arXiv subjects

L. Pietronero

Publications and source records attributed to L. Pietronero.

At least 91 records · Page 5Linked to original sources

arXiv1997

Scale-invariance of galaxy clustering

Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not homogeneous up to the limits of the available catalogs. The usual statistical methods, which are based on the assumption of homogeneity, are therefore inconsistent for all the length scales probed so far, and a new, more general, conceptual framework is necessary to identifythe real physical properties of these structures. In the last few years the 3-d catalogs have been significatively improved and we have extended our methods to the analysis of number counts and angular catalogs. This has led to a complete analysis of all the available data that we present in this review. The result is that galaxy structures are highly irregular and self-similar: all the available data are consistent with each other and show fractal correlations (with dimension $D \simeq 2$) up to the deepest scales probed so far ($1000 \hmp$) and even more as indicated from the new interpretation of the number counts. The evidence for scale-invariance of galaxy clustering is very strong up to $150 \hmp$ due to the statistical robustness of the data but becomes progressively weaker (statistically) at larger distances due to the limited data. In These facts lead to fascinating conceptual implications about our knowledge of the universe and to a new scenario for the theoretical challenge in this field.

astro-ph↗

arXiv1997

Correlation properties of the large scale matter distribution and galaxy number counts

We introduce the basic techniques used for the analysis of three dimensional and two dimensional galaxy samples. We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each other and manifest fractal correlations (with dimension $D \simeq 2$) up to the present observational limits without any tendency towards homogenization. This result points to a new interpretation of the galaxy number counts. We show that an analysis of the small scale fluctuations allows us to reconcile the correlation analysis and the number counts in a new perspective which has a number of important implications.

astro-ph↗

arXiv1997

On the Average Density of Galaxies

The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a crossover to an homogeneous one at large scale. However up to now, the quantitative determination of this presumed homogeneity scale is still lacking. Contrary to such expectations, observational results show, in fact, a very inhomogeneous galaxy distribution. Some years ago we criticise the standard statistical approach and proposed a new one based on the concepts and methods of modern statistical analysis. The main result of new analysis is that, contrary to the conclusion of standard methods, the distribution of galaxies in the available samples, does not show any crossover to homogeneity, but has fractal correlations (with dimension $D \approx 2$) up to the limits of present three dimensional catalogs ($\approx 1000 h^{-1} Mpc$). The very first consequence of this result is that the standard approach is incorrect for all the length scale probed until now; moreover it calls for fascinating conceptual implication for the theoretical challenge in this field.

astro-ph↗

arXiv1997

The Visible Universe at the Light of Modern Statistical Physics

In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop spontaneously correlations with power law behaviour both in space and time. Pattern formation, aggregation phenomena, biological systems, geological systems, disordered materials, clustering of matter in the universe are just some of the fields in which scale invariance has been observed as a common and basic feature. However, the fact that certain structures exhibit fractal and complex properties does not tell us why this happens. A crucial point to understand is therefore the origin of the general scale-invariance of natural phenomena. This would correspond to the understanding of the origin of fractal structures and of the properties of Self- Organized Criticality (SOC) from the knowledge of the microscopic physical processes at the basis of these phenomena. Fractal geometry can play a crucial role in extracting the correct physical properties from experimental data. In particular, the recent availability of complete three dimensional samples of galaxies and clusters permits a direct study of their spatial properties. We present a brief review of galaxy correlations based on the methods of modern Statistical Physics. These methods are able to identify self-similar and non-analytical properties, and allow us to test the usual homogeneity assumption of luminous matter distribution. The new analysis shows that all the available data are consistent with each other and show fractal correlations (with dimension $D \simeq 2$) up to the deepest scales probed until now ($1000 \hmp$)

astro-ph↗

arXiv1997

Galaxy number counts and Fractal correlations

We report the correlation analysis of various redshift surveys which shows that the available data are consistent with each other and manifest fractal correlations (with dimension $D \simeq 2$) up to the present observational limits ($\approx 150 \hmp$) without any tendency towards homogenization. This result points to a new interpretation of the number counts that represents the main subject of this letter. We show that an analysis of the small scale fluctuations allows us to reconcile the correlation analysis and the number counts in a new perspective which has a number of important implications.

