arXiv subjects

Andrea Gabrielli

Publications and source records attributed to Andrea Gabrielli.

At least 91 records · Page 5Linked to original sources

arXiv2007

Critical transient in the Barabási model of human dynamics

We introduce an exact probabilistic description for L=2 of the Barabási model for the dynamics of a list of L tasks. This permits to study the problem out of stationarity, and to solve explicitly the extremal limit case where a critical behavior for the waiting time distribution is observed. This behavior deviates at any finite time from that of the stationary state. We study also the characteristic relaxation time for finite time deviations from stationarity in all cases showing that it diverges in the extremal limit confirming that this deviations are important at all time.

physics.soc-ph↗

arXiv2006

Gravitational Dynamics of an Infinite Shuffled Lattice of Particles

We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static euclidean space, starting from a simple class of infinite ``shuffled lattice'' initial conditions. These are obtained by applying independently to each particle on an infinite perfect lattice a small random displacement, and are characterized by a power spectrum (structure factor) of density fluctuations which is quadratic in the wave number k, at small k. For a specified form of the probability distribution function of the ``shuffling'' applied to each particle, and zero initial velocities, these initial configurations are characterized by a single relevant parameter: the variance $δ^2$ of the ``shuffling'' normalized in units of the lattice spacing $\ell$. The clustering, which develops in time starting from scales around $\ell$, is qualitatively very similar to that seen in cosmological simulations, which begin from lattices with applied correlated displacements and incorporate an expanding spatial background. From very soon after the formation of the first non-linear structures, a spatio-temporal scaling relation describes well the evolution of the two-point correlations. At larger times the dynamics of these correlations converges to what is termed ``self-similar'' evolution in cosmology, in which the time dependence in the scaling relation is specified entirely by that of the linearized fluid theory. Comparing simulations with different $δ$, different resolution, but identical large scale fluctuations, we are able to identify and study features of the dynamics of the system in the transient phase leading to this behavior. In this phase, the discrete nature of the system explicitly plays an essential role.

cond-mat.stat-mech↗

arXiv2006

Chemical etching of a disordered solid: from experiments to field theory

We present a two-dimensional theoretical model for the slow chemical corrosion of a thin film of a disordered solid by suitable etching solutions. This model explain different experimental results showing that the corrosion stops spontaneously in a situation in which the concentration of the etchant is still finite while the corrosion surface develops clear fractal features. We show that these properties are strictly related to the percolation theory, and in particular to its behavior around the critical point. This task is accomplished both by a direct analysis in terms of a self-organized version of the Gradient Percolation model and by field theoretical arguments.

cond-mat.stat-mech↗

arXiv2006

Scale invariant forces in 1d shuffled lattices

In this paper we present a detailed and exact study of the probability density function $P(F)$ of the total force $F$ acting on a point particle belonging to a perturbed lattice of identical point sources of a power law pair interaction. The main results concern the large $F$ tail of $P(F)$ for which two cases are mainly distinguished: (i) Gaussian-like fast decreasing $P(F)$ for lattice with perturbations forbidding any pair of particles to be found arbitrarily close to one each other; (ii) Lévy-like power law decreasing $P(F)$ when this possibility is instead permitted. It is important to note that in the second case the exponent of the power law tail of $P(F)$ is the same for all perturbation (apart from very singular cases), and is in an one to one correspondence with the exponent characterizing the behavior of the pair interaction with the distance between the two particles.

cond-mat.stat-mech↗

arXiv2004

Point processes and stochastic displacement fields

The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact transformation equations for the two-point correlation function and the power spectrum of the point process are found, and a detailed study of them with important paradigmatic examples is done. The results are general and in any dimension. A particular attention is devoted to the kind of large scale correlations that can be introduced by the displacement field, and to the realizability of arbitrary ``superhomogeneous'' point processes.

cond-mat.stat-mech↗

arXiv2004

Voronoi and Voids Statistics for Super-homogeneous Point Processes

We study the Voronoi and void statistics of super-homogeneous (or hyperuniform) point patterns in which the infinite-wavelength density fluctuations vanish. Super-homogeneous or hyperuniform point patterns arise in one-component plasmas, primordial density fluctuations in the Universe, and in jammed hard-particle packings. We specifically analyze a certain one-dimensional model by studying size fluctuations and correlations of the associated Voronoi cells. We derive exact results for the complete joint statistics of the size of two Voronoi cells. We also provide a sum rule that the correlation matrix for the Voronoi cells must obey in any space dimension. In contrast to the conventional picture of super-homogeneous systems, we show that infinitely large Voronoi cells or voids can exist in super-homogeneous point processes in any dimension. We also present two heuristic conditions to identify and classify any super-homogeneous point process in terms of the asymptotic behavior of the void size distribution.

