Related papers: Field sensitivity to L^p variations of a scatterer
Recently, reduced order modeling methods have been applied to solving inverse boundary value problems arising in frequency domain scattering theory. A key step in projection-based reduced order model methods is the use of a sesquilinear…
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…
We study a quite general class of stochastic dispersive equations with linear multiplicative noise, including especially the Schr\"odinger and Airy equations. The pathwise Strichartz and local smoothing estimates are derived here in both…
We consider the wave and Klein-Gordon equations on the real hyperbolic space $\mathbb{H}^{n}$ ($n \geq2$) in a framework based on weak-$L^{p}$ spaces. First, we establish dispersive estimates on Lorentz spaces in the context of…
This paper is concerned with developing efficient numerical methods for acoustic wave scattering in random media which can be expressed as random perturbations of homogeneous media. We first analyze the random Helmholtz problem by deriving…
An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is…
We explore the Lipschitz stability of solutions to the Hunter-Saxton equation with respect to the initial data. In particular, we study the stability of $ \alpha $-dissipative solutions constructed using a generalised method of…
A method is given for evaluating electromagnetic scattering by an irregular surface with spatially-varying impedance. This uses an operator expansion with respect to impedance variation and allows examination of its effects and the…
We prove quantitative versions of the following statement: If a solution of the 1+1-dimensional wave equation has spatially compact support and consists mainly of positive frequencies, then it must have a significant high-frequency…
Spatially localized oscillations in periodically forced systems are intriguing phenomena. They may occur in spatially homogeneous media (oscillons), but quite often emerge in heterogeneous media, such as the auditory system, where localized…
We propose a new method for calculating reflection and transmission coefficients for an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional dielectric medium of finite thickness and with dielectric permittivity…
We prove a new uniqueness theorem for an inverse scattering problem without the phase information for the 3-D Helmholtz equation. The spatially distributed dielectric constant is the subject of the interest in this problem. We consider the…
We consider the resonance and scattering properties of a composite medium containing scatterers whose properties are modulated in time. When excited with an incident wave of a single frequency, the scattered field consists of a family of…
We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scatterers. The theoretical justification of our novel sampling…
We have experimentally measured the distribution of the second-harmonic intensity that is generated inside a highly-scattering slab of porous gallium phosphide. Two complementary techniques for determining the distribution are used. First,…
We study the reflection and transmission coefficients and the absorption cross section for scalar fields in the background of a Lifshitz black hole in three-dimensional conformal gravity with $z=0$, and we show that the absorption cross…
Negative refractive index materials have attracted significant research attention due to their unique electromagnetic response characteristics. In this paper, we employ the complementing boundary condition to establish rigorous a priori…
In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a…
Using the brick wall method, we study statistical entropy for spherically symmetric black holes in Ho\v{r}ava-Lifshitz gravity. In particular, a Lifshitz scalar field is considered in order to incorporate foliation preserving diffeomorphism…
The current study investigates the asymptotic spectral properties of a finite difference approximation of nonlocal Helmholtz equations with a Caputo fractional Laplacian and a variable coefficient wave number $\mu$, as it occurs when…