Related papers: Scattering theory with a natural regularization: R…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…
A distorted-wave version of the renormalisation group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wave function satisfies a Schroedinger equation…
Scattering from large, open cavity structures is of importance in a variety of electromagnetic applications. In this paper, we propose a new well conditioned integral equation for scattering from general open cavities embedded in an…
We explore wave-mechanical scattering in two spatial dimensions assuming that the corresponding potential is invariant under linear symmetry transforms such as rotations, reflections and coordinate exchange. Usually the asymptotic…
We consider the focusing wave equation with energy supercritical nonlinearity in dimension four. We prove that any radial solution that remains bounded in the critical Sobolev space is global and scatters to free waves as $t \to \pm…
In this work we consider a wide range of energy critical wave equation in 3-dimensional space with radial data. We are interested in exterior scattering phenomenon, in which the asymptotic behaviour of a solutions $u$ to the non-linear wave…
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…
The relation between the R- and P-matrix approaches and the harmonic oscillator representation of the quantum scattering theory (J-matrix method) is discussed. We construct a discrete analogue of the P-matrix that is shown to be equivalent…
The superposition principle is fundamental to linear wave systems, ensuring that their physical behaviour is independent of the chosen basis representation. While this principle underpins many analytical techniques, including modal…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
We consider the scattering of time-harmonic plane waves by a compactly supported inhomogeneous scattering obstacle governed by the Helmholtz equation. Given far field observations of the scattered fields corresponding to plane wave incident…
We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal…
Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae…
The paper is concerned with the three-dimensional electromagnetic scattering from a large open rectangular cavity that is embedded in a perfectly electrically conducting infinite ground plane. By introducing a transparent boundary…
The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the…
Various regularization methods have been used to compute the self-force acting on a static particle in a static, curved spacetime. Many of these are based on Hadamard's two-point function in three dimensions. On the other hand, the…
Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of…
In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…
In this article we prove a regularization by noise phenomenon for the energy-critical and mass-critical nonlinear Schr\"odinger equations. We show that for any deterministic data, the probability that the corresponding solution exists…