Bayesian statistical modeling of microcanonical melting times at the superheated regime

Resultado de la investigación: Article

Resumen

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.

Idioma originalEnglish
Páginas (desde-hasta)546-557
Número de páginas12
PublicaciónPhysica A: Statistical Mechanics and its Applications
Volumen515
DOI
EstadoPublished - 1 feb 2019

Huella dactilar

Bayesian Modeling
Statistical Modeling
Melting
melting
simulation
Simulation Methods
Distribution Function
Crystal
distribution functions
Simulation
Self-diffusion
Vacancy
Energy
Statistical Inference
Kinetic energy
inference
Probabilistic Model
Truncation
crystals
Well-defined

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Citar esto

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title = "Bayesian statistical modeling of microcanonical melting times at the superheated regime",
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 = "Bayesian, Gamma distribution, Melting, Microcanonical, Waiting times",
author = "Sergio Davis and Claudia Loyola and Joaqu{\'i}n Peralta",
year = "2019",
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doi = "10.1016/j.physa.2018.09.174",
language = "English",
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journal = "Physica A: Statistical Mechanics and its Applications",
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TY - JOUR

T1 - Bayesian statistical modeling of microcanonical melting times at the superheated regime

AU - Davis, Sergio

AU - Loyola, Claudia

AU - Peralta, Joaquín

PY - 2019/2/1

Y1 - 2019/2/1

N2 - 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.

AB - 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.

KW - Bayesian

KW - Gamma distribution

KW - Melting

KW - Microcanonical

KW - Waiting times

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U2 - 10.1016/j.physa.2018.09.174

DO - 10.1016/j.physa.2018.09.174

M3 - Article

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

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