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none6siLecture Notes in Computer Science, Vol. 5217openV. Maniezzo ; M. Roffilli ; R. Gabrielli ; A. Guidazzi ; M. Otero ; R. TrujilloV. Maniezzo ; M. Roffilli ; R. Gabrielli ; A. Guidazzi ; M. Otero ; R. Trujill
Peaks in the CMBR power spectrum. I. Mathematical analysis of the associated real space features
The purpose of our study is to understand the mathematical origin in real
space of modulated and damped sinusoidal peaks observed in cosmic microwave
background radiation anisotropies. We use the theory of the Fourier transform
to connect localized features of the two-point correlation function in real
space to oscillations in the power spectrum. We also illustrate analytically
and by means of Monte Carlo simulations the angular correlation function for
distributions of filled disks with fixed or variable radii capable of
generating oscillations in the power spectrum. While the power spectrum shows
repeated information in the form of multiple peaks and oscillations, the
angular correlation function offers a more compact presentation that condenses
all the information of the multiple peaks into a localized real space feature.
We have seen that oscillations in the power spectrum arise when there is a
discontinuity in a given derivative of the angular correlation function at a
given angular distance. These kinds of discontinuities do not need to be abrupt
in an infinitesimal range of angular distances but may also be smooth, and can
be generated by simply distributing excesses of antenna temperature in filled
disks of fixed or variable radii on the sky, provided that there is a non-null
minimum radius and/or the maximum radius is constrained.Comment: accepted to be published in Physica
Etching of random solids: hardening dynamics and self-organized fractality
When a finite volume of an etching solution comes in contact with a
disordered solid, a complex dynamics of the solid-solution interface develops.
Since only the weak parts are corroded, the solid surface hardens
progressively. If the etchant is consumed in the chemical reaction, the
corrosion dynamics slows down and stops spontaneously leaving a fractal solid
surface, which reveals the latent percolation criticality hidden in any random
system. Here we introduce and study, both analytically and numerically, a
simple model for this phenomenon. In this way we obtain a detailed description
of the process in terms of percolation theory. In particular we explain the
mechanism of hardening of the surface and connect it to Gradient Percolation.Comment: Latex, aipproc, 6 pages, 3 figures, Proceedings of 6th Granada
Seminar on Computational Physic
Statistical physics for cosmic structures
The recent observations of galaxy and dark matter clumpy distributions have
provided new elements to the understating of the problem of cosmological
structure formation. The strong clumpiness characterizing galaxy structures
seems to be present in the overall mass distribution and its relation to the
highly isotropic Cosmic Microwave Background Radiation represents a fundamental
problem. The extension of structures, the formation of power-law correlations
characterizing the strongly clustered regime and the relation between dark and
visible matter are the key problems both from an observational and a
theoretical point of view. We discuss recent progresses in the studies of
structure formation by using concepts and methods of statistical physics.Comment: 8 pages, 4 figures, European Physical Journal B - STATPHYS 23 topical
issue in the press (2007
Gravitational Structure Formation, the Cosmological Problem and Statistical Physics
Models of structure formation in the universe postulate that matter
distributions observed today in galaxy catalogs arise, through a complex
non-linear dynamics, by gravitational evolution from a very uniform initial
state. Dark matter plays the central role of providing the primordial density
seeds which will govern the dynamics of structure formation. We critically
examine the role of cosmological dark matter by considering three different and
related issues: Basic statistical properties of theoretical initial density
fields, several elements of the gravitational many-body dynamics and key
correlation features of the observed galaxy distributions are discussed,
stressing some useful analogies with known systems in modern statistical
physics.Comment: 5 pages 1 postscript figure. Proceeding of the conference Proceedings
of the 3rd International Conference NEXT-SigmaPh
Gravitational collapse in an expanding background and the role of substructure II: Excess power at small scales and its effect of collapse of structures at larger scales
We study the interplay of clumping at small scales with the collapse and
relaxation of perturbations at larger scales using N-Body simulations. We
quantify the effect of collapsed haloes on perturbations at larger scales using
two point correlation function, moments of counts in cells and mass function.
The purpose of the study is twofold and the primary aim is to quantify the role
played by collapsed low mass haloes in the evolution of perturbations at large
scales, this is in view of the strong effect seen when the large scale
perturbation is highly symmetric. Another reason for this study is to ask
whether features or a cutoff in the initial power spectrum can be detected
using measures of clustering at scales that are already non-linear. The final
aim is to understand the effect of ignoring perturbations at scales smaller
than the resolution of N-Body simulations. We find that these effects are
ignorable if the scale of non-linearity is larger than the average
inter-particle separation in simulations. Features in in the initial power
spectrum can be detected easily if the scale of these features is in the linear
regime, detecting such features becomes difficult as the relevant scales become
non-linear. We find no effect of features in initial power spectra at small
scales on the evolved power spectra at large scales. We may conclude that in
general, the effect on evolution of perturbations at large scales of clumping
on small scales is very small and may be ignored in most situations.Comment: Accepted for publication in MNRA
Gravitational fluctuations of the galaxy distribution
We study the statistical properties of the gravitational field generated by
galaxy distribution observed bythe Sloan Digital Sky Survey (DR7). We
characterize the probability density function of gravitational force
fluctuations and relate its limiting behaviors to the correlation properties of
the underlying density field. In addition, we study whether the PDF converges
to an asymptotic shape within sample volumes. We consider several
volume-limited samples of the Sloan Digital Sky Survey and we compute the
gravitational force probability density function (PDF). The gravitational force
is computed in spheres of varying radius as is its PDF. We find that (i) the
PDF of the force displays features that can be understood in terms of galaxy
two-point correlations and (ii) density fluctuations on the largest scales
probed, i.e. r~100 Mpc/h, still contribute significantly to the amplitude of
the gravitational force. Our main conclusion is that fluctuations in the
gravitational force field generated by galaxy structures are also relevant on
scales ~ 100 Mpc/h. By assuming that the gravitational fluctuations in the
galaxy distribution reflect those in the whole matter distribution, and that
peculiar velocities and accelerations are simply correlated, we may conclude
that large-scale fluctuations in the galaxy density field may be the source of
the large-scale flows recently observed.Comment: 6 pages, 4 figures. Accepted for publication in Astronomy and
Astrophysics. Version v2 matches the published pape
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