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We present in detail two variants of the lattice Monte Carlo method aimed at tackling systems in external trapping potentials: a uniform-lattice approach with hard-wall boundary conditions, and a non-uniform Gauss-Hermite lattice approach.…

Kinetic approaches are routinely employed to simulate the dynamics of systems that are too rarified to be described by the Navier-Stokes equations. However, generally they are far too computationally expensive to be applied for systems that…

We develop off-lattice simulations of semiflexible polymer chains subjected to applied mechanical forces using Markov Chain Monte Carlo. Our approach models the polymer as a chain of fixed-length bonds, with configurations updated through…

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…

Rigid bodies, made of smaller composite beads, are commonly used to simulate anisotropic particles with molecular dynamics or Monte Carlo methods. To accurately represent the particle shape and to obtain smooth and realistic effective pair…

Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…

We present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of…

A brief introduction is given to Kinetic Monte Carlo (KMC) simulations of epitaxial crystal growth. Molecular Beam Epitaxy (MBE) serves as the prototype example for growth far from equilibrium. However, many of the aspects discussed hear…

This review gives an overview on the research of algorithms for dynamical fermions used in large scale lattice QCD simulations. First a short overview on the state-of-the-art of ensemble generation at the physical point is given. Followed…

We propose a lattice model to simulate the influence of porous medium on the Nematic - Isotropic transition of liquid crystal confined to the pores. The effects of pore size and pore connectivity are modelled through a disorder parameter.…

Accelerated algorithms for simulating the morphological evolution of strained heteroeptiaxy based on a ball and spring lattice model in three dimensions are explained. We derive exact Green's function formalisms for boundary values in the…

A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…

The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…

We employ constrained path Auxiliary Field Quantum Monte Carlo (AFQMC) in the pursuit of studying physical nuclear systems using a lattice formalism. Since AFQMC has been widely used in the study of condensed-matter systems such as the…

We present a fast Monte-Carlo algorithm for simulating epitaxial surface growth, based on the continuous-time Monte-Carlo algorithm of Bortz, Kalos and Lebowitz. When simulating realistic growth regimes, much computational time is consumed…

Monte Carlo techniques play a central role in statistical mechanics approaches for connecting macroscopic thermodynamic and kinetic properties to the electronic structure of a material. This paper describes the implementation of Monte Carlo…

Ab initio quantum Monte Carlo (QMC) is a stochastic approach for solving the many-body Schr\"odinger equation without resorting to one-body approximations. QMC algorithms are readily parallelizable via ensembles of $N_w$ walkers, making…

The Cooperative Motion Algorithm is an efficient lattice method to simulate dense polymer systems and is often used with two different criteria to generate a Markov chain in the configuration space. While the first method is the…

Recent years have seen a growing interest in the thermodynamic cost of dissipative structures formed by active particles. Given the strong finite-size effects of such systems, it is essential to develop efficient numerical approaches that…

An anisotropic random barrier model is presented, in which the transition probabilities in different directions have different probability density functions. At low temperatures, the anisotropic long--time diffusion coefficients, obtained…