相关论文: Application of the three-dimensional telegraph equ…
Diffusive cosmic-ray transport in nonuniform large-scale magnetic fields in the presence of boundaries is considered. Reflecting and absorbing boundary conditions are derived for a modified telegraph equation with a convective term.…
A new way for finding analytical solutions of the three-dimensional sine-Gordon equation is presented. The method is based on the established relation between the solutions of the three-dimensional wave equation and solutions of the…
We show the necessity for a new approach towards comprehensive and consistent simulations of the propagation of galactic cosmic rays. Our developments are optimised for addressing the spatially 3-dimensional inhomogeneous diffusion problem…
The radiative transport equation in a three-dimensional infinite medium is considered. The coefficients of the radiative transport equation are assumed to be constant. For a pencil beam, we extend the analytical discrete-ordinates method to…
In a recent publication [R. C. Tautz and I. Lerche, Res. Astron. Astrophys. 16, 162 (2016); arXiv:1606.08272], the authors present a derivation of the Green's function for the three-dimensional telegraph equation (also known as the heat…
In this paper we exactly solve the diffusion-advection equation for cosmic-ray transport. With this purpose we use the Theory of Ultradistributions of J. Sebastiao e Silva, to give a general solution for this equation. From this solution,…
A numerical scheme is proposed for the solution of the three-dimensional radiative transfer equation with variable optical depth. We show that time-dependent ray tracing is an attractive choice for simulations of astrophysical ionization…
The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph…
A detailed consideration of the Klein-Gordon equation in relativistic quantum mechanics is presented in order to offer more clarity than many standard approaches. The equation is frequently employed in the research literature, even though…
We present a numerical algorithm for the incorporation of the active cosmic ray transport, into the ZEUS-3D magnetohydrodynamical code. The cosmic ray transport is described by the diffusion-advection equation. The applied form of the…
In linear transport theory, three-dimensional equations reduce to one-dimensional equations by means of rotated reference frames. In this paper, we illustrate how the technique works and three-dimensional transport theories are obtained.
We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions…
In this paper it is shown that an equivalent to the complex Klein-Gordon equation can be obtained from the (2+3) dimensional Einstein equations coupled to a conserved energy momentum tensor. In an explicit toy model we give matching…
In this paper, the photon stationary transport equation has been extended from $\mathbb{R}^3$ to $\mathbb{C}^3$. A solution of the inverse problem is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transform,…
We discuss solutions of the one-dimensional telegrapher's equation in the presence of boundary conditions. We revisit the case of a radiation boundary condition and obtain an alternative expression for the already known Green's function.…
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…
In this effort we exactly solve the fractional diffusion-advection equation for solar cosmic-ray transport proposed in \cite{LE2014} and give its {\it general solution} in terms of hypergeometric distributions. Also, we regain all the…
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…
Cosmic rays (CR), constrained by scattering on magnetic irregularities, are believed to propagate diffusively. But a well-known defect of diffusive approximation whereby some of the particles propagate unrealistically fast has directed…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…