Collective translational and rotational Monte Carlo cluster move for general pairwise interaction

Abstract

Original citation:Růžička, Štěpán and Allen, M. P.. (2014) Copies of full items can be used for personal research or study, educational, or not-for profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way.Publisher's statement: © 2014 APS http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.033302 A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. Virtual move Monte Carlo (VMMC) is a cluster algorithm which was originally developed for strongly attractive colloidal, molecular or atomistic systems in order to both approximate the collective dynamics and avoid sampling of unphysical kinetic traps. In this paper, we present the algorithm in the form, which selects the moving cluster through a wider class of virtual states, and which is applicable to general pairwise interactions, including hard-core repulsion. The newly proposed way of selecting the cluster increases the acceptance probability by up to several orders of magnitude especially for rotational moves. The results have their applications in simulations of systems interacting via anisotropic potentials both to enhance the sampling of the phase space and to approximate the dynamics.

Improving the acceptance in Monte Carlo simulations: Sampling through intermediate states

“…[3][4][5][6] and the references therein) as well as for the coarse-graining from the atomistic to the mesoscopic scale [7][8][9][10][11][12][13][14][15][16][17][18]. Ranging from properly tailored biases [5,[19][20][21][22][23][24][25][26] and the sampling of 'rejectable' states [27,28] to the combination of Nonequilibrium Candidate Monte Carlo with Configurational Freezing [29][30][31], up to now a large number of strategies and alternative algorithms aimed to improve the acceptance of random moves constitute the vast realm of MC methods for the simulation of physical systems. Among all these methods, in this paper we focus on multiple-proposal schemes, in which the outcoming configuration is selected among a number ≥1 of trial configurations.…”

Monte Carlo simulation of kinetically slowed down phase separation

“…Systems of these particles are quenched from the fluid phase to the region of the phase diagram where condensation into liquid drops ensues. Monte Carlo techniques [18,26,27] are then used to study the competition between the kinetics of crystallization in the drops, and the aggregation of the drops into a single domain, or multiple metastable domains.…”

“…If non-local moves were used [19], the system studied here would eventually reach the thermodynamically stable state where gas coexists with a crystal. Translational and rotational MC cluster moves [20,18,26,27], known as virtual move Monte Carlo (VMMC), have been used here to model the dynamics. The algorithm selects the moving particles or clusters according to the local forcefields, and turned out to be particularly efficient in the simulation of aggregation in low-density systems [18,26,27].…”

“…Translational and rotational MC cluster moves [20,18,26,27], known as virtual move Monte Carlo (VMMC), have been used here to model the dynamics. The algorithm selects the moving particles or clusters according to the local forcefields, and turned out to be particularly efficient in the simulation of aggregation in low-density systems [18,26,27]. Another advantage of the VMMC algorithm is the ability to control the acceptance rate of differently sized moving clusters, thus distinguishing between their diffusion rates.…”

Design strategies for self-assembly of discrete targets

“…For example, such approaches have been useful in modelling relatively dense colloidal suspensions. 60,61 Monte Carlo is particularly appealing for models with a mixture of hard and continuous interactions, 62 such as the model detailed in Section II, since Monte Carlo does not require explicit forces and torques and hence derivatives of the potential. However, we envisage our self-assembling system being spatially highly inhomogeneous because the overall suspension of building blocks is dilute, while the assembling clusters themselves are locally dense.…”