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Scattering problems are important in describing light propagation in wide ranging media such as the atmosphere, colloidal solutions, metamaterials, glass ceramic composites, transparent polycrystalline ceramics, and surfaces. The Rayleigh…
In this work we consider a wide range of energy critical wave equation in 3-dimensional space with radial data. We are interested in exterior scattering phenomenon, in which the asymptotic behaviour of a solutions $u$ to the non-linear wave…
Scattering of radial $H^1$ solutions to the 3D focusing cubic nonlinear Schr\"odinger equation below a mass-energy threshold $M[u]E[u] < M[Q]E[Q]$ and satisfying an initial mass-gradient bound $\|u_0\|_{L^2} \|\nabla u_0 \|_{L^2} <…
Collective coherent scattering of laser light by an ensemble of polarizable point particles creates long range interactions, whose properties can be tailored by choice of injected laser powers, frequencies and polarizations. We use a…
The present work describes some extensions of an approach, originally developed by V.V. Yatsyk and the author, for the theoretical and numerical analysis of scattering and radiation effects on infinite plates with cubically polarized…
Context: Knowledge about hot, massive stars is usually inferred from quantitative spectroscopy. To analyse non-spherical phenomena, the existing 1D codes must be extended to higher dimensions, and corresponding tools need to be developed.…
It is generally assumed that magnetic fields play an important role in the formation and evolution of protoplanetary disks. One way of observationally constraining magnetic fields is to measure polarized emission and absorption produced by…
The behavior of magnetic field lines in a turbulent plasma is a key property of the medium, with important consequences for plasma dynamics and charged-particle transport. We study the diffusion properties of magnetic field lines in…
The Rayleigh conjecture about convergence up to the boundary of the series representing the scattered field in the exterior of an obstacle $D$ is widely used by engineers in applications. However this conjecture is false for some obstacles.…
Model independent radiative correction to the recoil proton polarization for the elastic electron-proton scattering is calculated within method of electron structure functions. The explicit expressions for the recoil proton polarization are…
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…
Observations of scattering polarization and the Hanle effect in various spectral lines are increasingly used to complement traditional solar magnetic field determination techniques. One of the strongest scattering polarization signals in…
We find the forms of the transfer equations for polarized cyclotron radiation in the atmospheres of compact stars, which are simple enough to allow practical implementation and still preserve all important physical effects. We take into…
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…
We discuss the implementation of physically meaningful branching ratios between the CRD and PRD contributions to the emissivity of a polarized multi-term atom in the presence of both inelastic and elastic collisions. Our derivation is based…
Reaction-nonlinear diffusion (RND) partial differential equations are a fruitful playground to model the formation of sharp travelling fronts, a fundamental pattern in nature. In this work, we demonstrate the utility and scope of…
The Rayleigh conjecture on the representation of the scattered field in the exterior of an obstacle $D$ is widely used in applications. However this conjecture is false for some obstacles. AGR introduced the Modified Rayleigh Conjecture…
The small perturbations method has been extensively used for waves scattering by rough surfaces. The standard method developped by Rice is difficult to apply when we consider second and third order of scattered fields as a function of the…
The polarization properties of the elastic electron scattering on H-like ions are investigated within the framework of the relativistic QED theory. The polarization properties are determined by a combination of relativistic effects and spin…
We investigate the scattering phenomena in two dimensions produced by a general finite-range nonseparable potential. This situation can appear either in a Cartesian geometry or in a heterostructure with cylindrical symmetry. Increasing the…