Bayesian statistical modeling of microcanonical melting times at the superheated regime

Sergio Davis, Claudia Loyola and Joaquín Peralta

Physica A: Statistical Mechanics and its Applications, 2019, vol. 515, issue C, 546-557

Abstract: Homogeneous melting of superheated crystals at constant energy is a dynamical process, believed to be triggered by the accumulation of thermal vacancies and their self-diffusion. From microcanonical simulations we know that if an ideal crystal is prepared at a given kinetic energy, it takes a random time tw until the melting mechanism is actually triggered. In this work we have studied in detail the statistics of tw for melting at different energies by performing a large number of Z-method simulations and applying state-of-the-art methods of Bayesian statistical inference. By focusing on a small system size and short-time tail of the distribution function, we show that tw is actually gamma-distributed rather than exponential (as asserted in a previous work), with decreasing probability near tw∼0. We also explicitly incorporate in our model the unavoidable truncation of the distribution function due to the limited total time span of a Z-method simulation. The probabilistic model presented in this work can provide some insight into the dynamical nature of the homogeneous melting process, as well as giving a well-defined practical procedure to incorporate melting times from simulation into the Z-method in order to correct the effect of short simulation times.

Keywords: Melting; Microcanonical; Bayesian; Gamma distribution; Waiting times (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:515:y:2019:i:c:p:546-557

DOI: 10.1016/j.physa.2018.09.174

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