Comptes Rendus
no. 3-4
Development of fractal geometry in a one-dimensional gravitational system
[Développement de la géométrie fractale dans un système gravitationnel à une dimension]
Bruce N. Miller1  ; Jean-Louis Rouet2, 3
1 Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX 76129, USA
2 Institut des sciences de la terre d'Orléans (ISTO), UMR6113 CNRS/université d'Orléans, 1A, rue de la Férollerie, 45071 Orléans cedex 2, France
3 Laboratoire de mathématique, applications et physique mathématique, UMR 6628, université d'Orléans, UFR des sciences, 45067 Orléans cedex 2, France
Comptes Rendus. Physique, Statistical mechanics of non-extensive systems, Volume 7 (2006) no. 3-4, pp. 383-390.

Nous étudions l'evolution d'un système gravitationnel instable à une dimension dans un univers dominé par la matière. Des transformations d'échelle en espace et temps conduisent à un problème à N-corps décrit par un ensemble autonome d'équations couplées donnant l'évolution du système dans l'espace des phases. Les simulations numériques montrent que le système construit une structure hiérarchique. Comme pour les observations de galaxies, l'analyse des résultats suggère qu'au cours du temps, la distribution des positions des particules développe une géométrie bifractale.

We study a one dimensional model of gravitational instability in a matter dominated universe. Careful scaling in both space and time results in an N-body problem governed by an autonomous set of coupled equations for the evolution of the system in phase space. Using dynamical simulation, we demonstrate that the system exhibits hierarchical structure formation. In common with galaxy observations, careful analysis suggests that, as time evolves, the distribution of particle positions develops bifractal geometry.

Publié le :
DOI : 10.1016/j.crhy.2006.02.005
Keywords: Gravity, Fractal, Cosmology, Hierarchical structure
Mots-clés : Gravité, Fractal, Cosmologie, Structure hiérarchique

Bruce N. Miller 1 ; Jean-Louis Rouet 2, 3

1 Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX 76129, USA
2 Institut des sciences de la terre d'Orléans (ISTO), UMR6113 CNRS/université d'Orléans, 1A, rue de la Férollerie, 45071 Orléans cedex 2, France
3 Laboratoire de mathématique, applications et physique mathématique, UMR 6628, université d'Orléans, UFR des sciences, 45067 Orléans cedex 2, France 
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Bruce N. Miller; Jean-Louis Rouet. Development of fractal geometry in a one-dimensional gravitational system. Comptes Rendus. Physique, Statistical mechanics of non-extensive systems, Volume 7 (2006) no. 3-4, pp. 383-390. doi : 10.1016/j.crhy.2006.02.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.02.005/

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