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A treatment of direct simulation Monte Carlo method (DSMC) as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived…
Monte Carlo (MC) simulation is considered the gold standard method for radiotherapy dose calculation. However, achieving high precision requires a large number of simulation histories, which is time consuming. The use of computer graphics…
A stochastic optimal control problem for incompressible Newtonian channel flow past a circular cylinder is used as a prototype optimal control problem for the stochastic Navier-Stokes equations. The inlet flow and the rotation speed of the…
The low-variance direct simulation Monte Carlo (LVDSMC) is a powerful method to simulate low-speed rarefied gas flows. However, in the near-continuum flow regime, due to limitations on the time step and spatial cell size, it takes plenty of…
Quantum Monte Carlo (QMC) methods represent a powerful family of computational techniques for tackling complex quantum many-body problems and performing calculations of stationary state properties. QMC is among the most accurate and…
The numerical simulation of rarefied gas mixture dynamics with disparate masses using the direct simulation Monte Carlo (DSMC) method is slow, primarily because the time step is constrained by that of the lighter species, necessitating an…
We analyse convergence of a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with time-scale separation between the (fast) evolution of individual trajectories and the (slow) evolution of…
Computer simulation plays a central role in modern day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of…
An open source software package for simulating thermal neutron propagation in geometry is presented. In this system, neutron propagation can be treated by either the particle transport method or the ray-tracing method. Supported by an…
Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…
The Derivative Source Method (DSM) takes derivatives of a particle transport equation with respect to selected parameters and solves them via the standard Monte Carlo random walk simulation along with the original transport problem. The…
The small magnitude and long-range character of non-covalent interactions pose a significant challenge for computational quantum chemical and electronic-structure methods alike. State-of-the-art coupled cluster (CC) theory and…
Speed of sound is a key parameter for the compressibility effects in multiphase flow. We present a new approach to do direct numerical simulations on the speed of sound in compressible two-phase flow, based on the stratified multiphase flow…
A variant of the Direct Simulation Monte Carlo method is used to study the behavior of a granular gas, in two and three dimensions, under varying density, restitution coefficient, and inelasticity regimes, for realistic vibrating wall…
Characterizing the properties and orientations of sub-voxel fiber populations, although essential to study white-matter architecture, microstructure and connectivity, remains one of the main challenges faced by the MRI microstructure…
Boson lattices are theoretically well described by the Hubbard model. The basic model and its variants can be effectively simulated using Monte Carlo techniques. We describe two newly developed approaches, the Stochastic Series Expansion…
We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…
Acoustic microstreaming has several industrial, therapeutic, and biomedical applications - Acoustic cleaning, micromixing, microfluid transport, hemolysis, sonoporation. The acoustic microstreaming due to the oscillation of ultrasound…
Mechanisms for non-invasive target drug delivery using microbubbles and ultrasound have attracted growing interest. Microbubbles can be loaded with a therapeutic payload and tracked via ultrasound imaging to selectively release their…
The rarefied flows encountered by the hypersonic vehicles in their high-altitude flights call for investigations coupling the shock-shock interaction and the rarefied-gas effect. An in-house direct simulation Monte Carlo (DSMC) solver is…