astro-ph↗

arXiv1997

Laplacian Fractal Growth in Media with Quenched Disorder

We analyze the combined effect of a Laplacian field and quenched disorder for the generation of fractal structures with a study, both numerical and theoretical, of the quenched dielectric breakdown model (QDBM). The growth dynamics is shown to evolve from the avalanches of invasion percolation (IP) to the smooth growth of Laplacian fractals, i. e. diffusion limited aggregation (DLA) and the dielectric breakdown model (DBM). The fractal dimension is strongly reduced with respect to both DBM and IP, due to the combined effect of memory and field screening. This implies a specific relation between the fractal dimension of the breakdown structures (dielectric or mechanical) and the microscopic properties of disordered materials.

cond-mat.dis-nn↗

arXiv1997

Theory of Self-organized Criticality for Problems with Extremal Dynamics

We introduce a general theoretical scheme for a class of phenomena characterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic one with cognitive memory and on other concepts which permit a mathematical characterization of the self-organized nature of the avalanche type dynamics. In addition it is possible to compute the relevant critical exponents directly from the microscopic model. A specific application to Invasion Percolation is presented but the approach can be easily extended to various other problems.

cond-mat.dis-nn↗

arXiv1997

Frequently asked questions about fractals

In this lecture we will try to address the "frequently asked questions about fractals" in the field of large scale galaxy distribution. This paper takes its origin from a very interesting discussion we had at this meeting. A lot of points were raised, and we try to make clear the fundamental ones.

astro-ph↗

arXiv1996

On the Fractal Structure of the Visible Universe

Some years ago we proposed a new approach for the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical physics. This led to the surprising result that galaxy correlations are fractal and not homogeneous up to the limits of the available catalogues. In the meantime many more redshifts have been measured and we have extended our methods also to the analysis of number counts and angular catalogues. This has led to a complete analysis of all the available data that we are going to present in detail in this lecture. In particular we will discuss the properties of the following catalogues: CfA, Perseus-Pisces, SSRS, IRAS, LEDA, Las Campanas and ESP for galaxies and Abell and ACO for clusters. The usual statistical methods, that are based on the assumption of homogeneity, are therefore inconsistent for all the length scales probed until now. A new, more general, conceptual framework is necessary to identify the real physical properties of these structures. In the range of self-similarity theories should shift from "amplitudes" to "exponents". The new analysis shows that all the available data are consistent with each other and show fractal correlations (with dimension $D \simeq 2$) up to the deepest scales probed until now ($1000 h^{-1}Mpc$) and even more as indicated from the new interpretation of the number counts. The distribution of luminous matter in the universe is therefore fractal and not homogeneous. The evidence for this being very strong up to $150 h^{-1}Mpc$ due to the statistical roboustness of the data and progressively weaker (statistically) at larger distances due to the limited data. These facts lead to fascinating conceptual implications about our knowledge of the universe and to a new scenario for the theoretical challenge in this field.

astro-ph↗

arXiv1996

Earthquake statistics and fractal faults

We introduce a Self-affine Asperity Model (SAM) for the seismicity that mimics the fault friction by means of two fractional Brownian profiles (fBm) that slide one over the other. An earthquake occurs when there is an overlap of the two profiles representing the two fault faces and its energy is assumed proportional to the overlap surface. The SAM exhibits the Gutenberg-Richter law with an exponent $β$ related to the roughness index of the profiles. Apart from being analytically treatable, the model exhibits a non-trivial clustering in the spatio-temporal distribution of epicenters that strongly resembles the experimentally observed one. A generalized and more realistic version of the model exhibits the Omori scaling for the distribution of the aftershocks. The SAM lies in a different perspective with respect to usual models for seismicity. In this case, in fact, the critical behaviour is not Self-Organized but stems from the fractal geometry of the faults, which, on its turn, is supposed to arise as a consequence of geological processes on very long time scales with respect to the seismic dynamics. The explicit introduction of the fault geometry, as an active element of this complex phenomenology, represents the real novelty of our approach.

