Rejection-Free Geometric Cluster Algorithm for Complex Fluids

Liu, Jiwen; Luijten, Erik

doi:10.1103/physrevlett.92.035504

Cited by 135 publications

(175 citation statements)

References 21 publications

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“…This means that the cluster is accepted whenever the boundary only contains outright failed links and is rejected otherwise. This form of the acceptance probability is similar to the original rejection-free cluster algorithms [3,5], and represents an example where the early rejection scheme is useful when applied to many-particle moves [19].…”

Section: Free Cluster Selectionmentioning

confidence: 97%

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Collective translational and rotational Monte Carlo moves for attractive particles

Růžička

Allen

2014

Phys. Rev. E

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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 American Physical Society Published version: http://dx.doi.org/10.1103/PhysRevE.89.033307 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 is a Monte Carlo (MC) cluster algorithm forming clusters via local energy gradients and approximating the collective kinetic or dynamic motion of attractive colloidal particles. We carefully describe, analyze, and test the algorithm. To formally validate the algorithm through highlighting its symmetries, we present alternative and compact ways of selecting and accepting clusters which illustrate the formal use of abstract concepts in the design of biased MC techniques: the superdetailed balance and the early rejection scheme. A brief and comprehensive summary of the algorithms is presented, which makes them accessible without needing to understand the details of the derivation.

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Section: Free Cluster Selectionmentioning

confidence: 97%

“…Virtual move Monte Carlo (VMMC) is a sequel to other cluster algorithms [1][2][3][4][5][6] for the computer simulation of atomic systems. Its basis is to apply a Monte Carlo (MC) move map to all particles in a cluster.…”

Section: Introductionmentioning

confidence: 99%

Collective translational and rotational Monte Carlo moves for attractive particles

Růžička

Allen

2014

Phys. Rev. E

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“…6 In special cases it is possible to choose the trial probability R ij in such a way that all trial moves are accepted. [7][8][9][10] Usually, however, P acc (on) e 1, and there is a probability 1 -P acc (on) that the trial move will be rejected. In that case the new state is rejected, and all information about it is discarded.…”

mentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10] The core of any MCMC program is an algorithm that generates a Markov chain of configurations. By a judicious choice of the transition probability from one point in the chain to the next, the overall probability of visiting each microstate can be made proportional to its statistical weight F (e.g.…”

mentioning

confidence: 99%

Monte Carlo Sampling of a Markov Web

Boulougouris

Frenkel

2005

J. Chem. Theory Comput.

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Abstract:The efficiency of Markov-Chain Monte Carlo simulations can be enhanced by exploiting information about trial moves that would normally be rejected. The original presentation of this approach was limited to a specific MC sampling scheme. Here we present a general derivation of a method to improve the sampling efficiency of Monte Carlo simulations by collecting information about the microstates that can be linked directly to the sampled point via an independent Markov transition matrix. As an illustration, we show that our approach greatly enhances the efficiency of a scheme to compute the density of states of a square-well fluid.

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“…To obtain estimates for B eff 3 we deploy the geometrical cluster algorithm (GCA) [25,26]. This efficient rejectionfree Monte Carlo scheme can generate equilibrium configurations at practically any value of q.…”

mentioning

confidence: 99%

Quantifying the effects of neglecting many-body interactions in coarse-grained models of complex fluids

Ashton

Wilding

2014

Phys. Rev. E

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We describe a general simulation scheme for assessing the thermodynamic consequences of neglecting many-body effects in coarse-grained models of complex fluids. The method exploits the fact that the asymptote of a simple-to-measure structural function provides direct estimates of virial coefficients. Comparing the virial coefficients of an atomistically detailed system with those of a coarse-grained version described by pair potentials, permits the role of many-body effects to be quantified. The approach is applied to two models: (i) a size-asymmetrical colloid-polymer mixture, and (ii) a solution of star polymers. In the latter case, coarse-graining to an effective fluid described by pair potentials is found to neglect important aspects of the true behaviour.Many-body forces occur when the net interaction between two particles is not simply pairwise additive, but depends on the presence of other particles. They appear in a wide range of physical systems including dense phases of noble gases [1], molecular systems [2], nuclear matter [3], superconductors [4] and complex fluids such as polymers [5], lipid membranes [6,7] and colloidal dispersions [8][9][10][11]. In seeking to make theoretical and computational progress with such systems one often attempts to simplify matters by "coarse-graining" ie. integrating over the degrees of freedom on small length or times scales. This leads to a description of the system in term of an effective Hamiltonian describing the interactions among the remaining degrees of freedom. These interactions are inherently many-body in character, even if the original system involves only pairwise interactions.To appreciate how many-body interactions arise in coarse-grained (CG) representations of complex fluids, consider the case of colloids dispersed in a sea of much smaller polymers. This system is commonly modelled as a highly size-asymmetrical mixture of spheres as shown in the simulation snapshot of Fig. 1(a). However, since dealing with components of disparate sizes is theoretically and computationally problematic, one typically seeks to integrate out the polymer degrees of freedom to yield an effective one-component model. But the colloidal interactions arise from the modulation of the polymer density distribution by all the colloids, and consequently, the effective one-component description is many-body in form. A second example is shown in Fig. 1(b) which depicts three star polymers in solution. A common CG model replaces each star by a single effective particle. However, the net interaction between two polymers depends on the proximity of a third, and hence the effective Hamiltonian has a many-body character [12].Computer simulation is a powerful route for designing CG models for complex fluids, which is currently receiving considerable attention. Indeed, in principle it can be used to determine a many-body potential for the CG coordinates which is consistent with the underlying atomistic model [13,14]. But implementing such approaches (Color online).(a) Snapshot of a highly siz...

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Rejection-Free Geometric Cluster Algorithm for Complex Fluids

Cited by 135 publications

References 21 publications

Collective translational and rotational Monte Carlo moves for attractive particles

Collective translational and rotational Monte Carlo moves for attractive particles

Monte Carlo Sampling of a Markov Web

Quantifying the effects of neglecting many-body interactions in coarse-grained models of complex fluids

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