Termodinâmica estatística e redes neurais aplicadas ao estudo de fluidos atômicos

• Ano de defesa: 2022
• Autor(a) principal: Felipe Silva Carvalho
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; Brasil; ICX - DEPARTAMENTO DE QUÍMICA; Programa de Pós-Graduação em Química; UFMG
• Palavras-chave em Português: Equação de Ornstein-Zernike; Percus-Yevick; Hypernetted-Chain; Relações de fecho gerais; Função de Mittag-Leffler de dois parâmetros; Rede neural de Hopfield; Derivada de Gâteaux; Physics informed neural networks; Ornstein-Zernike equation; General closure relation; Two parameter Mittag-Leffler function; Hopfield Neural Network; Gateaux derivative; Físico-química; Redes neurais (Computação); Termodinâmica estatística; Dinâmica molecular; Funcionais de densidade; Equações integrais; Problemas inversos (Equações diferenciais); Fourier, Transformações de; Dinâmica dos fluidos
• Link de acesso: http://hdl.handle.net/1843/45976

The study of classical fluids can be carried out by different techniques, as for example: molecular dynamics, classical density functional theory or integral equations. One of the most successful integral equation was obtained in 1914 by L. S. Ornstein e F. Zernike and published in the paper "Accidental deviations of density and opalescence at the critical point of a single substance". This equation connects the total and direct correlation functions, h(r) and C(r). However, solving this equation requires the knowledge of an additional relation between these functions, which is called a closure relation. In this work it will be given attention to this problem. The Percus-Yevick (PY) and Hypernetted-Chain (HNC) closures will be presented, since these are very important and wildely applied in sciences. Then, two general closure relations will be proposed, for which PY and HNC are special cases. The hard sphere and Lennard-Jones fluids will be discussed, developing new closure relations that improves results for the radial distribution function, g(r), for hard spheres and to acquire thermodynamic consistent results using the Lennard-Jones potential. Also, an indirect method for solving the Ornstein-Zernike equation will be given in which the Hopfield Neural Network (HNN) is used along with experimental results for neutron scattering process. This method is further generalised using the Gâteaux derivative definition. Them, a recent proposal for neural networs, called Physics Informed Neural Networks, will be used to carry out both direct (solution of Ornstein-Zernike equation) and inverse (acquisition of g(r) from S(q)) problems discussed previously in this work. Although the theoretical background is given in several textbooks, all definitions and deductions necessaries in this work will be presented through the chapters so the reader will not need to search for these concepts in an external material.