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Title: Parallelized event chain algorithm for dense hard sphere and polymer systems

Abstract

We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into simulation cells. We find that it is crucial for correctness to ensure detailed balance on the level of Monte Carlo sweeps by drawing the starting sphere of event chains within each simulation cell with replacement. We analyze the performance gains for the parallelized event chain and find a criterion for an optimal degree of parallelization. Because of the cluster nature of event chain moves massive parallelization will not be optimal. Finally, we discuss first applications of the event chain algorithm to dense polymer systems, i.e., bundle-forming solutions of attractive semiflexible polymers.

Authors:
; ;
Publication Date:
OSTI Identifier:
22382172
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 281; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; COMPUTERIZED SIMULATION; DRAWING; FILAMENTS; GAIN; MAGNETIC DISKS; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; PARTITION; PERFORMANCE; POLYMERS; SPHERES

Citation Formats

Kampmann, Tobias A., E-mail: tobias.kampmann@tu-dortmund.de, Boltz, Horst-Holger, and Kierfeld, Jan, E-mail: jan.kierfeld@tu-dortmund.de. Parallelized event chain algorithm for dense hard sphere and polymer systems. United States: N. p., 2015. Web. doi:10.1016/J.JCP.2014.10.059.
Kampmann, Tobias A., E-mail: tobias.kampmann@tu-dortmund.de, Boltz, Horst-Holger, & Kierfeld, Jan, E-mail: jan.kierfeld@tu-dortmund.de. Parallelized event chain algorithm for dense hard sphere and polymer systems. United States. doi:10.1016/J.JCP.2014.10.059.
Kampmann, Tobias A., E-mail: tobias.kampmann@tu-dortmund.de, Boltz, Horst-Holger, and Kierfeld, Jan, E-mail: jan.kierfeld@tu-dortmund.de. Thu . "Parallelized event chain algorithm for dense hard sphere and polymer systems". United States. doi:10.1016/J.JCP.2014.10.059.
@article{osti_22382172,
title = {Parallelized event chain algorithm for dense hard sphere and polymer systems},
author = {Kampmann, Tobias A., E-mail: tobias.kampmann@tu-dortmund.de and Boltz, Horst-Holger and Kierfeld, Jan, E-mail: jan.kierfeld@tu-dortmund.de},
abstractNote = {We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into simulation cells. We find that it is crucial for correctness to ensure detailed balance on the level of Monte Carlo sweeps by drawing the starting sphere of event chains within each simulation cell with replacement. We analyze the performance gains for the parallelized event chain and find a criterion for an optimal degree of parallelization. Because of the cluster nature of event chain moves massive parallelization will not be optimal. Finally, we discuss first applications of the event chain algorithm to dense polymer systems, i.e., bundle-forming solutions of attractive semiflexible polymers.},
doi = {10.1016/J.JCP.2014.10.059},
journal = {Journal of Computational Physics},
number = ,
volume = 281,
place = {United States},
year = {Thu Jan 15 00:00:00 EST 2015},
month = {Thu Jan 15 00:00:00 EST 2015}
}
  • Vapor-liquid equilibria (VLE) for solvent-polymer mixtures at modest pressures are obtained from a perturbed hard-sphere-chain equation of state. This equation of state is the sum of a hard-sphere-chain term as the reference system and a van der Waals attractive term as the perturbation. The reference equation follows from the Percus-Yevick integral theory coupled with chain connectivity as described by Chiew. The effect of specific interactions, such as hydrogen bonding, is introduced through the proposal of Veytsman based on the statistical distribution of hydrogen bonds between donor and acceptor sites suggested by molecular structure. Calculated and observed vapor-liquid equilibria are presentedmore » for nonpolar, polar, and hydrogen-bonding solvent + homopolymer systems. Pure-component parameters (number of segments per molecule, segment-segment energy, and segment diameter) are obtained from pure-component properties: liquid density and vapor pressure data for normal fluids and pressure-volume-temperature data for polymers. A binary energy interaction parameter must be obtained from limited VLE data for each binary system; this parameter appears to be independent of temperature and composition over a useful range. Theoretical correlations and predictions are in good agreement with experiment.« less
