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In plasma edge simulations, the behavior of neutral particles is often described by a Boltzmann--BGK equation. Solving this kinetic equation and estimating the moments of its solution are essential tasks, typically carried out using Monte…
In plasma edge simulations, kinetic Monte Carlo (MC) is often used to simulate neutral particles and estimate source terms. For large-sized reactors, like ITER and DEMO, high particle collision rates lead to a substantial computational cost…
We develop a novel multilevel asymptotic-preserving Monte Carlo method, called Multilevel Kinetic-Diffusion Monte Carlo (ML-KDMC), for simulating the kinetic Boltzmann transport equation with a Bhatnagar-Gross-Krook (BGK) collision…
A kinetic Monte Carlo (KMC) method is used to study the structural properties and dynamics of a supercooled binary Lennard-Jones liquid around the glass transition temperature. This technique permits us to explore the potential energy…
Cellular scale decision making is modulated by the dynamics of signalling molecules and their diffusive trajectories from a source to small absorbing sites on the cellular surface. Diffusive capture problems are computationally challenging…
This article reviews the basic computational techniques for carrying out multi-scale simulations using statistical methods, with the focus on simulations of epitaxial growth. First, the statistical-physics background behind Monte Carlo…
The Dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian Dynamics or Molecular Dynamics simulation, DMC is…
While boundary plasmas in present-day tokamaks generally fall in a fluid regime, neutral species near the boundary often require kinetic models due to long mean-free-paths compared to characteristic spatial scales in the region. Monte-Carlo…
Kinetic Monte Carlo (KMC) is a powerful method for simulation of diffusion processes in various systems. The accuracy of the method, however, relies on the extent of details used for the parameterization of the model. Migration barriers are…
Particle-based kinetic Monte Carlo simulations of neutral particles is one of the major computational bottlenecks in tokamak scrape-off layer simulations. This computational cost comes from the need to resolve individual collision events in…
We present a multi-lattice kinetic Monte Carlo (kMC) approach that efficiently describes the atomistic dynamics of morphological transitions between commensurate structures at crystal surfaces. As an example we study the reduction of a…
To better understand the capture process by a nanopore, we introduce an efficient Kinetic Monte Carlo (KMC) algorithm that can simulate long times and large system sizes by mapping the dynamic of a point-like particle in a 3D spherically…
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…
The Kinetic Monte Carlo (KMC) method has become an important tool for examination of phenomena like surface diffusion and thin film growth because of its ability to carry out simulations for time scales that are relevant to experiments. But…
A kinetic Monte Carlo (KMC) method is presented to simulate the electrodeposition of a metal on a single crystal surface of the same metal under galvanostatic conditions. This method utilizes the multi-body embedded-atom method (EAM)…
Kinetic Monte Carlo (KMC) is an important computational tool in physics and chemistry. In contrast to standard Monte Carlo, KMC permits the description of time dependent dynamical processes and is not restricted to systems in equilibrium.…
This review article is intended as a practical guide for newcomers to the field of kinetic Monte Carlo (KMC) simulations, and specifically to lattice KMC simulations as prevalently used for surface and interface applications. We will…
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…
A massively parallel kinetic Monte Carlo (kMC) approach is proposed for simulating ionic migration in a crystal system by introducing the atomic fragmentation scheme (fragment kMC). The fragment kMC method achieved a reasonable parallel…
This paper presents a class of one-dimensional cellular automata (CA) models on traffic flows, featuring nonlocal look-ahead interactions. We develop kinetic Monte Carlo (KMC) algorithms to simulate the dynamics. The standard KMC method can…