Computer Physics Communications 180 (2009) 621–624 Contents lists available at ScienceDirect Computer Physics Communications www.elsevier.com/locate/cpc Extreme event dynamics in the formation of galaxy-sized dark matter structures Reinaldo R. Rosa a,∗ , Fernando M. Ramos a , Cesar A. Caretta b , Haroldo F. Campos Velho a a Núcleo para Simulação e Análise de Sistemas Complexos, Laboratório Associado de Computação e Matemática Aplicada (LAC), Instituto Nacional de Pesquisas Espaciais (INPE), 12201-970 São José dos Campos, SP, Brazil b Departamento de Astronomía, Universidad de Guanajuato, Guanajuato, Gto., Mexico article info abstract Article history: Received 1 October 2008 Received in revised form 17 November 2008 Accepted 18 November 2008 Available online 24 November 2008 PACS: 95.75.Pq 95.30.Sf 47.52.+j 05.10.Gg 04.40.-b 98.80.-k Keywords: Gravitational clustering Numerical N-body simulations Chaotic advection Galaxies: structure and evolution Methods: statistical The search for turbulent-like patterns in nonlinear gravitational clustering has recently advanced due to N-body simulations based on the cold dark matter scenario. In this work we present a computational statistical analysis of the formation of galaxy halos by gravitational collapse in N-body simulation from the Virgo Consortium Data. We find that rescaled data points of gravitational energy for different redshifts collapse into similar patterns, well approximated by a Generalized Extreme Value (GEV) distribution. Once similar statistical behavior was found for chaotic advection, this result is discussed in the context of non-dissipative turbulent-like behavior. From our analysis the unstable gravity field itself behaves as a chaotic advecting flow where the particles (galaxies) can be interpreted as turbulent tracers.  2008 Elsevier B.V. All rights reserved. 1. Introduction In recent years, computational simulation and high resolution astrophysical observations have shown that under the mutual at- traction of gravity the initially cosmological smooth distribution of matter develops inhomogeneous large scale structures. Thus, from a dynamical point of view, in the early universe gravitational in- stabilities were large enough to produce galaxies and clusters of galaxies observed today. Although the theoretical understanding of the nonlinear gravi- tational clustering has greatly advanced in the last decades, in par- ticular by the outstanding improvement on numerical N -body sim- ulations, the physics behind this process is not fully discerned. Re- cently, a detailed percolation analysis of the Virgo data for different redshifts has shown that the gravitational clustering of dark mat- ter may admit a turbulent-like representation [1]. From this ap- proach, local dynamical scaling processes involving unstable grav- itational galaxy interactions can act to form the significantly non- homogeneous structures observed in low redshifts (see Fig. 1). In * Corresponding author. E-mail address: reinaldo@lac.inpe.br (R.R. Rosa). this approach, gravitational energy spectra for cluster-sized halos and galaxy-sized halos, for redshifts from 10 to 0, have been inter- preted as a phenomenological signature of a possible turbulent-like mechanism characterized by combinations of small-scale eddies and larger flow-like structures due to the nonlinear gravitational galaxy–galaxy local interactions. However, we must note that since the cosmological simulated system is non-dissipative, a conserva- tive turbulent-like mechanism must be addressed [2,3]. Recently, the non-dissipative concentration fluctuation in La- grangian turbulence (or chaotic advection in the phase space [4]) has been studied using techniques of extreme value theory to pre- dict extreme concentrations by modeling the upper tail of the probability density function of the fluid inhomogeneties [5]. Data from large eddy dynamics obtained from both the simulations and experiments have been analysed and validate by calculating the maximum concentration normalized by the local mean concentra- tion (or by the local r.m.s. of concentration fluctuation). In probability theory and computational statistics, non-Gaussian fluctuations usually are characterized taking into account general- ized probability distributions [6]. The generalized extreme value distribution (GEV) is a family of continuous probability distribu- tions developed within extreme value theory to combine the Gum- bel, Fréchet and Weibull families also known as type I, II and III 0010-4655/$ – see front matter  2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cpc.2008.11.018