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The theory and numerical modelling of radiation processes and radiative transfer play a key role in astrophysics: they provide the link between the physical properties of an object and the radiation it emits. In the modern era of increasingly high-quality observational data and sophisticated physical theories, development and exploitation of a variety of approaches to the modelling of radiative transfer is needed. In this article, we focus on one remarkably versatile approach: Monte Carlo Radiative Transfer (MCRT). We describe the principles behind this approach, and highlight the relative ease with which they can (and have) been implemented for application to a range of astrophysical problems. All MCRT methods have in common a need to consider the adverse consequences of Monte Carlo noise in simulation results. We overview a range of methods used to suppress this noise and comment on their relative merits for a variety of applications. We conclude with a brief review of specific applications for which MCRT methods are currently popular and comment on the prospects for future developments.
A crucial aspect of 3D Monte Carlo radiative transfer is the choice of the spatial grid used to partition the dusty medium. We critically investigate the use of octree grids in Monte Carlo dust radiative transfer, with two different octree constructi
We present a new algorithm for radiative transfer, based on a statistical Monte-Carlo approach, that does not suffer from teleportation effects on the one hand, and yields smooth results on the other hand. Implicit-Monte-Carlo (IMC) techniques for mo
Context: The Monte Carlo method is the most widely used method to solve radiative transfer problems in astronomy, especially in a fully general 3D geometry. A crucial concept in any Monte Carlo radiative transfer code is the random generation of the
We combine a Monte Carlo radiative transfer code with an SPH code, so that -- assuming thermal equilibrium -- we can calculate dust-temperature fields, spectral energy distributions, and isophotal maps, for the individual time-frames generated by an
The Monte Carlo method is a powerful tool for performing radiative equilibrium calculations, even in complex geometries. The main drawback of the standard Monte Carlo radiative equilibrium methods is that they require iteration, which makes them nume