Multilevel coarse graining and nano-pattern discovery in many particle stochastic systems

Evangelia Kalligiannaki*, Markos A. Katsoulakis, Petr Plecháč, Dionisios G. Vlachos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In this work we propose a hierarchy of Markov chain Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub-steps efficiently coupling coarse and finer state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.

Original languageEnglish (US)
Pages (from-to)2599-2620
Number of pages22
JournalJournal of Computational Physics
Issue number6
StatePublished - Mar 20 2012
Externally publishedYes

Bibliographical note

Funding Information:
The research was supported by the National Science Foundation, E.K. and P.P. under the Grant NSF-CMMI-0835582, M.A.K. under the Grant NSF-CMMI-0835673 and DMS-715125 and D.G.V. under the Grant NSF-CMMI-0835548.


  • Coarse graining
  • Lattice systems
  • Markov chain Monte Carlo
  • Pattern formation
  • Phase transitions

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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