Examinando por Autor "Peralta, Joaquín"
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Ítem A Bayesian interpretation of first-order phase transitions(Springer Science and Business Media, LLC, 2016-03) Davis, Sergio; Peralta, Joaquín; Navarrete, Yasmín; González, Diego; Gutiérrez, GonzaloIn this work we review the formalism used in describing the thermody namics of first-order phase transitions from the point of view of maximum entropy inference. We present the concepts of transition temperature, latent heat and entropy difference between phases as emergent from the more fundamental concept of internal energy, after a statistical inference analysis. We explicitly demonstrate this point of view by making inferences on a simple game, resulting in the same formalism as in thermodynamical phase transitions. We show that analogous quantities will inevitably arise in any problem of inferring the result of a yes/no question, given two different states of knowledge and information in the form of expectation values. This exposi tion may help to clarify the role of these thermodynamical quantities in the context of different first-order phase transitions such as the case of magnetic Hamiltonians (e.g. the Potts model).Ítem Bayesian statistical modeling of microcanonical melting times at the superheated regime(Physica A: Statistical Mechanics and its Applications, 2019-02-01) Davis, Sergio; Loyola, Claudia; Peralta, JoaquínHomogeneous 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.Ítem Configurational density of states and melting of simple solids(Elsevier B. V., 2023-11-01) Davis, Sergio; Loyola, Claudia; Peralta, JoaquínWe analyze the behavior of the microcanonical and canonical caloric curves for a piecewise model of the configurational density of states of simple solids in the context of melting from the superheated state, as realized numerically in the Z-method via atomistic molecular dynamics. A first-order phase transition with metastable regions is reproduced by the model, being therefore useful to describe aspects of the melting transition. Within this model, transcendental equations connecting the superheating limit, the melting point, and the specific heat of each phase are presented and numerically solved. Our results suggest that the essential elements of the microcanonical Z curves can be extracted from simple modeling of the configurational density of states.Ítem Desarrollo e implementación de métodos de cómputo para densidades de estados, usando ensambles generalizados(Universidad Andrés Bello, 2022) Moreno Muñoz, Felipe Eduardo; Peralta, Joaquín; Davis, Sergio; Faraggi, Alberto; Gutiérrez, Gonzalo; Molina, Francisco; Poblete, Simón; Facultad de Ciencias ExactasEl presente trabajo se enfoca en el desarrollo e implementación de algoritmos de simulación que permitan calcular la Densidad de Estados (DOS) de sistemas de muchas partículas interactuantes usando ensambles generalizados. Métodos para obtener las propiedades de un sistema que se basan en el uso de ensambles canónicos o microcanónicos—como el popular algoritmo de Metropolis—se han usado durante ya un largo tiempo. Sin embargo, el empleo de ensambles generalizados muestra ser una alternativa que permite generar curvas más suaves con menor número de simulaciones, además de evitar ciertos problemas típicos de esos métodos como el tener dificultades para muestrear correctamente sistemas con muchos mínimos locales. En este trabajo se presenta una implementación flexible y modular del algoritmo de Wang–Landau, además de un novedoso algoritmo basado en un método Bayesiano para el cálculo directo de la DOS, los cuales puede ser usados para obtener las propiedades termodinámicas de un sistema con una superficie de energía potencial compleja. Nuestros resultados muestran que los algoritmos son capaces de calcular la DOS con razonable precisión. Hemos estudiado, como aplicación de los métodos anteriormente mencionados, las propiedades termodinámicas de un modelo de Potts de 3 estados modificado, en el contexto de la aproximación de “lattice gas” para partículas cargadas confinadas en un volumen.Ítem Statistical distribution of thermal vacancies close to the melting point(Elsevier, 2015-01) Pozo, María José; Davis, Sergio; Peralta, JoaquínA detailed description of the statistical distribution of thermal vacancies in an homogeneous crystal near its melting point is presented, using the embedded atom model for copper as an example. As the temperature increase, the average number of thermal vacancies generated by atoms migrating to neighboring sites increases according to Arrhenius' law. We present for the first time a model for the statistical distribution of thermal vacancies, which according to our atomistic computer simulations follow a Gamma distribution. All the simulations are carried out by classical molecular dynamics and the recognition of vacancies is achieved via a recently developed algorithm. Our results could be useful in the further development of a theory explaining the mechanism of homogeneous melting, which seems to be mediated by the accumulation of thermal vacancies near the melting point. © Elsevier B.V. All rights reserved.