Related papers: Low-frequency scattering defined by the Helmholtz …
The interaction between radiation and superconductors is explored in this paper. In particular, the calculation of a plane standing wave scattered by an infinite cylindrical superconductor is performed by solving the Helmholtz equation in…
We present theoretical calculations of the ensemble-averaged (a.k.a. effective or coherent) wavefield propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that…
We study environmental echoes induced by a weak potential barrier outside a Schwarzschild black hole. In the low-finesse limit, the time domain response is governed by a sequence of transient wave packets formed by finite round-trip…
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium…
Electromagnetic wave scattering by many parallel infinite cylinders is studied asymptotically as $a\to 0$. Here $a$ is the radius of the cylinders. It is assumed that the points $\hat{x}_m$ are distributed so that…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
In the context of providing a mathematical framework for the propagation of ultrasound waves in a random multiscale medium, we consider the scattering of classical waves (modeled by a divergence form scalar Helmholtz equation) by a bounded…
We investigate elliptic fractional equations in the whole space, involving zero order perturbations of the fractional Laplacian $(-\Delta)^s$, $0<s<1$. Our main objective is to determine appropriate radiation conditions at infinity that…
This paper focuses on the well-posedness (or lack thereof) of three-dimensional time-harmonic wave propagation problems modeled by the Helmholtz equation. It is well-known that if the problem is set in bounded domain with Dirichlet boundary…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
In this paper, we investigate wave scattering by a pair of closely spaced inclusions embedded in a homogeneous medium, characterized by a high contrast physical parameters. The system is modeled by the two-dimensional Helmholtz equation. We…
A reduction of the Maxwell's system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the…
Electromagnetic waves propagate in the Schwarzschild spacetime like in a nonuniform medium with a varying refraction index. A fraction of the radiation scatters off the curvature of the geometry. The energy of the backscattered part of an…
Limited-diffraction beams are a class of waves that may be localized in space and time. Theoretically, these beams are propagation invariant and can propagate to an infinite distance without spreading. In practice, when these beams are…
The Helmholtz equation is a prototypical model for time-harmonic wave propagation. Numerical solutions become increasingly challenging as the wave number $k$ grows, due to the equation's elliptic yet noncoercive character and the highly…
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…
Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic…
A propagator for the one dimensional time-dependent Schr\"odinger equation with an asymmetric rectangular potential is obtained using the multiple-scattering theory approach. It allows for the consideration of the reflection and…
The purpose of these lectures is to give an accessible and self contained introduction to quantum scattering theory in one dimension. Part A defines the theoretical playground, and develops basic concepts of scattering theory in the time…
The propagation of incoherent elastic energy in a three-dimensional solid due to the scattering by many, randomly placed and oriented, pinned dislocation segments, is considered in a continuum mechanics framework. The scattering mechanism…