Related papers: Singular eigenfunctions for the three-dimensional …
The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance…
We study an inverse uniqueness with a knowledge of spectral data in the interior transmission problem defined by an index of refraction in a simple domain. We expand the solution in such a domain into a series of one dimensional problems.…
The construction of exact solutions for radiative transfer in a plane-parallel medium has been addressed by Hemsch and Ferziger in 1972 for a partial frequency redistribution model of the formation of spectral lines consisting in a linear…
We consider an inverse problem for a radiative transport equation (RTE) in which boundary sources and measurements are restricted to a single subset $E$ of the boundary of the domain $\Omega$. We show that this problem can be solved…
The covariant kinetic approach for the radiative plasma, a mixture of a relativistic moving gas plus radiation quanta (photons, neutrinos, or gravitons) is generalized to D spatial dimensions. The operational and physical meaning of…
A numerical model is proposed to compute the eigenmodes and the forced response of multilayered elastic spheres. The main idea is to describe analytically the problem along the angular coordinates with spherical harmonics and to discretize…
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…
We study the cooperative optical coupling between regularly spaced atoms in a one-dimensional waveguide using decompositions to subradiant and superradiant collective excitation eigenmodes, direct numerical solutions, and analytical…
We have derived the radiative-transfer equation for a point source with a specified intensity and spectrum, originating in the early Universe between the epochs of annihilation and recombination, at redshifts $z_\s =10^8\div 10^4$. The…
Given a set of transmission eigenvalues, its density function inversely determines the form of the indicator function. This is one application of the Cartwright's theory in inverse problems. We use the indicator function inversely to…
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
We consider a one dimensional transport model with nonlocal velocity given by the Hilbert transform and develop a global well-posedness theory of probability measure solutions. Both the viscous and non-viscous cases are analyzed. Both in…
We present a transport equation for the incoherent propagation of radiation inside a quasi-resonant atomic gas at low temperature. The derivation is based on a generalized Bethe-Salpeter equation taking into account the motion of the atoms.…
We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…
Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact…
We derive a grey linear diffusion equation for photons with respect to inertial (or lab-frame) space and time, using asymptotic analysis in 1D planar geometry. The solution of the equation is the comoving radiation energy density. Our…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…
Radiation transport plays a crucial role in star formation models, as certain questions within this field cannot be accurately addressed without taking it into account. Given the high complexity of the interstellar medium from which stars…
In this study, two initial boundary value problems for one dimensional advection-dispersion equation are solved by differential quadrature method based on sine cardinal functions. Pure advection problem modeling transport of conservative…
We study the Radiative Transfer equations coupled with the time dependent temperature equation of a fluid: existence, uniqueness, a maximum principle are established. A short numerical section illustrates the pros and cons of the method.