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A. Rapisarda

Publications and source records attributed to A. Rapisarda.

At least 37 records · Page 2Linked to original sources
arXiv2008

A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model

We give a closer look at the Central Limit Theorem (CLT) behavior in quasi-stationary states of the Hamiltonian Mean Field model, a paradigmatic one for long-range-interacting classical many-body systems. We present new calculations which show that, following their time evolution, we can observe and classify three kinds of long-standing quasi-stationary states (QSS) with different correlations. The frequency of occurrence of each class depends on the size of the system. The different microsocopic nature of the QSS leads to different dynamical correlations and therefore to different results for the observed CLT behavior.

cond-mat.stat-mech↗
arXiv2007

Anomalous diffusion and quasistationarity in the HMF model

We explore the quasistationary regime of the Hamiltonian Mean Field Model (HMF) showing that at least three different classes of events exist, with a different diffusive behavior and with a relative frequency which depends on the size of the system. Along the same line of a recent work \cite{epl}, these results indicate that one must be very careful in exchanging time averages with ensemble averages during the non-ergodic metastable regime and at the same time they emphasize the role of finite size effects in the evaluation of the diffusive properties of the system.

cond-mat.stat-mech↗
arXiv2007

Self-Organized Criticality and earthquakes

We discuss recent results on a new analysis regarding models showing Self-Organized Criticality (SOC), and in particular on the OFC one. We show that Probability Density Functions (PDFs) for the avalanche size differences at different times have fat tails with a q-Gaussian shape. This behavior does not depend on the time interval adopted and it is also found when considering energy differences between real earthquakes.

physics.geo-ph↗
arXiv2007

Nonergodicity and Central Limit Behavior for Long-range Hamiltonians

We present a molecular dynamics test of the Central Limit Theorem (CLT) in a paradigmatic long-range-interacting many-body classical Hamiltonian system, the HMF model. We calculate sums of velocities at equidistant times along deterministic trajectories for different sizes and energy densities. We show that, when the system is in a chaotic regime (specifically, at thermal equilibrium), ergodicity is essentially verified, and the Pdfs of the sums appear to be Gaussians, consistently with the standard CLT. When the system is, instead, only weakly chaotic (specifically, along longstanding metastable Quasi-Stationary States), nonergodicity (i.e., discrepant ensemble and time averages) is observed, and robust $q$-Gaussian attractors emerge, consistently with recently proved generalizations of the CLT.

cond-mat.stat-mech↗
arXiv2007

Detection of Complex Networks Modularity by Dynamical Clustering

Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and real-world networks whose modular structure is already known or has been studied by means of other methods. The algorithm attains a high level of precision, especially when the modular units are very mixed and hardly detectable by the other methods, with a computational effort ${\cal O}(KN)$ on a generic graph with $N$ nodes and $K$ links.

physics.soc-ph↗
arXiv2006

Comment on "Entropy of Classical Systems with Long-Range Interactions" by T.M. Rocha Filho et al, PRL 95, 190601 (2005)

In a recent letter (PRL 95, 190601 (2005)), T.M. Rocha Filho and coworkers address the very interesting issue of the entropic form to be used for Hamiltonians with long-range interactions. In our opinion the letter misses several points quite debated in the recent literature which are of fundamental importance for a complete discussion of this problem. Moreover it contains several statements which are not true or not corroborated by any evidence. In this comment we discuss these arguments and severely question the generality of the conclusions of this letter.

cond-mat.stat-mech↗
arXiv2005

The Olami-Feder-Christensen model on a small-world topology

We study the effects of the topology on the Olami-Feder-Christensen (OFC) model, an earthquake model of self-organized criticality. In particular, we consider a 2D square lattice and a random rewiring procedure with a parameter $0<p<1$ that allows to tune the interaction graph, in a continuous way, from the initial local connectivity to a random graph. The main result is that the OFC model on a small-world topology exhibits self-organized criticality deep within the non-conservative regime, contrary to what happens in the nearest-neighbors model. The probability distribution for avalanche size obeys finite size scaling, with universal critical exponents in a wide range of values of the rewiring probability $p$. The pdf's cutoff can be fitted by a stretched exponential function with the stretching exponent approaching unity within the small-world region.

cond-mat.stat-mech↗
arXiv2005

Metastability and anomalous behavior in the HMF Model: connections to nonextensive thermodynamics and glassy dynamics

We review some of the most recent results on the dynamics of the Hamiltonian Mean Field (HMF) model, a systems of N planar spins with ferromagnetic infinite-range interactions. We show, in particular, how some of the dynamical anomalies of the model can be interpreted and characterized in terms of the weak-ergodicity breaking proposed in frameworks of glassy systems. We also discuss the connections with the nonextensive thermodynamics proposed by Tsallis.

