Related papers: Using Spherical Harmonics to solve the Boltzmann e…
We introduce an algorithm for the solution of a system of radial Schr\"odinger equations describing the inelastic scattering of particles with spin in a partial wave with definite total angular momentum. The system of differential equations…
In this work, we extend the solid harmonics derivation, which was used by Ackroyd et al to derive the steady-state SP$_N$ equations, to transient problems. The derivation expands the angular flux in ordinary surface harmonics but uses…
Conventional approaches for scattering manipulations rely on the technique of field expansions into spherical harmonics (electromagnetic multipoles), which nevertheless is non-generic (expansion coefficients depend on the position of the…
The study of strongly out-of-equilibrium states and their time evolution towards thermalization is critical to the understanding of an ever widening range of physical processes. We present a numerical method that for the first time allows…
In this paper, explicit method of constructing approximations (the Triangle Entropy Method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a…
We consider time-harmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on the knowledge of the two-point correlation of the domain…
We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…
Many optical measurement techniques, such as light scattering from wavelength-scale particles or detecting motion from a surface with an optical lever, encode information in a complex radiation pattern. Extracting all available information…
We consider the resonance and scattering properties of a composite medium containing scatterers whose properties are modulated in time. When excited with an incident wave of a single frequency, the scattered field consists of a family of…
The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation…
We develop an efficient numerical method for calculating the image stress field induced by spherical voids in materials. The method is applied to dislocation-void interactions in dislocation dynamics simulations. We obtain a complete set of…
We present a framework for the solution of Boltzmann's equation in the swarm limit for arbitrary mass ratio, allowing for solutions of electron or ion transport. An arbitrary basis set can be used in the framework, which is achieved by…
The purpose of this paper is to study the evolution of moving interacting particles on the mesoscopic scale. We will introduce an uncertainty principle and a new priori bound for the evolution of particles subject to a general mesoscopic…
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process.…
We present a theoretical framework for electromagnetic scattering by particles with a permittivity that is periodically varying in time, based on a perturbative approach. Within this framework, we derive explicit expressions for the…
For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…
A phenomenological model of the time evolution of a particle wavepacket is presented that is subject to scattering event with small momentum transfer. It is suited for three dimensions and allows for an additional potential. For a random…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
We derive quantum Boltzmann equations from Schwinger-Dyson equations in gradient expansion for a weakly coupled scalar field theory with a spatially varying mass. We find that at higher order in gradients a full description of the system…
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…