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We present two novel additions to the semi-analytic solution of Lyman $\alpha$ (Ly$\alpha$) radiative transfer in spherical geometry: (1) implementation of the correct boundary condition for a steady source, and (2) solution of the…
A boundary-based net-exchange Monte Carlo method was introduced in [1] that allows to bypass the difficulties encountered by standard Monte Carlo algorithms in the limit of optically thick absorption (and/or for quasi-isothermal…
This work concerns the modeling of radiative transfer in anisotropic turbid media using diffusion theory. A theory for the relationship between microscopic scattering properties (i.e., an arbitrary differential scattering cross-section) and…
For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions,…
We present a Monte Carlo simulation for the scattering of light in the case of an isotropic light source. The scattering phase functions are studied particularly in detail to understand how they can affect the multiple light scattering in…
An empirical numerical model that includes nuclear absorption, multiple Coulomb scattering, and energy loss is presented in this work to calculate the transmission of the thick objects in high energy proton radiography, and in this…
We investigate ways of accurately simulating the propagation of energetic charged particles over small times where the standard Monte Carlo approximation to diffusive transport breaks down. We find that a small-angle scattering procedure…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
The theory of both transmission and grazing incidence M\"ossbauer spectroscopy is re-analyzed. Starting with the nuclear susceptibility tensor a common concise first order perturbation formulation is given by introducing the forward…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…
The diffusion limit of the linear Boltzmann equation with a strong magnetic field is performed. The giration period of particles around the magnetic field is assumed to be much smaller than the collision relaxation time which is supposed to…
We present a hybrid method for time-dependent particle transport that combines Monte Carlo (MC) estimation with a deterministic discrete ordinates (\(S_N\)) solve, augmented by quasi-Monte Carlo (QMC) sampling. For spatial discretizations,…
Starting from the radiative transfer equation and its usual boundary conditions, the objective of this work is to design Monte Carlo algorithms estimating the specific intensity spatial and angular derivatives as well as its geometric…
Several models for the Monte Carlo simulation of Compton scattering on electrons are quantitatively evaluated with respect to a large collection of experimental data retrieved from the literature. Some of these models are currently…
Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)…
Monte Carlo radiative transfer, which has been demonstrated as a successful algorithm for modeling radiation transport through the astrophysical medium, relies on sampling of scattering phase functions. We review several classic sampling…
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…
Directly computing mass transport coefficients in stochastic models requires integrating over time the equilibrium correlations between atomic displacements. Here, we show how to accelerate the computations via \green{correlation splitting…
This work is devoted to radiative transfer equations with long-range interactions. Such equations arise in the modeling of high frequency wave propagation in random media with long-range dependence. In the regime we consider, the singular…
Monte Carlo methods are state-of-the-art when it comes to dosimetric computations in radiotherapy. However, the execution time of these methods suffers in high-collisional regimes. We address this problem by introducing a kinetic-diffusion…