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Massive replica exchange Monte Carlo: a tool to access high pressure thermodynamics of hard systems

Abstract

We have explored the idea of producing the equilibrium equation of state, i. e. the pressure as a function packing fraction, βP(φ), of a confined system up to very high pressures to yield the configuration that leads to the maximum packing fraction. For this purpose we have massively implemented the replica exchange Monte Carlo algorithm in graphic processing units (GPUs), in such a way that each GPU core handles a single simulation cell. This yields a very easy scheme to implement parallelization for a very large amount of replicas (thousands), which densely sample configuration space. We have tested this idea with a very well studied system, i.~e.~discs confined by a circular cavity, for a number of particles N ≤ 125. In all cases, our outcomes for configurations having maximum packing fractions are in perfect agreement with those already reported and conjectured optimal in the literature, for which there is no formal mathematical prove, strongly suggesting they are indeed optimal configurations. Furthermore, for most cases, we have obtained the same function βP(φ), by compressing loose random configurations and by decompressing copies of the configuration having the largest packing fraction. This supports numerically that the so obtained maximum packing configurations are, indeed, the correct answer.

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Publication details

The article was received on 12 Jun 2018, accepted on 08 Oct 2018 and first published on 10 Oct 2018


Article type: Paper
DOI: 10.1039/C8CP03727B
Citation: Phys. Chem. Chem. Phys., 2018, Accepted Manuscript
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    Massive replica exchange Monte Carlo: a tool to access high pressure thermodynamics of hard systems

    E. Basurto, C. Haro-Pérez, C. A. Vargas and G. Odriozola, Phys. Chem. Chem. Phys., 2018, Accepted Manuscript , DOI: 10.1039/C8CP03727B

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