cond-mat.stat-mech↗

arXiv2004

Complexity in cosmic structures

We discuss correlation properties of a general mass density field introducing a classification of structures based on their complexity. Standard cosmological models for primordial mass fluctuations are characterized by a sort of large-scale stochastic order, that we call super-homogeneity to highlight the fact that mass fluctuations increase as a function of scale in the slowest possible way for any stochastic mass field. On the other hand the galaxy spatial distribution show complex structures with a high degree of inhomogeneity and fractal-like spatial correlations up to some relevant cosmological scale. The theoretical problem of cosmological structure formation should then explain the growth of strongly correlated and non-linear structures from the very uniform field of density fluctuations given as standard initial condition.

astro-ph↗

arXiv2003

Gravitational force in weakly correlated particle distributions

We study the statistics of the gravitational (Newtonian) force in a particular kind of weakly correlated distribution of point-like and unitary mass particles generated by the so-called Gauss-Poisson point process. In particular we extend to these distributions the analysis a' la Chandrasekhar introduced for purely Poisson processes. In this way we can find the asymptotic behavior of the probability density function of the force for large values of the field as a generalization of the Holtzmark statistics. The validity of the introduced approximations is positively tested through a direct comparison with the analysis of the statistics of the gravitational force in numerical simulations of Gauss-Poisson processes. Moreover the statistics of the force felt by a particle due to only its first nearest neighbor is analytically a numerical studied, resulting to be the dominant contribution to the total force.

astro-ph↗

arXiv2003

Bias and the power spectrum beyond the turn-over

Threshold biasing of a Gaussian random field gives a linear amplification of the reduced two point correlation function at large distances. We show that for standard cosmological models this does not translate into a linear amplification of the power spectrum (PS) at small k. For standard CDM type models this means that the``turn-over'' at small k of the original PS disappears in the PS of the biased field for the physically relevant range of the threshold parameter. In real space this difference is manifest in the asymptotic behaviour of the normalised mass variance in spheres of radius R, which changes from the ``super-homogeneous'' behaviour to a Poisson-like behaviour.This qualitative change results from the intrinsic stochasticity of the threshold sampling. While our quantitative results are specific to the simplest threshold biasing model, we argue that our qualitative conclusions should be valid generically for any biasing mechanism involving a scale-dependent amplification of the correlation function. One implication is that the real-space correlation function will be a better instrument to probe for the underlying Harrison Zeldovich spectrum in the distribution of visible matter, as the characteristic asymptotic negative power-law ξ(r) \sim -r^{-4} tail is undistorted by biasing.

astro-ph↗

arXiv2002

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 $P(0)=0$, 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.

astro-ph↗

arXiv2002

Real space statistical properties of standard cosmological models

After reviewing some basic relevant properties of stationary stochastic processes (SSP), we discuss the properties of the so-called Harrison-Zeldovich like spectra of mass density perturbations. These correlations are a fundamental feature of all current standard cosmological models. Examining them in real space we note they imply a "sub-poissonian" normalised variance in spheres $σ_M^2(R) \sim R^{-4} \ln R$. In particular this latter behaviour is at the limit of the most rapid decay ($\sim R^{-4}$) of this quantity possible for any stochastic distribution (continuous or discrete). In a simple classification of all SSP into three categories, we highlight with the name ``super-homogeneous'' the properties of the class to which models like this, with $P(0)=0$, belong. In statistical physics language they are well described as lattice or glass-like. We illustrate their properties through two simple examples: (i) the ``shuffled'' lattice and the One Component Plasma at thermal equilibrium.

astro-ph↗

arXiv2002

The Glass-like Universe: Real-space correlation properties of standard cosmological models

