Related papers: A Fast Iterative Method for Chandrasekhar's H-func…
We first establish a simple procedure to obtain with 11-figure accuracy the values of Chandrasekhar's H-function for isotropic scattering using a closed-form integral representation and the Gauss-Legendre quadrature. Based on the numerical…
In this paper, the new forms obtained for Chandrasekhar's H- function in Radiative Transfer by one of the authors both for non-conservative and conservative cases for isotropic scattering in a semi-infinite plane parallel atmosphere are…
This work shows that it is possible to calculate numerical values of the Chandrasekhar $H$-function for isotropic scattering at least with 15-digit accuracy by making use of the double exponential formula (DE-formula) of Takahashi and Mori…
This study provides an exact solution to Chandrasekhar's H function for isotropic scattering. The H function, which is governed by a nonlinear integral equation, plays a central role in radiative transfer theory. To facilitate the solution,…
We have established an iterative scheme to calculate with 15-digit accuracy the numerical values of Ambartsumian-Chandrasekhar's H-functions for anisotropic scattering characterized by the four-term phase function: the method incorporates…
Chandrasekhar's H(mu)-function forms the foundation of radiative transfer theory for semi-infinite, isotropically scattering atmospheres under external illumination. However, the classical formulation does not account for thermal emission…
The solutions of the \textit{diffuse reflection finite atmosphere problem} are very useful in the astrophysical context. Chandrasekhar was the first to solve this problem analytically, by considering atmospheric scattering. These results…
Context: The analytical results of Chandrasekhar's semi-infinite diffuse reflection problem is crucial in the context of stellar or planetary atmosphere. However, the atmospheric emission effect was not taken into account in this model, and…
High frequency integral equation methodologies display the capability of reproducing single-scattering returns in frequency-independent computational times and employ a Neumann series formulation to handle multiple-scattering effects. This…
An efficient hybrid numerical method for multiple scattering calculations is proposed. We use the well established doubling--adding method to find the reflection function of the lowermost homogeneous slab comprising the atmosphere of our…
Numerical calculations of light propagation in random media demand the multiply scattered Stokes intensities to be written in a common fixed reference. A particularly useful way to perform automatically these basis transformations is to…
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
We consider the focusing generalized Hartree equation in $H^1(\R^3)$ with a potential, \begin{equation*} iu_t + \Delta u - V(x)u + (I_\gamma \ast |u|^p )|u|^{p-2} u=0, \end{equation*} where $I_\gamma = \frac{1}{|x|^{3-\gamma}}$, $p \geq 2$…
Predicting the optical response of macroscopic arrangements of individual scatterers is a computational challenge, as the problem involves length scales across multiple orders of magnitude. We present a full-wave optical method to highly…
Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering…
An iterative algorithm is adopted to construct approximate representations of matrices describing the scattering properties of arbitrary objects. The method is based on the implicit evaluation of scattering responses from iteratively…
Study of scattering process in the nonlocal interaction framework leads to an integro-differential equation. The purpose of the present work is to develop an efficient approach to solve this integro-differential equation with high degree of…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…
Exactly soluble models in the theory of electromagnetic propagation and scattering are essentially restricted to horizontally stratified or spherically symmetric geometries, with results also available for certain waveguide geometries.…
A number of new problems in remote sensing and identification of buried compact metallic targets motivate the search for new models that, if not exact, at least enable extremely rapid numerical predictions of electromagnetic…