Related papers: An improved version of the Implicit Integral Metho…
The representation of the usual integral dispersion relations (IDR) of scattering theory through series of derivatives of the amplitudes is discussed, extended, simplified, and confirmed as mathematical identities. Forms of derivative…
We present a general method to calculate radiative transfer including scattering in the continuum as well as in lines in spherically symmetric systems that are influenced by the effects of general relativity (GR). We utilize a comoving…
This paper proposes a direct-indirect mixed Burton-Miller boundary integral equation for solving Helmholtz scattering problems with transmissive scatterers. The proposed formulation has three unknowns, one more than the number of unknowns…
Electromagnetic Inverse Scattering Problems (EISP) have gained wide applications in computational imaging. By solving EISP, the internal relative permittivity of the scatterer can be non-invasively determined based on the scattered…
We consider the scattering results of the radial solutions below the ground state to the focusing inhomogeneous nonlinear Schr\"odinger equation $$i\partial_tu+\Delta u +|x|^{-b}|u|^{p}u=0$$ in two dimension, where $0<b<1$ and…
For line-driven winds from hot, luminous OB stars, we examine the subtle but important role of diffuse, scattered radiation in determining both the topology of steady-state solutions and intrinsic variability in the transonic wind base. We…
In this paper, we investigate on the direct and inverse scattering problem by an unbounded penetrable rough surface in a lossless medium. The cases that the transmission coefficient $\mu\neq1$ and $\mu=1$, which creates certain difficulties…
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…
Approximate methods to estimate solutions to the radiative transfer equation are essential for the understanding of atmospheres of exoplanets and brown dwarfs. The simplest and most popular choice is the "two-stream method" which is often…
Problem solutions in area of diffraction and of scattering theory are considered from one point of view. The method common for them is based on approximate orthogonality of solution constituents, which oscillate on a body long frontier.…
State-of-the-art methods in multidimensional NLTE radiative transfer are based on the use of local approximate lambda operator within either Jacobi or Gauss-Seidel iterative schemes. Here we propose another approach to the solution of 2D…
In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…
We systematically report a rigorous theory of the inverse scattering transforms (ISTs) for the derivative nonlinear Schrodinger (DNLS) equation with both zero boundary condition (ZBC)/non-zero boundary conditions (NZBCs) at infinity and…
A general approach for the calculation of the incoherent intensity scattered by a random medium with rough boundaries has been developed using a Green function formalism. The random medium consists of spherical particles whose physical…
The Rayleigh conjecture about convergence up to the boundary of the series representing the scattered field in the exterior of an obstacle $D$ is widely used by engineers in applications. However this conjecture is false for some obstacles.…
The highly convergent iterative methods developed by Trujillo Bueno and Fabiani Bendicho (1995) for radiative transfer (RT) applications are generalized to spherical symmetry with velocity fields. These RT methods are based on Jacobi,…
Two-stream radiative transfer is a workhorse in the Earth, planetary and exoplanetary sciences due to its simplicity and ease of implementation. However, a longstanding limitation of the two-stream approximation is its inaccuracy in the…
We study the standard spectral line radiative transfer equation for media consisting of resonant atoms and non-resonant components (the dust grains and the atoms without considered spectral transition). Our goal is to study the intensity…
(Abridged) We describe a new algorithm for solving the coupled frequency-integrated transfer equation and the equations of magnetohydrodynamics when the light-crossing time is only marginally shorter than dynamical timescales. The transfer…
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic…