Stochastic Kinetic Monte Carlo algorithms for long-range Hamiltonians

Mason, D R; Rudd, R E; Sutton, A P

Title: Stochastic Kinetic Monte Carlo algorithms for long-range Hamiltonians

Full Record
Other Related Research

Abstract

We present a higher order kinetic Monte Carlo methodology suitable to model the evolution of systems in which the transition rates are non- trivial to calculate or in which Monte Carlo moves are likely to be non- productive flicker events. The second order residence time algorithm first introduced by Athenes et al.[1] is rederived from the n-fold way algorithm of Bortz et al.[2] as a fully stochastic algorithm. The second order algorithm can be dynamically called when necessary to eliminate unproductive flickering between a metastable state and its neighbors. An algorithm combining elements of the first order and second order methods is shown to be more efficient, in terms of the number of rate calculations, than the first order or second order methods alone while remaining statistically identical. This efficiency is of prime importance when dealing with computationally expensive rate functions such as those arising from long- range Hamiltonians. Our algorithm has been developed for use when considering simulations of vacancy diffusion under the influence of elastic stress fields. We demonstrate the improved efficiency of the method over that of the n-fold way in simulations of vacancy diffusion in alloys. Our algorithm is seen to be an order of magnitudemore »« less

Authors:: Mason, D R; Rudd, R E; Sutton, A P

Publication Date:: Mon Oct 13 00:00:00 EDT 2003

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 15013627

Report Number(s):: UCRL-JRNL-200451
Journal ID: ISSN 0010-4655; CPHCBZ; TRN: US200604%%50

DOE Contract Number:: W-7405-ENG-48

Resource Type:: Journal Article

Journal Name:: Computer Physics Communications

Additional Journal Information:: Journal Volume: 160; Journal Issue: 2; Journal ID: ISSN 0010-4655

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; ALLOYS; DIFFUSION; EFFICIENCY; HAMILTONIANS; KINETICS; MAGNESIUM; METASTABLE STATES; TRAPPING; VACANCIES

Citation Formats


                    Mason, D R, Rudd, R E, and Sutton, A P. Stochastic Kinetic Monte Carlo algorithms for long-range Hamiltonians.  United States: N. p., 2003. 
        Web.

Copy to clipboard


                    Mason, D R, Rudd, R E, & Sutton, A P. Stochastic Kinetic Monte Carlo algorithms for long-range Hamiltonians.  United States.

Copy to clipboard


                    Mason, D R, Rudd, R E, and Sutton, A P. 2003.  
        "Stochastic Kinetic Monte Carlo algorithms for long-range Hamiltonians".  United States.  https://www.osti.gov/servlets/purl/15013627.

Copy to clipboard


                    
@article{osti_15013627,

  title        = {Stochastic Kinetic Monte Carlo algorithms for long-range Hamiltonians},

  author       = {Mason, D R and Rudd, R E and Sutton, A P},

  abstractNote = {We present a higher order kinetic Monte Carlo methodology suitable to model the evolution of systems in which the transition rates are non- trivial to calculate or in which Monte Carlo moves are likely to be non- productive flicker events. The second order residence time algorithm first introduced by Athenes et al.[1] is rederived from the n-fold way algorithm of Bortz et al.[2] as a fully stochastic algorithm. The second order algorithm can be dynamically called when necessary to eliminate unproductive flickering between a metastable state and its neighbors. An algorithm combining elements of the first order and second order methods is shown to be more efficient, in terms of the number of rate calculations, than the first order or second order methods alone while remaining statistically identical. This efficiency is of prime importance when dealing with computationally expensive rate functions such as those arising from long- range Hamiltonians. Our algorithm has been developed for use when considering simulations of vacancy diffusion under the influence of elastic stress fields. We demonstrate the improved efficiency of the method over that of the n-fold way in simulations of vacancy diffusion in alloys. Our algorithm is seen to be an order of magnitude more efficient than the n-fold way in these simulations. We show that when magnesium is added to an Al-2at.%Cu alloy, this has the effect of trapping vacancies. When trapping occurs, we see that our algorithm performs thousands of events for each rate calculation performed.},

  doi          = {},

  url          = {https://www.osti.gov/biblio/15013627},
  journal      = {Computer Physics Communications},

  issn         = {0010-4655},

  number       = 2,

  volume       = 160,

  place        = {United States},

  year         = {Mon Oct 13 00:00:00 EDT 2003},

  month        = {Mon Oct 13 00:00:00 EDT 2003}

}

Copy to clipboard

Journal Article:

