding all…