Related papers: A Monte Carlo Algorithm for Immiscible Two-Phase F…
We construct an ensemble distribution to describe steady immiscible two-phase flow of two incompressible fluids in a porous medium. The system is found to be ergodic. The distribution is used to compute macroscopic flow parameters. In…
The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to…
We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a…
We show that the common local Monte Carlo rules used to simulate the motion of driven flux lines in disordered media cannot capture the interplay between elasticity and disorder which lies at the heart of these systems. We therefore discuss…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…
Many problems in the physical sciences, machine learning, and statistical inference necessitate sampling from a high-dimensional, multi-modal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this…
Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…
We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to…
We introduce a modification of the well-known Metropolis importance sampling algorithm by using a methodology inspired on the consideration of the reparametrization invariance of the microcanonical ensemble. The most important feature of…
Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…
A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape…
A general synthetic iterative scheme is proposed to solve the Enskog equation within a Monte Carlo framework. The method demonstrates rapid convergence by reducing intermediate Monte Carlo evolution and preserves the asymptotic-preserving…
Recently, Velazquez and Curilef have proposed a methodology to extend Monte Carlo algorithms based on canonical ensemble, which is aimed to overcome slow sampling problems associated with temperature-driven discontinuous phase transitions.…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
An open-sourced multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume…
We consider the application of multilevel Monte Carlo methods to steady state Darcy flow in a random porous medium, described mathematically by elliptic partial differential equations with random coefficients. The levels in the multilevel…
Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a…
We present several implementations of the Metropolis method, an adaptive Monte Carlo algorithm, which allow for the calculation of multi-dimensional integrals over arbitrary on-shell four-momentum phase space. The Metropolis technique…
Phase transitions appear all over science, and are familiar from everyday life, as water boiling, sugar melting into caramel or as nematic molecules turning smectic in liquid-crystal displays. The dynamics of phase transitions can be…