arXiv subjects

M. Falcioni

Publications and source records attributed to M. Falcioni.

17 recordsLinked to original sources

arXiv2011

Estimate of temperature and its uncertainty in small systems

The energy of a finite system thermally connected to a thermal reservoir may fluctuate, while the temperature is a constant representing a thermodynamic property of the reservoir. The finite system can also be used as a thermometer for the reservoir. From such a perspective the temperature has an uncertainty, which can be treated within the framework of estimation theory. We review the main results of this theory, and clarify some controversial issues regarding temperature fluctuations. We also offer a simple example of a thermometer with a small number of particles. We discuss the relevance of the total observation time, which must be much longer than the decorrelation time.

cond-mat.stat-mech↗

arXiv2003

Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems

Discretization of phase space usually nullifies chaos in dynamical systems. We show that if randomness is associated with discretization dynamical chaos may survive and be indistinguishable from that of the original chaotic system, when an entropic, coarse-grained analysis is performed. Relevance of this phenomenon to the problem of quantum chaos is discussed.

nlin.CD↗

arXiv2001

Predictability: a way to characterize Complexity

Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a characterization of the unpredictability of a system gives a measure of its complexity. Adopting this point of view, we review some developments in the characterization of the predictability of systems showing different kind of complexity: from low-dimensional systems to high-dimensional ones with spatio-temporal chaos and to fully developed turbulence. A special attention is devoted to finite-time and finite-resolution effects on predictability, which can be accounted with suitable generalization of the standard indicators. The problems involved in systems with intrinsic randomness is discussed, with emphasis on the important problems of distinguishing chaos from noise and of modeling the system. The characterization of irregular behavior in systems with discrete phase space is also considered.

nlin.CD↗

arXiv2000

Exit-Times and {\Large $ε$}-Entropy for Dynamical Systems, Stochastic Processes, and Turbulence

We present a comprehensive investigation of $ε$-entropy, $h(ε)$, in dynamical systems, stochastic processes and turbulence. Particular emphasis is devoted on a recently proposed approach to the calculation of the $ε$-entropy based on the exit-time statistics. The advantages of this method are demonstrated in examples of deterministic diffusive maps, intermittent maps, stochastic self-affine and multi-affine signals and experimental turbulent data. Concerning turbulence, the multifractal formalism applied to the exit time statistics allows us to predict that $h(ε)\sim ε^{-3}$ for velocity time measurement. This power law is independent of the presence of intermittency and has been confirmed by the experimental data analysis. Moreover, we show that the $ε$-entropy density of a 3-dimensional velocity field is affected by the correlations induced by the sweeping of large scales.

nlin.CD↗

arXiv2000

Chaos or Noise - Difficulties of a Distinction

In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high embedding dimension. These restrictions limit our ability to distinguish between signals generated by different systems, such as regular, chaotic or stochastic ones, when analyzed from a time series point of view. We propose to classify the signal behavior, without referring to any specific model, as stochastic or deterministic on a certain scale of the resolution $ε$, according to the dependence of the $(ε,τ)$-entropy, $h(ε, τ)$, and of the finite size Lyapunov exponent, $λ(ε)$, on $ε$.

nlin.CD↗

arXiv1999

An exit-time approach to $ε$-entropy

An efficient approach to the calculation of the $ε$-entropy is proposed. The method is based on the idea of looking at the information content of a string of data, by analyzing the signal only at the instants when the fluctuations are larger than a certain threshold $ε$, i.e., by looking at the exit-time statistics. The practical and theoretical advantages of our method with respect to the usual one are shown by the examples of a deterministic map and a self-affine stochastic process.

chao-dyn↗

arXiv1998

Macroscopic chaos in globally coupled maps

We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to the evolution of the single (or microscopic) elements of the system. The usual Lyapunov exponent is not able to capture the essential features of this macroscopic phenomenon. Using the recently introduced notion of finite size Lyapunov exponent, we characterize, in a consistent way, these macroscopic behaviours. Basically, at small values of the perturbation we recover the usual (microscopic) Lyapunov exponent, while at larger values a sort of macroscopic Lyapunov exponent emerges, which can be much smaller than the former. A quantitative characterization of the chaotic motion at hydrodynamical level is then possible, even in the absence of the explicit equations for the time evolution of the macroscopic observables.

chao-dyn↗

arXiv1998

Anisotropic Membranes

We describe the statistical behavior of anisotropic crystalline membranes. In particular we give the phase diagram and critical exponents for phantom membranes and discuss the generalization to self-avoiding membranes.

hep-lat↗

arXiv1998

Characterization of the spatial complex behavior and transition to chaos in flow systems

