Multifractal Behavior in Hierarchical Structure Formation

Details Multifractal Behavior in Hierarchical Structure Formation Multifractal Behavior in Hierarchical Structure Formation

Oct 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004aps..tsf.b1008m&link_type=abstract

American Physical Society, Texas Section Fall Meeting, 7-9 October, 2004, Waco, TX. MEETING ID: TSF04, abstract #B1.008

Physics

Scientific paper

We study gravitational instability in a one dimensional model of an Einstein-de Sitter universe. Careful scaling in both space and time results in an autonomous set of coupled Vlasov-Poisson equations for the gravitational field and phase space density, as well as the N-body problem, in which the coefficients are independent of time. We obtain general properties of the evolution from the Vlasov-Poisson equations and use particle simulation to study the evolution of a wide class of initial conditions, finding direct evidence of hierarchical clustering. A recent multi-fractal analysis of both the phase space and density simulations reveals a robust scaling for negative dimension and weaker, less convincing, scaling for positive dimensions. There are similarities with observations of the distribution of galaxies and less precise, three dimensional, simulations.

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