  • We continue here our series of studies in which integral-equation theory is developed and used for the monomer-monomer correlation functions in a fluid of multicomponent freely jointed hard-sphere polymers. In this study our approach is based on Wertheim{close_quote}s polymer Percus{endash}Yevick (PPY) theory supplemented by the ideal-chain approximation; it can be regarded as a simplified version of Wertheim{close_quote}s four-density PPY approximation for associating fluids considered in the complete-association limit. The numerical procedure of this simplified theory is much easier than that of the original Wertheim{close_quote}s four-density PPY approximation, but the degree of accuracy is reduced. The theory can also be regardedmore » as an extension of the PPY theory for the homonuclear polymer system proposed by Chang and Sandler [J. Chem. Phys. {bold 102}, 437 (1995)]. Their work is based upon a description of a system of hard-sphere monomers that associate into a polydisperse system of chains of prescribed mean length. Our theory instead directly describes a multicomponent system of associating monomers that form monodisperse chains of prescribed length upon complete association. An analytical solution of the PPY ideal-chain approximation for the general case of a multicomponent mixture of heteronuclear hard-sphere linear chain molecules is given. Its use is illustrated by numerical results for two models of copolymer fluids, a symmetrical diblock copolymer system, and an alternating copolymer system. The comparison with Monte Carlo simulations is given to gauge the accuracy of the theory. We find for the molecules we study here that predictions of our theory for heteronuclear chain systems have the same degree of accuracy as Chang and Sandler{close_quote}s theory for homonuclear chain systems. {copyright} {ital 1998 American Institute of Physics.}« less
  • Using Parsons-type scaling, the Onsager theory for theisotropic-nematic (I-N) transition of rigid-rod lyotropic polymer liquidcrystals is combined with the equation of state for hard-sphere-chainfluids of Chapman et al. and that of Hu et al. The equation of Hu et al.gives the I-N transition pressure and density in good agreement withcomputer simulation by Wilson and Allen for a semi-flexible hard-spherechain consisting of seven segments. For real semi-flexible polymers, wefollow the Khokhlov-Semenov theory of persistent chains that introduceschain flexibility into the Onsager theory. Using a consistent procedureto regress the equation-of-state parameters, the equations of Chapman etal. and Hu et al. are alsomore » compared with the theory of DuPre and Yangthat uses the equation of Lee for hard spherocylinders. These models arecompared with experiment for two binary polymer solutions containingpoly(hexyl isocyanate) and another solution containing polysaccharideschizophyllan. The concentration of polymer at the I-N transition ispredicted as a function of the molecular weight of polymer. All modelsperform similarly and show semi-quantitative agreement withexperiment.« less
  • The perturbative hypernetted-chain (PHNC) equation developed recently has been applied to the one-component plasma (OCP) and the one-component charged hard-sphere (OCCHS) systems in a uniform compensating background. Computed thermodynamic properties and pair correlation functions show that the PHNC gives excellent agreement with computer simulations and that it is as accurate as (or, in some cases, superior to) the reference-hypernetted chain and the hypernetted-chain-mean spherical equations, representing the two best currently available theories. The PHNC also predicts the OCP screening function at short range in close agreement with computer simulations and is superior to other theoretical results. Reliability of the radialmore » distribution function at the hard-sphere contact distance for the OCCHS is also discussed. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.« less
  • We present comprehensive results of large-scale molecular dynamics and Monte Carlo simulations of systems of dense hard spheres at volume fraction {phi} along the disordered, metastable branch of the phase diagram from the freezing-point {phi}{sub {ital f}} to random close packing volume {phi}{sub {ital c}}. It is shown that many previous simulations contained deficiencies caused by crystallization and finite-size effects. We quantify the degree of local crystallization through an order parameter and study it as a function of time and initial conditions to determine the necessary conditions to obtain truly random systems. This ordering criterion is used to show thatmore » previous methods employed to ascertain the degree of randomness are inadequate. A careful study of the pressure is also carried out along the entire metastable branch. In the vicinity of the random-close packing fraction, we show that the pressure scales as ({phi}{sub {ital c}}{minus}{phi}){sup {minus}{gamma}}, where {gamma}=1 and {phi}{sub {ital c}}=0.644{plus_minus}0.005. Contrary to previous studies, we find no evidence of a thermodynamic glass transition. {copyright} {ital 1996 American Institute of Physics.}« less