Related papers: Weak asymptotics of wave function for N-particle s…
We give a revealing expose that addresses an important issue in scattering theory of how to construct two asymptotically sinusoidal solutions of the wave equation with a phase shift using the same basis having the same boundary conditions…
A theoretical model of resonant hyper-Raman scattering by an ensemble of spherical semiconductor quantum dots has been developed. The electronic intermediate states are described as Wannier-Mott excitons in the framework of the envelope…
We experimentally study the scattering of guided matter waves on an amplitude-modulated optical lattice. We observe different types of frequency-dependent dips in the asymptotic output density distribution. Their positions are compared…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
In this paper, we prove the first asymptotic completeness result for a scalar quasilinear wave equation satisfying the weak null condition. The main tool we use in the study of this equation is the geometric reduced system introduced in…
We consider nonlinear filters for diffusion processes when the observation and signal noises are small and of the same order. As the noise intensities approach zero, the nonlinear filter can be approximated by a certain variational problem…
The filtering distribution is a time-evolving probability distribution on the state of a dynamical system, given noisy observations. We study the large-time asymptotics of this probability distribution for discrete-time, randomly…
High-contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localisation at low frequencies. We use an asymptotic framework to develop a landscape theory for high-contrast systems…
The interaction between radiation and superconductors is explored in this paper. In particular, the calculation of a plane standing wave scattered by an infinite cylindrical superconductor is performed by solving the Helmholtz equation in…
Collective Thomson scattering (CTS) in a beam-plasma system is reproduced by using 2D PIC simulations and the characteristics of the scattered wave spectrum are examined. By formulating the geometric shape of the scattered wave spectrum in…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…
We propose a new asymptotic expansion method for nonlinear filtering, based on a small parameter in the system noise. The conditional expectation is expanded as a power series in the noise level, with each coefficient computed by solving a…
Using a combination of multipole methods and the method of matched asymptotics, we present a solution procedure for acoustic plane wave scattering by a single Helmholtz resonator in two dimensions. Closed-form representations for the…
This paper investigates the asymptotic behaviors of time-harmonic acoustic waves generated by an incident wave illuminating inhomogeneous medium inclusions with high-contrast material parameters. We derive sharp asymptotic estimates and…
Understanding radiative transfer in random media like micro/nanoporous and particulate materials, allows people to manipulate the scattering and absorption of radiation, as well as opens new possibilities in applications such as imaging…
An experiment is presented in which the alleged progression of a photon's wave function is ``measured'' by a row of superposed atoms. The photon's wave function affects only one out of the atoms, regardless of its position within the row,…
We consider a two-dimensional analogue of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency equalling to the limit of poles generated by both the bounded component of the resonator…
An exploratory study of two-particle wave function is carried out with a four dimensional simple model. The wave functions not only for two-particle ground and first excited states but also for an unstable state are calculated from three-…
We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as $t\to -\infty$ to asymptotic dynamics as $t\to +\infty$. The main novelty is the construction of modified…
This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…