Thèse soutenue

Dynamique hors-équilibre des systèmes infinis auto-gravitants unidimensionnels
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Auteur / Autrice : François Sicard
Direction : Michael Joyce
Type : Thèse de doctorat
Discipline(s) : Physique théorique
Date : Soutenance en 2010
Etablissement(s) : Paris 6

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The formation of structures in the universe is one of the major questions in cosmology. The growth of structure in the linear regime of low amplitude fuctuations is well understood analytically, but N-body simulations remain the main tool to probe the "non-linear" regime where fuctuations are large. We study this question approaching the problem from the more general perspective to the usual one in cosmology, that of statistical physics and out-of-equilibrium dynamics of systems with long-range interaction. It is natural to improve our understanding of this system, reducing the question to fundamental aspects. We define a class of infnite 1D self-gravitating systems relevant to cosmology, and we observe strong qualitative similarities with the evolution of the analogous 3D systems. We highlight that the spatial clustering which develops may have scale invariant (fractal) properties, and that they display "self-similar" properties in their temporal evolution. We show that the measured exponents characterizing the scale-invariant clustering can be very well accounted for using a generalized "stable-clustering" hypothesis. Further by means of an analysis in terms of halo selected using a friend-of-friend algorithm we show that, in the corresponding spatial range, structures are, statistically virialized. Thus the non-linear clustering in these 1D models corresponds to the development of a "virialized fractal hierarchy". We conclude with a separate study which formalizes a classification of pair-interactions based on the convergence properties of the forces acting on particles as a function of system size, rather than the convergence of the potential energy