Session D13: Statistical and Nonlinear Physics: General
2:30 PM–5:30 PM, Monday, March 21, 2011
Room: D225/226
Sponsoring Unit:
GSNP
Chair: James Dufty, University of Florida
Abstract ID: BAPS.2011.MAR.D13.11
Abstract: D13.00011 : Cosmology in One Dimension: Fractal Geometry, Power Spectra and Correlation
4:30 PM–4:42 PM
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Abstract 
Authors:
Bruce Miller
(Texas Christian University)
Jean-Louis Rouet
(Universite d'Orleans)
Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter distribution may not exist. A point of controversy is whether the distribution is fractal and, if so,over what range of scales. One-dimensional models demonstrate that the important dynamics for cluster formation occur in the position-velocity plane. Here the development of scaling behavior and multifractal geometry is investigated for a family of one-dimensional models for three different, scale-free, initial conditions. A possible physical mechanism for understanding the self-similar evolution is introduced. It is shown that hierarchical cluster formation depends both on the model and the initial power spectrum. Under special circumstances a simple relation between the power spectrum, correlation function, and correlation dimension in the highly nonlinear regime is confirmed.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.MAR.D13.11