Related papers: Singular eigenfunctions for the three-dimensional …
A nonsingular analytical solution for the transfer equation in a pure absorber is obtained in central symmetry and in a monochromatic radiation field. The native regular singularity of the equation is removed by applying a linear…
A new method for the formal solution of the 2D radiative transfer equation in axial symmetry in the presence of arbitrary velocity fields is presented. The combination of long and short characteristics methods is used to solve the radiative…
We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These…
We investigate diffusion equations which have concentration dependent diffusion coefficients with physically two relevant Ans\"atze, the self-similar and the traveling wave Ansatz. We found that for power-law concentration dependence some…
The solitary wave solution and periodic solutions expressed in terms of elliptic Jacobi's functions are obtained for the nonlinear Schr\"{o}dinger equation governing the propagation of pulses in optical fibers including the effects of…
Self similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find…
The method of approximate automodel solution for the Green's function of the time-dependent superdiffusive (nonlocal) transport equations (J. Phys. A: Math. Theor. 49 (2016) 255002) is extended to the case of a finite velocity of carriers.…
We derive the radiative transfer equation for arbitrary stationary relativistic flows in stationary spacetimes, i.e. for steady-state transfer problems. We show how the standard characteristics method of solution developed by Mihalas and…
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region in $\R^3$. We consider a ray in this region, such that its direction is different from the…
We consider optical tomography with structured illumination in spatial-frequency domain using the three-dimensional radiative transport equation. Without the diffusion approximation, the radiative transport equation is solved by the…
Motivated by applications in quantitative photoacoustic imaging, we study inverse problems to a semilinear radiative transport equation (RTE) where we intend to reconstruct absorption coefficients in the equation from single and multiple…
We consider flame front propagation in channel geometries. The steady state solution in this problem is space dependent, and therefore the linear stability analysis is described by a partial integro-differential equation with a space…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
Exact solutions of the Klein-Gordon equation for a charged particle in the presence of three spatially varying electromagnetic fields, namely, (i) $\vec{E}=\alpha\beta_0e^{-\alpha x_2}\hat{x}_2$, $\vec{B}=\alpha\beta_1e^{-\alpha…
We come back to the Cauchy integral equations occurring in radiative transfer problems posed in finite, plane-parallel media with light scattering taken as monochromatic and isotropic. Their solution is calculated following the classical…
In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the solution we use periodic elastic layer potentials to show that the…
A full symmetry classification is given for models of energy transport in radiant plasma when the mass density is spatially variable and the diffusivity is nonlinear. A systematic search for conservation laws also leads to some potential…
We present a numerical method for handling the resolution of a general transport equation for radiative particles, aimed at physical problems with a general spherical geometry. Having in mind the computational time difficulties encountered…
We present a closed-form analytic solution for the propagation of an arbitrary charged scalar state in a non-uniform magnetic field. The dynamics are governed by classical beam optics parameters (Courant-Snyder parameters), the Twiss…
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we solve analytically a one-dimensional fractional diffusion-advection equation for the particle density. We…