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We study wave scattering by a finite transversal strip in a discrete square-lattice waveguide with Dirichlet boundary conditions imposed on the strip and the waveguide walls. The setting is motivated as a discrete analogue of the classical…

Mathematical Physics · Physics 2026-02-12 Elena Medvedeva , Raphael Assier , Anastasia Kisil

Nuclear data libraries (ENDF, JEFF, JENDL, CENDL, etc.) document our phenomenological knowledge of nuclear cross sections as interpreted by R-matrix theory. The R-matrix scattering model can parameterize the energy dependence of the…

Nuclear Theory · Physics 2021-06-23 Pablo Ducru , Vladimir Sobes , Gerald Hale , Mark Paris , Benoit Forget

We consider scattering theory for a pair of operators $H_0$ and $H=H_0+V$ on $L^2(M,m)$, where $M$ is a Riemannian manifold, $H_0$ is a multiplication operator on $M$ and $V$ is a pseudodifferential operator of order $-\mu$, $\mu>1$. We…

Analysis of PDEs · Mathematics 2014-08-01 Shu Nakamura

We study the scattering behavior of an anisotropic inhomogeneous Lipschitz medium at a fixed wave number, continuing our previous work [SIAM J. Math. Anal., 56(4):4834-4853, 2024] and using free boundary techniques from [arXiv:2506.22328].…

Analysis of PDEs · Mathematics 2026-03-30 Pu-Zhao Kow , Mikko Salo , Henrik Shahgholian

We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…

Analysis of PDEs · Mathematics 2020-12-16 Rémi Carles , Clément Gallo

The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…

Mathematical Physics · Physics 2019-10-23 P. Zhevandrov , A. Merzon , M. I. Romero Rodríguez , J. E. de la Paz Méndez

We study notions of isotopy and concordance for Riemannian metrics on manifolds with boundary and, in particular, we introduce two variants of the concept of minimal concordance, the weaker one naturally arising when considering certain…

Differential Geometry · Mathematics 2024-02-14 Alessandro Carlotto , Chao Li

We consider wave scattering from a system of highly contrasting resonators with time-modulated material parameters. In this setting, the wave equation reduces to a system of coupled Helmholtz equations that models the scattering problem. We…

Mathematical Physics · Physics 2024-01-05 Habib Ammari , Jinghao Cao , Erik Orvehed Hiltunen , Liora Rueff

In this note we prove a new $L^1$ criterion for the existence and completeness of the wave operators corresponding to the Laplace-Beltrami operators corresponding to two Riemannian metrics on a fixed noncompact manifold. Our result relies…

Spectral Theory · Mathematics 2024-11-06 Batu Güneysu , Maxime Marot

For analytic negatively curved Riemannian manifold with analytic strictly convex boundary, we show that the scattering map for the geodesic flow determines the manifold up to isometry. In particular one recovers both the topology and the…

Differential Geometry · Mathematics 2024-02-09 Yannick Guedes Bonthonneau , Colin Guillarmou , Malo Jézéquel

A matrix method is formulated in a Lagrangian representation for the solution of the characteristic value problem governing modes of oscillation and instability in a collisionless stellar system. The underlying perturbation equations govern…

Astrophysics · Physics 2009-11-07 Peter O. Vandervoort

Consider a compact Riemannian manifold with boundary endowed with a magnetic field. A path taken by a particle of unit charge, mass, and energy is called a magnetic geodesic. It is shown that if everything is real-analytic, the topology,…

Differential Geometry · Mathematics 2009-10-23 Pilar Herreros , James Vargo

This paper aims at providing a small-volume expansion framework for the scattering resonances of an open cavity perturbed by small particles. The induced shift of the scattering frequencies by the small particles is derived without…

Mathematical Physics · Physics 2018-10-26 Habib Ammari , Alexander Dabrowski , Brian Fitzpatrick , Pierre Millien

The spectral and scattering theory is investigated for a generalization, to scattering metrics on two-dimensional compact manifolds with boundary, of the class of smooth potentials on the Euclidean plane which are homogeneous of degree zero…

Analysis of PDEs · Mathematics 2007-05-23 Andrew Hassell , Richard B. Melrose , András Vasy

Scattering wave systems that are periodically modulated in time offer many new degrees of freedom to control waves both in spatial and frequency domains. Such systems, albeit linear, do not conserve frequency and require the adaptation of…

Applied Physics · Physics 2023-04-25 Matthieu Malléjac , Romain Fleury

Consider a compact manifold $M$ with smooth boundary $\partial M$. Suppose that $g$ and $\tilde{g}$ are two Riemannian metrics on $M$. We construct a family of metrics on $M$ which agrees with $g$ outside a neighborhood of $\partial M$ and…

Differential Geometry · Mathematics 2021-03-12 Tsz-Kiu Aaron Chow

We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on…

Spectral Theory · Mathematics 2012-11-29 Alexander Pushnitski , Alexander Volberg

Time modulation of the physical parameters offers interesting new possibilities for wave control. Examples include amplification of waves, harmonic generation and non-reciprocity, without resorting to non-linear mechanisms. Most of the…

Mathematical Physics · Physics 2025-07-25 Michaël Darche , Raphaël Assier , Sébastien Guenneau , Bruno Lombard , Marie Touboul

Non-relativistic quantum particles bounded to a curve in R^2 by attractive contact $\delta$-interaction are considered. The interval between the energy of the transversal bound state and zero is shown to belong to the absolutely continuous…

Mathematical Physics · Physics 2020-08-13 J. Dittrich

We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any…