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We point out that a newly introduced recursive algorithm for lattice polymers has a much wider range of applicability. In particular, we apply it to the simulation of off-lattice polymers with Lennard-Jones potentials between non-bonded…

Condensed Matter · Physics 2009-10-22 Peter Grassberger , Rainer Hegger

We interpret uncertainty in a model for seismic wave propagation by treating the model parameters as random variables, and apply the Multilevel Monte Carlo (MLMC) method to reduce the cost of approximating expected values of selected,…

Numerical Analysis · Mathematics 2019-09-06 Marco Ballesio , Joakim Beck , Anamika Pandey , Laura Parisi , Erik von Schwerin , Raul Tempone

Since the middle of the 1940's scientists have used Monte Carlo (MC) simulations to obtain information about physical processes. This has proved a accurate and and reliable method to obtain this information. Through out resent years…

Astrophysics of Galaxies · Physics 2012-07-02 Thomas Amby Ottosen

We investigate the collective behavior of an Ising lattice gas, driven to non-equilibrium steady states by being coupled to {\em two} thermal baths. Monte Carlo methods are applied to a two-dimensional system in which one of the baths is…

Statistical Mechanics · Physics 2009-10-31 E. L. Praestgaard , B. Schmittmann , R. K. P. Zia

Density matrix quantum Monte Carlo (DMQMC) is used to sample exact-on-average $N$-body density matrices for uniform electron gas systems of up to 10$^{124}$ matrix elements via a stochastic solution of the Bloch equation. The results of…

Strongly Correlated Electrons · Physics 2016-09-14 Fionn D. Malone , N. S. Blunt , Ethan W. Brown , D. K. K. Lee , J. S. Spencer , W. M. C. Foulkes , James J. Shepherd

We report developments of the kinetic Monte Carlo (KMC) method with improved accuracy and increased versatility for the description of atomic diffusivity on metal surfaces. The on-lattice constraint built into our recently proposed…

Materials Science · Physics 2008-11-27 Oleg Trushin , Handan Yildirim , Abdelkader Kara , Talat S. Rahman

We demonstrate the feasibility of realistic Shell-Model Monte Carlo (SMMC) calculations spanning multiple major shells, using a realistic interaction whose bad saturation and shell properties have been corrected by a newly developed general…

Nuclear Theory · Physics 2009-10-30 D. J. Dean , M. T. Ressell , M. Hjorth-Jensen , S. E. Koonin , K. Langanke , A. P. Zuker

We introduce a generalised micro-macro Markov chain Monte Carlo (mM-MCMC) method with pseudo-marginal approximation to the free energy, that is able to accelerate sampling of the microscopic Gibbs distributions when there is a time-scale…

Numerical Analysis · Mathematics 2023-03-28 Hannes Vandecasteele , Giovanni Samaey

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…

Soft Condensed Matter · Physics 2025-03-24 Ki-Won Kim , Euijoon Kwon , Yongjoo Baek

This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized…

Computational Engineering, Finance, and Science · Computer Science 2020-03-24 Armin Galetzka , Zeger Bontinck , Ulrich Römer , Sebastian Schöps

The discrete time path integral Monte Carlo (PIMC) with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action…

Statistical Mechanics · Physics 2015-06-25 Dong-Hee Kim , Yu-Cheng Lin , Heiko Rieger

Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…

Statistical Mechanics · Physics 2017-05-22 Manuel Athènes , Pierre Terrier

Lattice mismatch can substantially impact the spatial organization of heterogeneous materials. We examine a simple model for lattice-mismatched solids over a broad range of temperature and composition, revealing both uniform and spatially…

Statistical Mechanics · Physics 2019-10-02 Layne B. Frechette , Christoph Dellago , Phillip L. Geissler

The nature of freezing and melting transitions for a system of model colloids interacting by a DLVO potential in a spatially periodic external potential is studied using extensive Monte Carlo simulations. Detailed finite size scaling…

Statistical Mechanics · Physics 2009-11-07 W. Strepp , S. Sengupta , P. Nielaba

Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice however, sampling of the complete configuration space is often hindered by high energy barriers between different regions…

Statistical Mechanics · Physics 2020-05-04 Jonas A. Finkler , Stefan Goedecker

In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of…

High Energy Physics - Lattice · Physics 2022-12-07 Cagin Yunus , William Detmold

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…

Computation · Statistics 2016-08-22 Qingsha Chen , Ju Ming

The phase field crystal (PFC) method has emerged as a promising technique for modeling materials with atomistic resolution on mesoscopic time scales. The approach is numerically much more efficient than classical density functional theory…

Materials Science · Physics 2015-05-18 Michael Greenwood , Nikolas Provatas , Jörg Rottler

The multi-GPU open-source package QCDGPU for lattice Monte Carlo simulations of pure SU(N) gluodynamics in external magnetic field at finite temperature and O(N) model is developed. The code is implemented in OpenCL, tested on AMD and…

High Energy Physics - Lattice · Physics 2013-10-29 Vadim Demchik , Natalia Kolomoyets

The monolayer adsorption process of interacting binary mixtures of species $A$ and $B$ on square lattices is studied through grand canonical Monte Carlo simulation in the framework of the lattice-gas model. Four different energies have been…