After reviewing the basic relevant properties of stationary stochastic processes (SSP), defining basic terms and quantities, we discuss the properties of the so-called Harrison-Zeldovich like spectra. These correlations, usually characterized exclusively in k-space (i.e. in terms of power spectra P(k)), are a fundamental feature of all current standard cosmological models. Examining them in real space we note their characteristics to be a {\it negative} power law tail ξ(r) \sim - r^{-4} and a {\it sub-poissonian} normalised variance in spheres σ^2(R) \sim R^{-4} \ln R. We note in particular that this latter behaviour is at the limit of the most rapid decay (\sim R^{-4}) of this quantity possible for any stochastic distribution (continuous or discrete). This very particular characteristic is usually obscured in cosmology by the use of Gaussian spheres. In a simple classification of all SSP into three categories, we highlight with the name ``super-homogeneous'' the properties of the class to which models like this, with P(0)=0, belong. In statistical physics language they are well described as glass-like. They do not have either ``scale-invariant'' features, in the sense of critical phenomena, nor fractal properties. We illustrate their properties with some simple examples, in particular that of a ``shuffled'' lattice.

astro-ph↗

arXiv2001

Rayleigh loops in the random-field Ising model on the Bethe lattice

We analyze the demagnetization properties of the random-field Ising model on the Bethe lattice focusing on the beahvior near the disorder induced phase transition. We derive an exact recursion relation for the magnetization and integrate it numerically. Our analysis shows that demagnetization is possible only in the continous high disorder phase, where at low field the loops are described by the Rayleigh law. In the low disorder phase, the saturation loop displays a discontinuity which is reflected by a non vanishing magnetization m_\infty after a series of nested loops. In this case, at low fields the loops are not symmetric and the Rayleigh law does not hold.

cond-mat.stat-mech↗

arXiv2001

Statistical Physics for Cosmic Structures

Ideas of Statistical Physics are very relevant for cosmic structures especially considering that the field is undergoing a period of exceptional development with many new data appearing on a monthly basis. In the past years we have focused mostly on galaxy distributions and their statistical properties. This led to an interesting debate which will be resolved by the next generation of data in a couple of years. In addition here we discuss the statistical properties of the fluctuations of the cosmic microwave background which are small in amplitude but complex in structure. We finally discuss the connection between these observations and the Harrison-Zeldovich spectrum and its further implications on the theories of structure formation and the and the cosmological $N$-body simulations.

astro-ph↗

arXiv2001

Percolation in real Wildfires

This paper focuses on the statistical properties of wild-land fires and, in particular, investigates if spread dynamics relates to simple invasion model. The fractal dimension and lacunarity of three fire scars classified from satellite imagery are analysed. Results indicate that the burned clusters behave similarly to percolation clusters on boundaries and look more dense in their core. We show that Dynamical Percolation reproduces this behaviour and can help to describe the fire evolution. By mapping fire dynamics onto the percolation models the strategies for fire control might be improved.

cond-mat↗

arXiv2001

Field theory of self-organized fractal etching

We propose a phenomenological field theoretical approach to the chemical etching of a disordered-solid. The theory is based on a recently proposed dynamical etching model. Through the introduction of a set of Langevin equations for the model evolution, we are able to map the problem into a field theory related to isotropic percolation. To the best of the authors knowledge, it constitutes the first application of field theory to a problem of chemical dynamics. By using this mapping, many of the etching process critical properties are seen to be describable in terms of the percolation renormalization group fixed point. The emerging field theory has the peculiarity of being ``{\it self-organized}'', in the sense that without any parameter fine-tuning, the system develops fractal properties up to certain scale controlled solely by the volume, $V$, of the etching solution. In the limit $V \to \infty$ the upper cut-off goes to infinity and the system becomes scale invariant. We present also a finite size scaling analysis and discuss the relation of this particular etching mechanism with Gradient Percolation. Finally, the possibility of considering this mechanism as a new generic path to self-organized criticality is analyzed, with the characteristics of being closely related to a real physical system and therefore more directly accessible to experiments.

cond-mat↗

arXiv2001

Correlation and clustering

In this lecture we clarify the basic difference between the correlation properties for systems characterized by small or large fluctuations. The concepts of correlation length, homogeneity scale, scale invariance and criticality are discussed as well. We relate these concepts to the interpretation of galaxy clsutering.

astro-ph↗

arXiv2000

Scaling and fluctuations in galaxy distribution: two tests to probe large scale structures

We present a brief introduction to the statistical properties of systems with large fluctuations. We point out that for such systems the relevant statistical quantities are scaling exponents and the nature of fluctuations is completely different from the one belonging to system with small fluctuations. We then propose two test to be performed on galaxy counts data as a function of apparent magnitude, which may clarify in a direct way the nature of the large scale galaxy clustering

astro-ph↗