Gradient pattern analysis of cosmic structure formation: Norm and phase statistics

This paper presents the preliminary results of the characterization of pattern evolution in the process of cosmic structure formation. We are applying to N -body cosmological simulations data the technique proposed by Rosa et al. [R.R. Rosa, A.S. Sharma, J.A. Valdivia, Int. J. Modern Phys. C 10 (1999) 147] and Ramos et al. [F.M. Ramos, et al., Physica A 283 (2000) 171] to estimate the time behaviour of asymmetries in the gradient field. The gradient pattern analysis is a well tested tool, used to build asymmetrical fragmentation parameters estimated over a gradient field of an image matrix able to quantify a complexity measure of nonlinear extended systems. In this investigation we work with the high resolution cosmological data simulated by the Virgo consortium, in different time steps, in order to obtain a diagnostic of the spatio-temporal disorder in the matter density field. We perform the calculations of the gradient vectors statistics, such as mean, variance, skewness, kurtosis, and correlations on the gradient field. Our main goal is to determine different dynamic regimes through the analysis of complex patterns arising from the evolutionary process of structure formation. The results show that the gradient pattern technique, specially the statistical analysis of second and third gradient moment, may represent a very useful tool to describe the matter clustering in the Universe.