Related papers: Current distribution in an infinite plate
The electric and magnetic fields are investigated on the basis of quantum vacuum. The analysis of the electromagnetic energy and force indicates that an electric field is a polarized distribution of the vacuum virtual dipoles, and that a…
A novel form of the current potential, a mathematical tool for the design of stellarators and stellarator coils, is developed. Specifically, these are current potentials with a finite-element-like basis, called \textit{current potential…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
We evaluate the electrostatic potential and the electrostatic field created by a point charge and an arbitrarly oriented electrical dipole placed near a grounded perfectly conducting sphere. Induced surface charge distributions as well as…
Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. In the absence of spin-orbit scattering, the conductivity shows universal weak localization correction. In the presence of…
By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…
Spatial distributions in current, temperature, state-of-charge and degradation across the plane of large format lithium-ion battery pouch cells can significantly impact their performance, especially at high C-rates. In this paper, a method…
We have studied a finite two-dimensional electron system exposed to a normal nonhomogeneous magnetic field of a chess configuration. Using the conformal mapping method we obtain an exact analytical solution for the electric field…
A widely used stochastic plate equation is the classical plate equation perturbed by a term of It\^o's integral. However, it is known that this equation is not exactly controllable even if the controls are effective everywhere in both the…
We study the conductance of a quantum wire in the presence of weak electron-electron scattering. In a sufficiently long wire the scattering leads to full equilibration of the electron distribution function in the frame moving with the…
A free boundary problem modeling a microelectromechanical system (MEMS) consisting of a fixed ground plate and a deformable top plate is considered, the plates being held at different electrostatic potentials. It couples a second order…
We consider the model for the distribution of a long homopolymer in a potential field. The typical shape of the polymer depends on the temperature parameter. We show that at a critical value of the temperature the transition occurs from a…
Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…
We consider operators with random potentials on graphs, such as the lattice version of the random Schroedinger operator. The main result is a general bound on the probabilities of simultaneous occurrence of eigenvalues in specified distinct…
Radiation of relativistic charged particles in a system of randomly spaced plates is considered in the paper. It is shown that for large number of plates ($N \gg 1$), in the wavelength range $\lambda \ll l\ll L$ (where $l$ is the photon…
The old problem of a singular, inverse square potential in nonrelativistic quantum mechanics is treated employing a field-theoretic, functional renormalization method. An emergent contact coupling flows to a fixed point or develops a limit…
We derive a general expression for the low-temperature current distribution in a two-dimensional electron gas, subjected to a perpendicular magnetic field and in a confining potential that varies slowly on the scale of the magnetic length…
The Modern Theory of Polarization, which rigorously defines the spontaneous electric polarization of a periodic solid and provides a recipe for its computation in electronic structure codes, transformed our understanding of ferroelectricity…
The effect of an oscillating electric field normal to a metallic surface may be described by an effective potential. This induced potential is calculated using semiclassical variants of the random phase approximation (RPA). Results are…
The distribution of string tension on the contact line between an ideal string and a massive pulley is a frequently-discussed but incompletely-posed problem that confronts students in introductory mechanics. We highlight ambiguities in the…