Related papers: Weak asymptotics of wave function for N-particle s…
This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the…
A reduction of the Maxwell's system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the…
Recent advances in the treatment of scattering of charged composite particles are reviewed. In a first part I report on developments of the theory. Specifically I describe the recent completion of the derivation of the co-ordinate space…
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…
Some experimental implications of the recent progress on wave function collapse are calculated. Exact results are derived for the center-of-mass wave function collapse caused by random scatterings and applied to a range of specific…
The second order optical response of centrosymmetric materials manifests itself mostly at their surface, being strongly suppressed in their bulk. However, the overall surface response is also suppressed in nanoparticles with a…
A thin two-layered waveguide is considered. The governing equations for this waveguide is a matrix Klein--Gordon equation of dimension~2. A formal solution of this system in the form of a double integral can be obtained by using Fourier…
This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…
Integral representations play a prominent role in the analysis of entire functions. The representations of generalized Mittag-Leffler type functions and their asymptotics have been (and still are) investigated by plenty of authors in…
We reveal that an isotropic homogeneous subwavelength particle with a high refractive index can produce ultra-weak total scattering due to vanishing contribution of the electric dipole moment. This effect can be explained with the help of…
In conventional acoustic scattering theory, a large-distance asymptotic approximation is employed. In this approximation, a far-field pattern, an asymptotic approximation of the exact result, is used to describe a scattering process. The…
Theory of scattering by many small bodies is developed under various assumptions concerning the ratio $\frac{a}{d}$, where $a$ is the characteristic dimension of a small body and $d$ is the distance between neighboring bodies $d =…
In a framework for long-range density-functional theory we present a unified full-field treatment of the asymptotic van der Waals interaction for atoms, molecules, surfaces, and other objects. The only input needed consists of the electron…
Problems in exponential asymptotics are typically characterized by divergence of the associated asymptotic expansion in the form of a factorial divided by a power. In this paper, we demonstrate that in certain classes of problems that…
We calculate the differential, total, and transport cross-sections for scattering of two-dimensional massless Dirac electrons by a circular barrier. For scatterer of a small radius, the cross-sections are dominated by quantum effects such…
We present a new method for constructing solutions to nonlinear evolutionary equations describing the propagation and interaction of nonlinear waves.
We generalize the elementary mechanism of sampling with replacement $N$ times from a weighted population of size $N$, by introducing auxiliary variables and constraints on conditional independence characterised by modular congruence…
This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…
We prove local and global energy decay for the asymptotically periodic damped wave equation on the Euclidean space. Since the behavior of high frequencies is already mostly understood, this paper is mainly about the contribution of low…
The refraction of surface gravity waves by currents leads to spatial modulations in the wave field and, in particular, in the significant wave height. We examine this phenomenon in the case of waves scattered by a localised current feature,…