cond-mat↗

arXiv1996

Finite size effects on the galaxy number counts: evidence for fractal behavior up to the deepest scale

We introduce and study two new concepts which are essential for the quantitative analysis of the statistical quality of the available galaxy samples. These are the dilution effect and the small scale fluctuations. We show that the various data that are considered as pointing to a homogenous distribution are all affected by these spurious effects and their interpretation should be completely changed. In particular, we show that finite size effects strongly affect the determination of the galaxy number counts, namely the number versus magnitude relation ($N(<m)$) as computed from the origin. When one computes $N(<m)$ averaged over all the points of a redshift survey one observes an exponent $α= D/5 \approx 0.4$ compatible with the fractal dimension $D \approx 2$ derived from the full correlation analysis. Instead the observation of an exponent $α\approx 0.6$ at relatively small scales, where the distribution is certainly not homogeneous, is shown to be related to finite size effects. We conclude therefore that the observed counts correspond to a fractal distribution with dimension $D \approx 2$ in the entire range $12 \ltapprox m \ltapprox 28$, that is to say the largest scales ever probed for luminous matter. In addition our results permit to clarify various problems of the angular catalogs, and to show their compatibility with the fractal behavior. We consider also the distribution of Radio-galaxies, Quasars and $γ$ ray burst, and we show their compatibility with a fractal structure with $D \approx 1.6 ÷1.8$. Finally we have established a quantitative criterion that allows us to define and {\em predict} the statistical validity of a galaxy catalog (angular or three dimensional).

astro-ph↗

arXiv1996

Long-range (fractal) correlations in the LEDA database

All the recent redshift surveys show highly irregular patterns of galaxies on scales of hundreds of megaparsecs such as chains, walls and cells. One of the most powerful catalog of galaxies is represented by the LEDA database that contains more than 36,000 galaxies with redshift. We study the correlation properties of such a samplefinding that galaxy distribution shows well defined fractal nature up to R$_s \sim 150 h^{-1}Mpc $ with fractal dimension $D \approx 2$. We test the consistency of these results versus the incompleteness in the sample.

astro-ph↗

arXiv1995

The debate of galaxy correlations and its theoretical implications

We discuss the problem of galaxy correlations by considering the various methods by which this information can be obtained. We focus in particular on the volume limited three dimensional samples and discuss a new way to increase the scale of their statistical validity. From our previous results and the most recent ones on all the available catalogues we conclude that galaxy correlations show fractal properties with dimension $ D \approx 2$ up to the present observational limits ($200-800 \hmp$ depending on the catalogue) without any tendency towards homogenization. We also discuss the compatibility of this result with the galaxy counts as a function of magnitude and the angular catalogues. A new picture emerges which changes the standard ideas about the properties of the universe and requires a corresponding change in the theoretical concepts that one should use to describe it.

astro-ph↗

arXiv1995

The boson mediators of high-Tc superconductivity: phonons versus composite bosons from the superconducting phenomenology

We address the question of whether boson mediators of high-$T_c$ superconductivity are composite (electronic) or independent phonons. For s-wave superconductivity we show from the available experiments that the hypothesis of composite bosons is rather unlikely. Our analysis points naturally towards phonon mediators. In addition we point out that the eventual presence of a peak in the temperature dependence of the microwave conductivity while the Hebel-Slichter peak is absent in the temperature dependence of the NMR relaxation rate, can be understood within a phonon mechanism if one takes into account the modulation of the electron-phonon coupling (predominance of forward scattering) induced by Coulomb correlation of the carriers.

cond-mat↗

arXiv1995

Self-affine Asperity Model for earthquakes

A model for fault dynamics consisting of two rough and rigid brownian profiles that slide one over the other is introduced. An earthquake occurs when there is an intersection between the two profiles. The energy release is proportional to the overlap interval. Our model exhibits some specific features which follow from the fractal geometry of the fault: (1) non-universality of the exponent of the Gutenberg-Richter law for the magnitude distribution; (2) presence of local stress accumulation before a large seismic event; (3) non-trivial space-time clustering of the epicenters. These properties are in good agreement with various observations and lead to specific predictions that can be experimentally tested.