We introduce a ``spatial'' Lyapunov exponent to characterize the complex behavior of non chaotic but convectively unstable flow systems. This complexity is of spatial type and is due to sensitivity to the boundary conditions. We show that there exists a relation between the spatial-complexity index we define and the comoving Lyapunov exponents. In these systems the transition to chaos, i.e. the appearing of a positive Lyapunov exponent, can take place in two different ways. In the first one (from neither chaotic nor spatially complex behavior to chaos) one has the typical scenario; that is, as the system size grows up the spectrum of the Lyapunov exponents gives rise to a density. In the second one (when the chaos develops from a convectively unstable situation) one observes only a finite number of positive Lyapunov exponents.

chao-dyn↗

arXiv1997

Improved Algorithms for Simulating Crystalline Membranes

The physics of crystalline membranes, i.e. fixed-connectivity surfaces embedded in three dimensions and with an extrinsic curvature term, is very rich and of great theoretical interest. To understand their behavior, numerical simulations are commonly used. Unfortunately, traditional Monte Carlo algorithms suffer from very long auto-correlations and critical slowing down in the more interesting phases of the model. In this paper we study the performance of improved Monte Carlo algorithms for simulating crystalline membrane, such as hybrid overrelaxation and unigrid methods, and compare their performance to the more traditional Metropolis algorithm. We find that although the overrelaxation algorithm does not reduce the critical slowing down, it gives an overall gain of a factor 15 over the Metropolis algorithm. The unigrid algorithm does, on the other hand, reduce the critical slowing down exponent to z apprx. 1.7.

physics.comp-ph↗

arXiv1996

The flat phase of fixed-connectivity membranes

The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical understanding of the remarkable flat phase of such membranes. We then summarize the results of a recent large scale Monte Carlo simulation of the simplest conceivable discrete realization of this system \cite{BCFTA}. We verify the existence of long-range order, determine the associated critical exponents of the flat phase and compare the results to the predictions of various theoretical models.

hep-lat↗

arXiv1996

Characterization of a periodically driven chaotic dynamical system

We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a local--in--time version of these quantities. In systems where the time scale related to the time periodic variation of the parameter is much larger than the ``internal'' time scale, one has that the local quantities strongly depend on the phase of the cycle. In this case, the standard global quantities can give misleading information.

chao-dyn↗

arXiv1996

The Flat Phase of Crystalline Membranes

We present the results of a high-statistics Monte Carlo simulation of a phantom crystalline (fixed-connectivity) membrane with free boundary. We verify the existence of a flat phase by examining lattices of size up to $128^2$. The Hamiltonian of the model is the sum of a simple spring pair potential, with no hard-core repulsion, and bending energy. The only free parameter is the the bending rigidity $κ$. In-plane elastic constants are not explicitly introduced. We obtain the remarkable result that this simple model dynamically generates the elastic constants required to stabilise the flat phase. We present measurements of the size (Flory) exponent $ν$ and the roughness exponent $ζ$. We also determine the critical exponents $η$ and $η_u$ describing the scale dependence of the bending rigidity ($κ(q) \sim q^{-η}$) and the induced elastic constants ($λ(q) \sim μ(q) \sim q^{η_u}$). At bending rigidity $κ= 1.1$, we find $ν= 0.95(5)$ (Hausdorff dimension $d_H = 2/ν= 2.1(1)$), $ζ= 0.64(2)$ and $η_u = 0.50(1)$. These results are consistent with the scaling relation $ζ= (2+η_u)/4$. The additional scaling relation $η= 2(1-ζ)$ implies $η= 0.72(4)$. A direct measurement of $η$ from the power-law decay of the normal-normal correlation function yields $η\approx 0.6$ on the $128^2$ lattice.

cond-mat↗

arXiv1995

The Phase Diagram of Crystalline Surfaces

We report the status of a high-statistics Monte Carlo simulation of non-self-avoiding crystalline surfaces with extrinsic curvature on lattices of size up to $128^2$ nodes. We impose free boundary conditions. The free energy is a gaussian spring tethering potential together with a normal-normal bending energy. Particular emphasis is given to the behavior of the model in the cold phase where we measure the decay of the normal-normal correlation function.

hep-lat↗

arXiv1995

Broken ergodicity and glassy behavior in a deterministic chaotic map

A network of $N$ elements is studied in terms of a deterministic globally coupled map which can be chaotic. There exists a range of values for the parameters of the map where the number of different macroscopic configurations is very large, and there is violation of selfaveraging. The time averages of functions, which depend on a single element, computed over a time $T$, have probability distributions that do not collapse to a delta function, for increasing $T$ and $N$. This happens for both chaotic and regular motion, i.e. positive or negative Lyapunov exponent.

cond-mat↗

arXiv1994

Stochastic Resonance in Deterministic Chaotic Systems

We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the threshold for the onset of chaos, stochastic resonance effects appears. As a result one has an alternation of chaotic and regular, i.e. predictable, evolutions in an almost periodic way, so that the Lyapunov exponent is positive but some time correlations do not decay.

chao-dyn↗

arXiv1993

Critical Slowing Down of Cluster Algorithms for Ising Models Coupled to 2-d Gravity

We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.

hep-lat↗