19 research outputs found
Scaling in cosmic structures
The study of the properties of cosmic structures in the universe is one of
the most fascinating subject of the modern cosmology research. Far from being
predicted, the large scale structure of the matter distribution is a very
recent discovery, which continuosly exhibits new features and issues. We have
faced such topic along two directions; from one side we have studied the
correlation properties of the cosmic structures, that we have found
substantially different from the commonly accepted ones. From the other side,
we have studied the statistical properties of the very simplified system, in
the attempt to capture the essential ingredients of the formation of the
observed structures.Comment: 10 pages, 3 figures. Accepted for pubblication in Fractals
Clustering in N-Body gravitating systems
Self-gravitating systems have acquired growing interest in statistical
mechanics, due to the peculiarities of the 1/r potential. Indeed, the usual
approach of statistical mechanics cannot be applied to a system of many point
particles interacting with the Newtonian potential, because of (i) the long
range nature of the 1/r potential and of (ii) the divergence at the origin. We
study numerically the evolutionary behavior of self-gravitating systems with
periodical boundary conditions, starting from simple initial conditions. We do
not consider in the simulations additional effects as the (cosmological) metric
expansion and/or sophisticated initial conditions, since we are interested
whether and how gravity by itself can produce clustered structures. We are able
to identify well defined correlation properties during the evolution of the
system, which seem to show a well defined thermodynamic limit, as opposed to
the properties of the ``equilibrium state''.
Gravity-induced clustering also shows interesting self-similar
characteristics.Comment: 6 pages, 5 figures. To be published on Physica
Gravitational clustering in N-body simulations
In this talk we discuss some of the main theoretical problems in the
understanding of the statistical properties of gravity. By means of N-body
simulations we approach the problem of understanding the r\^ole of gravity in
the clustering of a finite set of N-interacting particles which samples a
portion of an infinite system. Through the use of the conditional average
density, we study the evolution of the clustering for the system putting in
evidence some interesting and not yet understood features of the process.Comment: 5 pages, 1 figur
A topological approach to neural complexity
Considerable efforts in modern statistical physics is devoted to the study of
networked systems. One of the most important example of them is the brain,
which creates and continuously develops complex networks of correlated
dynamics. An important quantity which captures fundamental aspects of brain
network organization is the neural complexity C(X)introduced by Tononi et al.
This work addresses the dependence of this measure on the topological features
of a network in the case of gaussian stationary process. Both anlytical and
numerical results show that the degree of complexity has a clear and simple
meaning from a topological point of view. Moreover the analytical result offers
a straightforward algorithm to compute the complexity than the standard one.Comment: 6 pages, 4 figure
Universality of power law correlations in gravitational clustering
We present an analysis of different sets of gravitational N-body simulations,
all describing the dynamics of discrete particles with a small initial velocity
dispersion. They encompass very different initial particle configurations,
different numerical algorithms for the computation of the force, with or
without the space expansion of cosmological models. Despite these differences
we find in all cases that the non-linear clustering which results is
essentially the same, with a well-defined simple power-law behaviour in the
two-point correlations in the range from a few times the lower cut-off in the
gravitational force to the scale at which fluctuations are of order one. We
argue, presenting quantitative evidence, that this apparently universal
behaviour can be understood by the domination of the small scale contribution
to the gravitational force, coming initially from nearest neighbor particles.Comment: 7 pages, latex, 3 postscript figures. Revised version to be published
in Europhysics Letters. Contains additional analysis showing more directly
the central role of nearest neighbour interactions in the development of
power-law correlation
Clustering in gravitating N-body systems
We study gravitational clustering of mass points in three dimensions with
random initial positions and periodic boundary conditions (no expansion) by
numerical simulations. Correlation properties are well defined in the system
and a sort of thermodynamic limit can be defined for the transient regime of
cluste ring. Structure formation proceeds along two paths: (i) fluid-like
evolution of density perturbations at large scales and (ii) shift of the
granular (non fluid) properties from small to large scales. The latter
mechanism finally dominates at all scales and it is responsible for the
self-similar characteristics of the clustering.Comment: 7 pages, 3 figures. Accepted for publication in Europhys. Let
Initial conditions, Discreteness and non-linear structure formation in cosmology
In this lecture we address three different but related aspects of the initial
continuous fluctuation field in standard cosmological models. Firstly we
discuss the properties of the so-called Harrison-Zeldovich like spectra. This
power spectrum is a fundamental feature of all current standard cosmological
models. In a simple classification of all stationary stochastic processes into
three categories, we highlight with the name ``super-homogeneous'' the
properties of the class to which models like this, with , belong. In
statistical physics language they are well described as glass-like. Secondly,
the initial continuous density field with such small amplitude correlated
Gaussian fluctuations must be discretised in order to set up the initial
particle distribution used in gravitational N-body simulations. We discuss the
main issues related to the effects of discretisation, particularly concerning
the effect of particle induced fluctuations on the statistical properties of
the initial conditions and on the dynamical evolution of gravitational
clustering.Comment: 28 pages, 1 figure, to appear in Proceedings of 9th Course on
Astrofundamental Physics, International School D. Chalonge, Kluwer, eds N.G.
Sanchez and Y.M. Pariiski, uses crckapb.st pages, 3 figure, ro appear in
Proceedings of 9th Course on Astrofundamental Physics, International School
D. Chalonge, Kluwer, Eds. N.G. Sanchez and Y.M. Pariiski, uses crckapb.st
Basic properties of galaxy clustering in the light of recent results from the Sloan Digital Sky Survey
We discuss some of the basic implications of recent results on galaxy
correlations published by the SDSS collaboration. In particular we focus on the
evidence which has been recently presented for the scale and nature of the
transition to homogeneity in the galaxy distribution, and results which
describe the dependence of clustering on luminosity. The two questions are in
fact strictly entangled, as the stability of the measure of the amplitude of
the correlation function depends on the scale at which the mean density becomes
well defined. We note that the recent results which indicate the convergence to
well defined homogeneity in a volume equivalent to that of a sphere of radius
70 Mpc/h, place in doubt previous detections of ``luminosity bias'' from
measures of the amplitude of the correlation function. We emphasize that the
way to resolve these issues is to first use, in volume limited samples
corresponding to different ranges of luminosity, the unnormalized two point
statistics to establish the scale (and value) at which the mean density becomes
well defined. We note also that the recent SDSS results for these statistics
are in good agreement with those obtained by us through analyses of many
previous samples, confirming in particular that the galaxy distribution is well
described by a fractal dimension D ~ 2 up to a scale of at least 20 Mpc/h. We
discuss critically the agreement of this new data with current theoretical
models.Comment: 6 pages, 1 figure. Revised version with minor corrections. To be
published in Astronomy and Astrophysic
Fractals vs. halos: Asymptotic scaling without fractal properties
Precise analyses of the statistical and scaling properties of galaxy
distribution are essential to elucidate the large-scale structure of the
universe. Given the ongoing debate on its statistical features, the development
of statistical tools permitting to discriminate accurately different spatial
patterns is highly desiderable. This is specially the case when non-fractal
distributions have power law two-point correlation functions, which are usually
signatures of fractal properties. Here we review some possible methods used in
the literature and introduce a new variable called "scaling gradient". This
tool and the conditional variance are shown to be effective in providing an
unambiguous way for such a distinction. Their application is expected to be of
outmost importance in the analysis of upcoming galaxy catalogues.Comment: 7 pages, 3 figure