Termodinâmica do modelo Bouncer: um gás unidimensional simplificado

• Autor(a) principal: Cespedes, André Machado [UNESP]
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/134014; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/12-01-2016/000856755.pdf
• topic: Thermodynamics; Termodinamica; Caos determinístico; Leis de escala (Fisica estatistica)

In this work we investigate some dynamical properties for an ensemble of particles in a dissipative bouncer model. The model consists of a classical particle (or an ensemble of them) colliding against a wall that oscillates as function of the time, under the action of a constant gravitational field. The equations that describe the complete model include two types of collisions: (i) direct and; (ii) indirect. There is a simplified version of the model which is equivalent to Chirikov's standard map. The map shows a transition from local to global chaos when the parameter reaches a critical value. The conservative model preserves the phase space area and, depending on the initial conditions as well as control parameter, can show unlimited growth of energy, a phenomenon known as Fermi acceleration. The phenomenon is suppressed by introducing dissipation via inelastic collisions. The transition between unlimited and limited growth of energy is described by scaling hypothesis. Such scaling leads to a generalized homogeneous function that provides two scaling laws, validated by well defined critical exponents. The analytical expression of the mean square velocity of particles leads to the calculation of these exponents of the transition, obtained independently of the simulations. An overlap of the curves Vrms vs. n validates the critical exponents obtained. The connection of the bouncer model with Thermodynamics is obtained by developing an expression for the Entropy, in agreement with the 3rd Postulate of Thermodynamics