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Méthodes géométriques pour l'étude des systèmes thermodynamiques et la génération d'équations d'état

Abstract : This thesis deals with applications of the theory of contact structures to phenomenological thermodynamics. We focus on using contact transformations for generating new equations of state in thermodynamics. In the first part, after some reminders on contact structures, we concentrate on contact transformations. They are defined by the determination of a function, the so-called contact hamiltonian, and allow us to transform a Legendre submanifold associated with a contact form to another one. We investigate the connection between the contact hamiltonian and these Legendre submanifolds. In the second part of the thesis, we emphasise that the formalism of contact structure is convenient for Gibbs thermodynamical theory. We propose new methods for generating thermodynamical models (a set of equations of state characterising a substance) from known models, by means of a contact transformation. This technique is carried out for completing a partially known model. Several methods for constructing contact hamiltonians are developed. The last part of the thesis is a presentation of the MAPLE software package daimon for generating new models.
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Submitted on : Wednesday, February 18, 2004 - 10:01:16 AM
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Loïc Benayoun. Méthodes géométriques pour l'étude des systèmes thermodynamiques et la génération d'équations d'état. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 1999. Français. ⟨tel-00004803⟩

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