English
Related papers

Related papers: A priori bounds for elastic scattering by determin…

200 papers

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…

Analysis of PDEs · Mathematics 2018-12-24 Yu Zhao , Guanghui Hu , Baoqiang Yan

We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modelling transmission of acoustic waves through an anisotropic penetrable obstacle. We first prove a well-posedness result and a frequency-explicit bound…

Analysis of PDEs · Mathematics 2022-09-20 Théophile Chaumont-Frelet , Euan A. Spence

This paper investigates the possible scattering and non-scattering behavior of an anisotropic and inhomogeneous Lipschitz medium at a fixed wave number and with a single incident field. We connect the anisotropic non-scattering problem to a…

Analysis of PDEs · Mathematics 2024-07-10 Pu-Zhao Kow , Mikko Salo , Henrik Shahgholian

Existence and uniqueness of the scattering solutions is proved for a class of bounded rough obstacles which is much larger than the class of Lipschitz obstacles. Integral equations method is not used. The approach is based on the…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm , M. Sammartino

An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By…

Analysis of PDEs · Mathematics 2022-06-28 George C. Hsiao , Tonatiuh Sánchez-Vizuet , Wolfgang L. Wendland

The ability to design the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success applying local optimization methods to electromagnetic…

This paper is concerned with inverse scattering of plane waves by a locally perturbed infinite plane (which is called a locally rough surface) with the modulus of the total-field data (also called the phaseless near-field data) at a fixed…

Numerical Analysis · Mathematics 2018-08-28 Xiaoxu Xu , Bo Zhang , Haiwen Zhang

This paper is concerned with the well-posedness and regularity of the distributional solutions for the stochastic acoustic and elastic scattering problems. We show that the regularity of the solutions depends on the regularity of both the…

Analysis of PDEs · Mathematics 2021-03-23 Peijun Li , Xu Wang

Scattering states with LEED asymptotics are calculated for a general non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction…

Materials Science · Physics 2009-10-30 S. Lorenz , C. Solterbeck , W. Schattke , J. Burmeister , W. Hackbusch

The main goal of this article is to understand how the length spectrum of a random surface depends on its genus. Here a random surface means a surface obtained by randomly gluing together an even number of triangles carrying a fixed metric.…

Geometric Topology · Mathematics 2016-04-28 Bram Petri

We derive a very simple and effective stickiness criterion for solids having random roughness using a new asymptotic theory, which we validate with that of Persson and Scaraggi and independent numerical experiments. Previous claims that…

Soft Condensed Matter · Physics 2018-10-26 G. Violano , L. Afferrante , A. Papangelo , M. Ciavarella

The lateral diffusion coefficient of a Brownian particle on a two-dimensional random surface is studied in the quenched limit for which the surface configuration is time-independent. We start with the stochastic equation of motion for a…

Soft Condensed Matter · Physics 2020-10-06 Takao Ohta , Shigeyuki Komura

An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm

We numerically analyze the distribution of scattering resonance widths in one- and quasi-one dimensional tight binding models, in the localized regime. We detect and discuss an algebraic decay of the distribution, similar, though not…

Mesoscale and Nanoscale Physics · Physics 2009-10-31 M. Terraneo , I. Guarneri

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…

Materials Science · Physics 2022-07-20 Dmitry Churochkin , Fernando Lund

We deal with the problem of the linearized and isotropic elastic inverse scattering by interfaces. We prove that the scattered $P$-parts or $S$-parts of the far field pattern, corresponding to all the incident plane waves of pressure or…

Analysis of PDEs · Mathematics 2013-11-19 Manas Kar , Mourad Sini

We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one…

Probability · Mathematics 2024-10-16 Paul Krühner , Shijie Xu

No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…

Statistical Mechanics · Physics 2007-05-23 Ingve Simonsen

Under the uniform H\"{o}rmander's hypothesis we study smoothness and exponential bounds of the density of the law of the solution of a stochastic differential equation (SDE) with locally Lipschitz drift that satisfy a monotonicity…

Probability · Mathematics 2024-07-23 Cristina Anton

We present a notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.

Algebraic Geometry · Mathematics 2019-01-23 Jay Yang