View Journal Article (0.85 MB)

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

A new class of accelerated kinetic Monte Carlo algorithms

Technical Report Bulatov, V; Oppelstrup, T; Athenes, M

Kinetic (aka dynamic) Monte Carlo (KMC) is a powerful method for numerical simulations of time dependent evolution applied in a wide range of contexts including biology, chemistry, physics, nuclear sciences, financial engineering, etc. Generally, in a KMC the time evolution takes place one event at a time, where the sequence of events and the time intervals between them are selected (or sampled) using random numbers. While details of the method implementation vary depending on the model and context, there exist certain common issues that limit KMC applicability in almost all applications. Among such is the notorious 'flicker problem' where themore »« less
https://doi.org/10.2172/1033740

Full Text Available
A First-Passage Kinetic Monte Carlo algorithm for complex diffusion-reaction systems

Journal Article Donev, Aleksandar; Bulatov, Vasily; Oppelstrup, Tomas; ... - Journal of Computational Physics

We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo (FPKMC) algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions. The FPKMC algorithm presented here is based on the method introduced in Oppelstrup et al. and is implemented in a robust and flexible framework. Unlike standard KMC algorithms such as the n-fold algorithm, FPKMC is most efficient at low densities where it replaces the many small hops needed for reactants to find each other with large first-passage hops sampled from exact time-dependent Green's functions, without sacrificing accuracy. We describemore »« less
https://doi.org/10.1016/j.jcp.2009.12.038
Homogeneous phase separation in binary alloys under ion irradiation conditions: Role of interstitial atoms

Journal Article Krasnochtchekov, P; Averback, R; Bellon, P - Physical Review. B, Condensed Matter and Materials Physics

Kinetic Monte Carlo simulations have been performed to investigate homogeneous precipitation in binary metal alloys under ion irradiation conditions. The kinetic model includes defect production, recombination, defect trapping, the formation of defect-solute complexes, and atomic mixing. While no special assumptions are made about vacancy diffusion, interstitial diffusion is assumed fast compared to the characteristic time scales of all other processes. The diffusion path of an interstitial, moreover, ends with one of the three possible outcomes: recombination, trapping in a solute-rich location, or clustering with other interstitials. Interstitials promote solute segregation in this model by the formation of mobile interstitial-solute complexes.more »« less
https://doi.org/10.1103/PHYSREVB.75.144107
Theory of Trotter Error with Commutator Scaling

Journal Article Childs, Andrew; Su, Yuan; Tran, Minh; ... - Physical Review X

The Lie-Trotter formula, together with its higher-order generalizations, provides a simple approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation andmore »« less
https://doi.org/10.1103/PhysRevX.11.011020
ON THE APPARENT NARROWING OF RADIO RECOMBINATION LINES AT HIGH PRINCIPAL QUANTUM NUMBERS

Journal Article Alexander, J; Gulyaev, S - Astrophysical Journal

We critically analyze the Bell et al. findings on 'anomalous' widths of high-order hydrogen radio recombination lines in the Orion Nebula at 6 GHz. We review their method of modified frequency switching and show that the way this method is used for large {Delta}n is not optimal and can lead to misinterpretation of measured spectral line parameters. Using a model of the Orion Nebula, conventional broadening theory, and Monte Carlo simulation, we determine a transition zone n = 224, ..., 241 ({Delta}n = 11, ..., 14), where measurement errors grow quickly with n and become comparable with the measurement valuesmore »« less
https://doi.org/10.1088/0004-637X/745/2/194

Similar Records