Related papers: Radiative equilibrium in Monte Carlo radiative tra…
The radiative transfer equation (RTE) is a cornerstone for describing the propagation of electromagnetic radiation in a medium, with applications spanning atmospheric science, astrophysics, remote sensing, and biomedical optics. Despite its…
Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to…
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…
We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the…
Elastic systems that are spatially heterogeneous in their mechanical response pose special challenges for molecular simulations. Standard methods for sampling thermal fluctuations of a system's size and shape proceed through a series of…
Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a Jastrow factor. In this paper we study the…
Quantum Monte Carlo methods are powerful techniques for studying strongly interacting Fermi systems. However, implementing these methods on computers with finite-precision arithmetic requires careful attention to numerical stability. In the…
Implicit Monte Carlo (IMC) and Discrete Diffusion Monte Carlo (DDMC) are methods used to stochastically solve the radiative transport and diffusion equations, respectively. These methods combine into a hybrid transport-diffusion method we…
On the base of the diffusion Monte-Carlo method we develop the method allowing to simulate the quantum systems with complex wave function. The method is exact and there are no approximations on the simulations of the module and the phase of…
This paper explains how to obtain the distribution function of minority ions in tokamak plasmas using the Monte Carlo method. Since the emphasis is on energetic ions, the guiding-center transformation is outlined, including also the…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
We present a novel Monte Carlo algorithm which enhances equilibrization of low-temperature simulations and allows sampling of configurations over a large range of energies. The method is based on a non-Boltzmann probability weight factor…
We present a diagrammatic Monte Carlo method for quantum impurity problems with general interactions and general hybridization functions. Our method uses a recursive determinant scheme to sample diagrams for the scattering amplitude. Unlike…
The classical approaches to numerically integrating a function $f$ are Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods. MC methods use random samples to evaluate $f$ and have error $O(\sigma(f)/\sqrt{n})$, where $\sigma(f)$ is the…
Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice however, sampling of the complete configuration space is often hindered by high energy barriers between different regions…
In these lectures we provide a short introduction to the Monte Carlo integration method and its applications. We show how the origin of ultraviolet divergences if Field Theories is in the undefined formal product of distributions and how…
A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated…
We present a simple approach to the fixed phase method in Quantum Monte Carlo. This applies to electrons in molecules and electron gas and is straightforwardly extended to the Schr\"odinger equation with magnetic field.
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
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…