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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Kalligiannaki, Evangelia¹  Katsoulakis, Markos A.^2,3,4  Plechac, Petr¹  Vlachos, Dionisios G.⁵ 

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[3] Univ Crete, Dept Appl Math, Khania, Greece

[4] Fdn Res & Technol Hellas, Hellas, Greece

[5] Univ Delaware, Dept Chem Engn, Newark, DE 19716 USA

关键词: Markov chain Monte Carlo;    Coarse graining;    Lattice systems;    Phase transitions;    Pattern formation;   

DOI  :  10.1016/j.jcp.2011.12.011

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free