cond-mat.stat-mech↗
arXiv2004

Changing Opinions in a Changing World: a New Perspective in Sociophysics

We propose a new model of opinion formation, the Opinion Changing Rate (OCR) model. Instead of investigating the conditions that allow consensus in a world of agents with different opinions, we study under which conditions a group of agents with a different natural tendency (rate) to change opinion can find agreement. The OCR is a modified version of the Kuramoto model, one of the simplest models for synchronization in biological systems, here adapted to a social context. By means of several numerical simulations we illustrate the richness of the OCR model dynamics and its social implications.

cond-mat.other↗
arXiv2002

Negative specific heat in out-of-equilibrium nonextensive systems

We discuss the occurrence of negative specific heat in a nonextensive system which has an equilibrium second-order phase transition.The specific heat is negative only in a transient regime before equilibration, in correspondence to long-lasting metastable states. For these states standard equilibrium Bolzmann-Gibbs thermodynamics does not apply and the system shows non-Gaussian velocity distributions, anomalous diffusion and correlation in phase space. Similar results have recently been found also in several other nonextensive systems, supporting the general validity of this scenario. These models seem also to support the conjecture that a nonexstensive statistical formalism, like the one proposed by Tsallis, should be applied in such cases. The theoretical scenario is not completely clear yet, but there are already many strong theoretical indications suggesting that, it can be wrong to consider the observation of an experimental negative specific heat as an unique and unambiguous signature of a standard equilibrium first-order phase transition.

nucl-th↗
arXiv2001

Comment on "Negative specific heat for a cluster of 147 Sodium atoms" by Schmidt et al

Schmidt et al (Phys Rev Lett 86, 1191 (2001)) observe and analyze a negative specific heat in Na clusters. The analysis is done within the framework of Boltzmann-Gibbs equilibrium statistical mechanics. We argue that this is not the only physical possibility to be taken into account. A possible connection with nonextensive statistical mechanics is considered as well.

cond-mat.stat-mech↗
arXiv2001

Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system

We study the dynamics of a Hamiltonian system of N classical spins with infinite-range interaction. We present numerical results which confirm the existence of metaequilibrium Quasi Stationary States (QSS), characterized by non-Gaussian velocity distributions, anomalous diffusion, Lévy walks and dynamical correlation in phase-space. We show that the Thermodynamic Limit (TL) and the Infinite-Time Limit (ITL) do not commute. Moreover, if the TL is taken before the ITL the system does not relax to the Boltzmann-Gibbs equilibrium, but remains in this new equilibrium state where nonextensive thermodynamics seems to apply.

cond-mat.stat-mech↗
arXiv2001

Non-Gaussian equilibrium in a long-range Hamiltonian system

We study the dynamics of a system of N classical spins with infinite-range interaction. We show that, when the thermodynamic limit is taken before the infinite-time limit, the system does not relax to the Boltzmann-Gibbs equilibrium, but exhibits different equilibrium properties, characterized by stable non-Gaussian velocity distributions and dynamical power-law correlation in phase-space.

cond-mat↗
arXiv2000

Time evolution of thermodynamic entropy for conservative and dissipative chaotic maps

We consider several low--dimensional chaotic maps started in far-from-equilibrium initial conditions and we study the process of relaxation to equilibrium. In the case of conservative maps the Boltzmann-Gibbs entropy S(t) increases linearly in time with a slope equal to the Kolmogorov-Sinai entropy rate. The same result is obtained also for a simple case of dissipative system, the logistic map, when considered in the chaotic regime. A very interesting results is found at the chaos threshold. In this case, the usual Boltzmann-Gibbs is not appropriate and in order to have a linear increase, as for the chaotic case, we need to use the generalized q-dependent Tsallis entropy $S_q(t)$ with a particular value of a q different from 1 (when q=1 the generalized entropy reduces to the Boltzmann-Gibbs). The entropic index q appears to be characteristic of the dynamical system.

cond-mat.stat-mech↗
arXiv2000

Microscopic dynamics of a phase transition: equilibrium vs out-of-equilibrium regime

We present for the first time to the nuclear physics community the Hamiltonian Mean Field (HMF) model. The model can be solved analytically in the canonical ensemble and shows a second-order phase transition in the thermodynamic limit. Numerical microcanonical simulations show interesting features in the out-of-equilibrium regime: in particular the model has a negative specific heat. The potential relevance for nuclear multifragmentation is discussed.

nucl-th↗