### 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 t_{w} until the melting mechanism is actually triggered. In this work we have studied in detail the statistics of t_{w} 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 t_{w} is actually gamma-distributed rather than exponential (as asserted in a previous work), with decreasing probability near t_{w}∼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 original | English |
---|---|

Páginas (desde-hasta) | 546-557 |

Número de páginas | 12 |

Publicación | Physica A: Statistical Mechanics and its Applications |

Volumen | 515 |

DOI | |

Estado | Published - 1 feb 2019 |

### Huella dactilar

### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics

### Citar esto

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**Bayesian statistical modeling of microcanonical melting times at the superheated regime.** / Davis, Sergio; Loyola, Claudia; Peralta, Joaquín.

Resultado de la investigación: Article

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

UR - http://www.scopus.com/inward/record.url?scp=85054578367&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2018.09.174

DO - 10.1016/j.physa.2018.09.174

M3 - Article

VL - 515

SP - 546

EP - 557

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -