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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…

Numerical Analysis · Mathematics 2023-02-15 Yi Sun , Changhui Tan

Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…

Computation · Statistics 2025-05-15 Abdul-Lateef Haji-Ali , Marcelo Pereyra , Luke Shaw , Konstantinos Zygalakis

We describe the development of a new object kinetic Monte Carlo code where the elementary defect objects are off-lattice atomistic configurations. Atomic-level transitions are used to transform and translate objects, to split objects and to…

Materials Science · Physics 2019-09-04 Daniel R. Mason , Andrea E. Sand , Sergei L. Dudarev

The reliability of kinetic Monte Carlo (KMC) simulations depends on accurate transition rates. The self-learning KMC method (Trushin et al 2005 Phys. Rev. B 72 115401) combines the accuracy of rates calculated from a realistic potential…

Materials Science · Physics 2013-01-01 A. Latz , L. Brendel , D. E. Wolf

We simulate the sintering of particle aggregates due to surface diffusion. As a method we use Kinetic Monte-Carlo simulations in which elasticity can explicitly be taken into account. Therefore it is possible to investigate the shape…

Statistical Mechanics · Physics 2007-05-23 F. Westerhoff , R. Zinetullin , D. E. Wolf

We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm.…

Probability · Mathematics 2014-04-10 Martin Hairer , Jonathan Weare

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…

Soft Condensed Matter · Physics 2020-07-15 Fabián A. García Daza , Alejandro Cuetos , Alessandro Patti

We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like…

Statistical Mechanics · Physics 2013-05-20 Karsten Schwarz , Heiko Rieger

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…

Fluid Dynamics · Physics 2014-04-18 Irina Sagert , Dirk Colbry , Terrance Strother , Rodney Pickett , Wolfgang Bauer

We present a cluster kinetic Monte-Carlo algorithm for active matter systems of self-propelled particles with special focus on steric interactions. The kinetic event-chain algorithm is based on the event-chain Monte-Carlo method and is…

Soft Condensed Matter · Physics 2026-05-07 Nico Schaffrath , Thevashangar Sathiyanesan , Tobias A. Kampmann , Jan Kierfeld

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…

Condensed Matter · Physics 2007-05-23 B. Abdullaev , M. Musakhanov , A. Nakamura

We created an efficient algorithm suitable for graphics processing units (GPUs) to perform Monte Carlo simulations of a subset of reaction-diffusion models. The algorithm uses techniques that are specific to GPU programming, and combines…

Computational Physics · Physics 2013-03-06 R. D. Schram

This work describes a new 1D hybrid approach for modeling atmospheric pressure discharges featuring complex chemistry. In this approach electrons are described fully kinetically using Particle-In-Cell/Monte-Carlo (PIC/MCC) scheme, whereas…

Plasma Physics · Physics 2016-01-20 Denis Eremin , Torben Hemke , Thomas Mussenbrock

We implement a computer-assisted approach that, under appropriate conditions, allows the bifurcation analysis of the coarse dynamic behavior of microscopic simulators without requiring the explicit derivation of closed macroscopic equations…

Pattern Formation and Solitons · Physics 2009-11-07 Alexei G. Makeev , Dimitrios Maroudas , Ioannis G. Kevrekidis

We have developed an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with…

Statistical Mechanics · Physics 2009-11-13 Tota Nakamura

A high-fidelity kinetic Monte Carlo (KMC) simulation method (T. Treeratanaphitak, M. Pritzker, N. M. Abukhdeir, Electrochim. Acta 121 (2014) 407--414) using the semi-empirical multi-body embedded-atom method (EAM) potential has been…

Chemical Physics · Physics 2014-07-22 Tanyakarn Treeratanaphitak , Mark D. Pritzker , Nasser Mohieddin Abukhdeir

We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…

Numerical Analysis · Mathematics 2012-08-06 Evangelia Kalligiannaki , Markos A. Katsoulakis , Petr Plechac

The investigation of freezing transitions of single polymers is computationally demanding, since surface effects dominate the nucleation process. In recent studies we have systematically shown that the freezing properties of flexible,…

Soft Condensed Matter · Physics 2012-07-18 Stefan Schnabel , Michael Bachmann , Wolfhard Janke

In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent…

Statistical Mechanics · Physics 2018-03-13 E. M. Inack , G. Giudici , T. Parolini , G. Santoro , S. Pilati

In molecular simulations, efficient methods for investigating equilibration and slow relaxation in dense systems are crucial yet challenging. This study focuses on the diffusional characteristics of monodisperse hard disk systems at…

Soft Condensed Matter · Physics 2024-10-21 Daigo Mugita , Masaharu Isobe