Related papers: Introducing a general method for solving electroma…
We present a new formal solution of the Lagrangian equation of radiative transfer that is useful in solving the equation of radiative transfer in the presence of arbitrary velocity fields. Normally a term due to the inclusion of the…
We offer a consistent dynamical formulation of stationary scattering in two and three dimensions that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear operator acting in an infinite-dimensional…
The difficulty of description of the radiative transfer in disordered photonic crystals arises from the necessity to consider on the equal footing the wave scattering by periodic modulations of the dielectric function and by its random…
Simulating the propagation of elastic waves in multi-layered media has many applications. A common approach is to use matrix methods where the elastic wave-field within each material layer is represented by a sum of partial-waves along with…
In this paper we study the application of a simplified method to solve the dynamic radiative transfer problem in expanding envelopes. The method, which requires a computational effort similar to that of the diffusion approximation, is based…
This paper presents a matrix formulation of the scalar laws of radiative transfer. The method applies to coupled mixed boundary condition problems on general domains. Participating media can range from transparent to absorbing, emitting,…
The Transfer Matrix Method is a powerful numerical tool for simulating wave propagation in layered media. It has been widely applied in many fields, although its use is typically restricted to passive media. In this paper, we develop the…
Birefringent crystals are extensively used to manipulate polarized light. The generalized transfer matrix developed allows efficient calculation of the full polarization state of light transmitted through and reflected by a stack of…
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…
The propagation of a wave in a medium is generally affected when the medium is moving with respect to the observer. Because plasma equilibria often involve plasma flows, for instance in astrophysics or in magnetic confinement nuclear fusion…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…
Disordered nanostructures are commonly encountered in many nanophotonic systems, from colloid dispersions for sensing, to heterostructured photocatalysts. Randomness, however, imposes severe challenges for nanophotonics modeling, often…
The problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the…
We adapt the transfer matrix ($\T$-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. In similarity to one-dimensional…
We introduce a numerical method that enables efficient modelling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each…
This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
We develop a transfer matrix formalism for four-flux radiative transfer models, which is ideally suited for studying transport through multiple scattering layers. The model, derived for spherical particles within the diffusion…
We derive the off-shell scattering matrix for a spherical scatterer. The result obtained generalizes the off-on-shell matrix commonly used in the theory of scalar waves propagation in random media.