Related papers: A Monte Carlo Method for 3D Radiative Transfer Equ…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
A covariant scattering kernel is a core component in any self-consistent general relativistic radiative transfer formulation in scattering media. An explicit closed-form expression for a covariant Compton scattering kernel with a good…
We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditional small diffusion hops and propagates the…
Computer simulations of radio energy transfer in the ionospheric layer with random small-scale irregularities for the case of a point ground-based source and total reflection have been carried out using specially designed algorithm based on…
Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated…
We present a new parton level Monte Carlo program for the calculation of jet cross sections in Deep Inelastic Scattering based on Born and next-to-leading order matrix elements. Using a class of invariant jet definition schemes, the program…
Nuclear physics seeks to describe both bound and unbound states within a unified predictive framework. While coordinate-space Quantum Monte Carlo (QMC) methods have successfully computed bound states for systems with $A \leq 12$, their…
In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial…
Monte Carlo sampling techniques are used to estimate high-dimensional integrals that model the physics of light transport in virtual scenes for computer graphics applications. These methods rely on the law of large numbers to estimate…
The Monte Carlo method is the most popular technique to perform radiative transfer simulations in a general 3D geometry. The algorithms behind and acceleration techniques for Monte Carlo radiative transfer are discussed extensively in the…
A Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
In this paper the application of the multi-level Monte Carlo (MLMC) method on numerical simulations of turbulent flows with uncertain parameters is investigated. Several strategies for setting up the MLMC method are presented, and the…
The radiative transfer equation models various physical processes ranging from plasma simulations to radiation therapy. In practice, these phenomena are often subject to uncertainties. Modeling and propagating these uncertainties requires…
A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state energy without an uncontrolled bias. This is achieved by confining signed…
A revised and greatly improved version of the 3D continuum radiative transfer code MC3D is presented. It is based on the Monte-Carlo method and solves the radiative transfer problem self-consistently. It is designed for the simulation of…
Recently, a diffusion Monte Carlo algorithm was applied to the study of spin dependent interactions in condensed matter. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a…
We discuss the use of a recent class of sequential Monte Carlo methods for solving inverse problems characterized by a semi-linear structure, i.e. where the data depend linearly on a subset of variables and nonlinearly on the remaining…
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…
The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. The method exhibits a reduced variance by assigning the samples to multiple models with a varying spatial resolution. For the given…