Related papers: Sommerfeld half-space problem revisited: Short-wav…
Successful wavelet estimation is an essential step for seismic methods like impedance inversion, analysis of amplitude variations with offset and full waveform inversion. Homomorphic deconvolution has long intrigued as a potentially elegant…
In this paper we consider the direct scattering problem of obliquely incident time-harmonic electromagnetic plane waves by an infinitely long dielectric cylinder. We assume that the cylinder and the outer medium are homogeneous and…
We present a time domain method to solve quantum scattering by an arbitrary potential of finite range. The scattering wave function in full space can be obtained, including the near field, the mid field (i.e. Fresnel region) and the far…
The author's recent results on an asymptotic description of the Schlesinger equation are generalized to the JMMS equation. As in the case of the Schlesinger equation, the JMMS equation is reformulated to include a small parameter…
A novel approach to improving the performances of confocal scanning imaging is proposed. We experimentally demonstrate its feasibility using acoustic waves. It relies on a new way to encode spatial information using the temporal dimension.…
The paper investigates a variant of semi-implicit spectral deferred corrections (SISDC) in which the stiff, fast dynamics correspond to fast propagating waves ("fast-wave slow-wave problem"). We show that for a scalar test problem with two…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave…
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…
We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…
We analyze systems of semilinear wave equations in $3+1$ dimensions whose associated asymptotic equation admit bounded solutions for suitably small choices of initial data. Under this special case of the weak null condition, which we refer…
Many advances in reflective metasurfaces have been made during the last few years, implementing efficient manipulations of wavefronts, especially for plane waves. Despite numerous solutions that have been developed throughout the years, a…
For the physical vacuum free boundary problem with the sound speed being $C^{{1}/{2}}$-H$\ddot{\rm o}$lder continuous near vacuum boundaries of the three-dimensional compressible Euler equations with damping, the global existence of…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector…
Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)…
Potential (electrostatic) surface waves in plasma half-space with degenerate electrons are studied using the quasi-classical mean-field kinetic model. The wave spectrum and the collisionless damping rate are obtained numerically for a wide…
A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…
Integral asymptotics play an important role in the analysis of differential equations and in a variety of other settings. In this work, we apply an integral asymptotics approach to study spatially localized solutions of a heterogeneous…
We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…