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Scattering of electromagnetic waves lies at the heart of most experimental techniques over nearly the entire electromagnetic spectrum, ranging from radio waves to optics and X-rays. Hence, deep insight into the basics of scattering theory…
Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small…
A Neumann problem for a wave equation perturbed by viscous terms with small parameters is considered. The interaction of waves with the diffusion effects caused by a higher-order derivative with small coefficient {\epsilon}, is…
This paper presents a computational framework for modeling wave propagation in geometrically linear elastic materials characterized by algebraically nonlinear constitutive relations. We derive a specific form of the nonlinear wave equation…
We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short…
An electron beam traversing a structured plasmonic field is shown to undergo diffraction with characteristic angular patterns of both elastic and inelastic outgoing electron components. In particular, a plasmonic {\it grating} (e.g., a…
Previous results on the scattering of surface waves by vertical vorticity on shallow water are generalized to the case of dispersive water waves. Dispersion effects are treated perturbatively around the shallow water limit, to first order…
Matter wave interferometry is becoming an increasingly important technique in quantum metrology. However, unlike its photonic counterpart, this technique relies on the interference of particles possessing a non-zero rest mass and an…
In this paper we review the results of the author on the theory of scalar and vector wave scattering by small bodies of an arbitrary shape with the emphasis on practical applicability of the formulas obtained and on the mathematical rigor…
In one-dimension, the diffusion of particles along a line is slowed by the addition of energy barriers. The same is true in two-dimensions, provided that the confining channel in which the particles move doesn't change shape. However, if…
We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…
The problem of a travelling wave over an arbitrary quasi-flat bathymetry in a semi infinite channel is studied in the shallow-water formulation. It is shown how the streamfunction can be cast, in the vicinity of an elliptic equilibrium for…
In this paper, we consider time-harmonic elastic wave scattering governed by the Lam\'e system. It is known that the elastic wave field can be decomposed into the shear and compressional parts, namely, the pressure and shear waves that are…
As the study of three-hadron physics from lattice QCD matures, it is necessary to develop proper analysis tools in order to reliably study a variety of phenomena, including resonance spectroscopy and nuclear structure. Reconstructing the…
Distorted-wave methods are used to remove the effects of one- and two-pion exchange up to order Q^3 from the empirical 1P1 phase shift. The one divergence that arises can be renormalised using an order-Q^2 counterterm which is provided by…
Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
Wavefront shaping is a technique for directing light through turbid media. The theoretical aspects of wavefront shaping are well understood, and under near-ideal experimental conditions, accurate predictions for the expected signal…
We study a 2D lattice model of forward-directed waves in which the integrated intensity for classical waves (or probability for quantum mechanical particles) is conserved. The model describes the time evolution of 1D quantum particle in a…
The dual wave-particle nature of quantum objects is a notoriously unintuitive feature of quantum theories. However, it is often deemed essential, due to quantum objects exhibiting diffraction and interference. We extend the work of…