cond-mat↗

arXiv1995

Cross-over from BCS superconductivity to Bose condensation and High-Tc Superconductors

We consider the Eliashberg theory in the coupling region where some fundamental qualitative deviations from the conventional BCS-like behaviour begin to appear. These deviations are identified as the onset of a cross-over from BCS superconductivity to Bose condensation. We point out that the beginning of this cross-over occurs when the gap $Δ_g$ becomes comparable to the boson energies $Ω_{ph}$. This condition is equivalent to the condition of Ref. \cite{Strinati} $k_Fξ\approx 2π$ and traduces the physical constraint that the distance the paired electron covers during the absorbtion of the virtual boson, cannot be larger than the coherence length. The frontier region of couplings is of the order of $λ\approx 3$, and high-$T_c$ materials are concerned. A clear qualitative indication of the occurence of a cross-over regime should be a dip structure above the gap in the density of states of excitations. Comparing our results with tunneling and photoemission experiments we conclude that high-$T_c$ materials (cuprates and fullerides) are indeed at the beginning of a cross-over from BCS superconductivity to Bose condensation, even though the fermionic nature still prevails. Taking into account the analysis of Ref. \cite{Strinati}, we predict a dip structure in heavy fermion and organic superconductors. Non-adiabatic effects beyond Migdal's theory are considered and give insight on the robustness of Eliashberg theory in describing qualitatively this cross-over regime, although for the quantitative interpretation of the results the inclusion of non-adiabatic corrections can be important.

cond-mat↗

arXiv1995

Density of States Driven Anisotropies Induced by Momentum Decoupling in High-Tc Superconductors

Momentum decoupling arises when small momentum transfer processes dominate the electron-phonon scattering and implies that anisotropies in superconductivity are driven by the anisotropies of the density of states. Considering an isotropic s-wave interaction in the momentum decoupling regime we give a natural simultaneous explanation to various aspects of ARPES and tunnel experiments on $Bi_2Sr_2CaCu_2O_8$, including the correlation of gap magnitude and visibility of the dip above the gap, the enhancement of anisotropy with temperature, the presence of gap minima away from the $Γ-X$ direction and a gap maximum in the $Γ-X$ direction, the similarity of tunnel and ARPES spectra in the $Γ-\bar{M}$ direction and the asymmetry in the SIN tunnel spectra where the dip structure is present only at negative sample bias.

cond-mat↗

arXiv1995

Spatial and Luminosity Properties of the Perseus-Pisces Redshift Survey

We analyze the spatial and the luminosity properties of the Perseus-Pisces redshift survey. We find that the two point correlation function (CF) $Γ(r)$ is a power law up to the sample effective depth ($\sim 30 h^{-1}Mpc$), showing the fractal nature of the galaxy distribution in this catalog. The fractal dimension turns out to be $D \approx 2$. We also consider the CF $ξ(r)$ and in particular the behavior of the "{\it correlation length}" $r_0$ ($ξ(r_{0})\equiv 1$) as function of the sample size. In this respect we find, unambiguously, that the luminosity segregation effect is not supported by any experimental evidence. In addition we have studied the galaxian number-density ($n(r)$) and number-counts ($N(m)$) in the VL subsamples finding a good agreement with the properties of a fractal distribution. In particular our conclusion is that the $n(r)$ relation allows to extend the analysis of the fractal nature up to a deeper depth than that reached by the CF analysis, and, we find evidence for fractal properties up to the limiting depth of $120-140 h^{-1} Mpc$. We stress that the $N(m)$ relation must be studied in VL subsamples rather than in magnitude limited ones as usually done. Finally we have considered the correlations between galaxy positions and luminosities by means of the multifractal analysis. We find clear evidence for self-similar behavior of the whole luminosity-space distribution. These results confirm and extend those of Coleman \& Pietronero (1992).

astro-ph↗