Monte Carlo simulation of dense polymer melts using event chain algorithms

Many Markov chain Monte Carlo techniques currently available rely on discrete-time reversible Markov processes whose transition kernels are variations of the Metropolis-Hastings algorithm. We explore and generalize an alternative scheme recently introduced in the physics literature [27] where the target distribution is explored using a continuous-time non-reversible piecewise-deterministic Markov process. In the Metropolis-Hastings algorithm, a trial move to a region of lower target density, equivalently of higher "energy", than the current state can be rejected with positive probability. In this alternative approach, a particle moves along straight lines around the space and, when facing a high energy barrier, it is not rejected but its path is modified by bouncing against this barrier. By reformulating this algorithm using inhomogeneous Poisson processes, we exploit standard sampling techniques to simulate exactly this Markov process in a wide range of scenarios of interest. Additionally, when the target distribution is given by a product of factors dependent only on subsets of the state variables, such as the posterior distribution associated with a probabilistic graphical model, this method can be modified to take advantage of this structure by allowing computationally cheaper "local" bounces which only involve the state variables associated to a factor, while the other state variables keep on evolving. In this context, by leveraging techniques from chemical kinetics, we propose several computationally efficient implementations. Experimentally, this new class of Markov chain Monte Carlo schemes compares favorably to state-of-the-art methods on various Bayesian inference tasks, including for high dimensional models and large data sets.

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“…where an event (a bounce or refreshment) affected it. By (19), this represents a sublist of the list of all event times. At each of those times t…”

Section: Local Bps: Algorithm Descriptionmentioning

confidence: 99%

The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method

Bouchard‐Côté

Vollmer

Doucet

2018

Journal of the American Statistical Association

191

301

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“…1 c; is the pair distribution function and the thermal energy. The event-chain MC simulation technique is ideally suited for dense mixed colloidal systems 54 , 57 and allows us to obtain the positional and angular dependence of the potential of mean force as shown in Fig. 3 .…”

Section: Resultsmentioning

confidence: 99%

“…To simulate hard disks in a suspension of hard needles the event-chain MC algorithm for many-body interactions is used 53 , 54 , 62 . This is a rejection-free MC method that performs very well for dense systems 57 , which makes it an excellent choice for needle systems in the nematic phase, for which it has been adapted in Ref. 54 .…”

Section: Methodsmentioning

confidence: 99%

Chaining of hard disks in nematic needles: particle-based simulation of colloidal interactions in liquid crystals

Muller

Kampmann

Kierfeld

2020

Sci Rep

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Colloidal particles suspended in liquid crystals can exhibit various effective anisotropic interactions that can be tuned and utilized in self-assembly processes. We simulate a two-dimensional system of hard disks suspended in a solution of dense hard needles as a model system for colloids suspended in a nematic lyotropic liquid crystal. The novel event-chain Monte Carlo technique enables us to directly measure colloidal interactions in a microscopic simulation with explicit liquid crystal particles in the dense nematic phase. We find a directional short-range attraction for disks along the director, which triggers chaining parallel to the director and seemingly contradicts the standard liquid crystal field theory result of a quadrupolar attraction with a preferred angle. Our results can be explained by a short-range density-dependent depletion interaction, which has been neglected so far. Directionality and strength of the depletion interaction are caused by the weak planar anchoring of hard rods. The depletion attraction robustly dominates over the quadrupolar elastic attraction if disks come close. Self-assembly of many disks proceeds via intermediate chaining, which demonstrates that in lyotropic liquid crystal colloids depletion interactions play an important role in structure formation processes.

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“…The polymers were placed randomly into the box with a bond distance of 0.9 σ. Next, the "slow push off" method [32][33][34] was used to remove the overlaps between the non-bonded repeat units. The repulsive Lennard-Jones interaction was slowly switched on during this process until all overlaps were removed.…”

Section: Simulation Methodsmentioning

confidence: 99%

Solvent quality influences surface structure of glassy polymer thin films after evaporation

Statt

Howard

Panagiotopoulos

2017

The Journal of Chemical Physics

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Molecular dynamic simulations are used to investigate the structural effects of treating a glassy polymer thin film with solvents of varying quality and subsequently evaporating the solvent. Both a monodisperse film and a polydisperse film are studied for poor to good solvent conditions, including the limit in which the polymer film is fully dissolved. In agreement with previous studies, the dissolved polymer-solvent mixtures form a polymer-rich skin on top of the forming film during evaporation. In the case of the polydisperse films, a segregation of the lower molecular weight polymer to the film interface is observed. We provide a detailed, systematic analysis of the interface structure and properties during and after evaporation. We find that for non-dissolved films, the surface width of the film after solvent evaporation is enhanced compared to the case without solvent. Our results show that due to the kinetic arrest of the surface structure, the increased surface width is preserved after solvent evaporation for both mono- and polydisperse films. We conclude that it is important to take poor solvent effects into account for the surface morphology of already formed thin glassy films, an effect which is often neglected.

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Monte Carlo simulation of dense polymer melts using event chain algorithms

Cited by 31 publications

References 35 publications

The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method

The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method

Chaining of hard disks in nematic needles: particle-based simulation of colloidal interactions in liquid crystals

Solvent quality influences surface structure of glassy polymer thin films after evaporation

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