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Due to its accuracy and generality, Monte Carlo radiative transfer (MCRT) has emerged as the prevalent method for Ly$\alpha$ radiative transfer in arbitrary geometries. The standard MCRT encounters a significant efficiency barrier in the…
This paper presents a novel, efficient, high-order accurate, and stable spectral element-based model for computing the complete three-dimensional linear radiation and diffraction problem for floating offshore structures. We present a…
We discuss Monte-Carlo techniques for addressing the 3-dimensional time-dependent radiative transfer problem in rapidly expanding supernova atmospheres. The transfer code SEDONA has been developed to calculate the lightcurves, spectra, and…
This paper extends the semianalytical treatment of fast ion current density to take into account time dependence and velocity diffusion using solutions of Boltzmann equation with a complete Coulomb collision term (Goncharov et al. 2010…
We present results obtained with a 3D, Ly alpha radiative transfer code, applied to a fully cosmological galaxy formation simulation. The developed Monte Carlo code is capable of treating an arbitrary distribution of source Ly alpha…
In this work, the higher-order dispersive nonlinear Schr\"{o}dinger equation with non-zero boundary conditions at infinity is investigated including the simple and double zeros of the scattering coefficients. We introduce a appropriate…
The Lyman alpha (LyA) line of neutral hydrogen plays a central role in observations of star-forming galaxies. However, resonant scattering makes it difficult to directly interpret LyA signatures. Monte Carlo radiative transfer (MCRT)…
We study the narrow escape problem in the disk, which consists in identifying the first exit time and first exit point distribution of a Brownian particle from the ball in dimension 2, with reflecting boundary conditions except on small…
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…
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 problem of sampling according to the probability distribution minimizing a given free energy, using interacting particles unadjusted kinetic Langevin Monte Carlo, is addressed. In this setting, three sources of error arise, related to…
A finite element method for solving the resonance line transfer problem in moving media is presented. The algorithm works in three spatial dimensions on unstructured grids which are adaptively refined by means of an a posteriori error…
We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the…
Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are…
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,…
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…
This proposal relates to the design, analysis and application of a novel numerical scheme for the solution of axisymmetric scattering problems. To this end, a procedure is introduced to iteratively evaluate the solution of the…
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…
We develop a Monte Carlo radiative transfer code to study the effect of turbulence with a finite correlation length on scattering of Lyman-alpha (Ly$\alpha$) photons propagating through neutral atomic hydrogen gas. We investigate how the…
We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…