arXiv subjects

Paolo Sibani

Publications and source records attributed to Paolo Sibani.

At least 37 records · Page 2Linked to original sources

arXiv2011

Non-stationary aging dynamics in ant societies

In recent experiments by Richardson et al. ((2010), PLoS ONE 5(3): e9621. doi:10.1371/ journal.pone.0009621) ant motion out of the nest is shown to be a non-stationary process intriguingly similar to the dynamics encountered in \emph{physical aging} of glassy systems. Specifically, exit events can be described as a Poisson process in logarithmic time, or, for short, a log-Poisson process. Nouvellet et al.(J. Theor. Biol. 266, 573. (2010)) criticized these conclusions and performed new experiments where the exit process could more simply be described by standard Poisson statistics. In their reply, (J Theor. Biol. 269, 356-358 (2011)) Richardson et al. stressed that the two sets of experiments were performed under very different conditions and claimed that this was the likely source of the discrepancy. The focal point of this work is whether log-Poisson and Poisson statistics both are possible under different external conditions. To this end, a model is introduced where interacting ants move in a stochastic fashion from one site to a neighboring site on a finite 2D lattice. The probability of each move is determined by the ensuing changes of a utility function which is a sum of pairwise interactions between ants, weighted by distance. Depending on how the interactions are defined and on a control parameter dubbed 'degree of stochasticity' (DS), the dynamics either quickly converges to a stationary state, where movements are a standard Poisson process, or may enter a non-stationary regime, where exits can be described as suggested by Richardson et al.

q-bio.PE↗

arXiv2010

Tempo and Mode of Evolution in the Tangled Nature Model

We study the Tangled Nature model of macro evolution and demonstrate that the co-evolutionary dynamics produces an increasingly correlated core of well occupied types. At the same time the entire configuration of types becomes increasing de-correlated. This finding is related to ecosystem evolution. The systems level dynamics of the model is subordinated to intermittent transitions between meta-stable states. We improve on previous studies of the statistics of the transition times and show that the fluctuations in the offspring probability decreases with number of transitions. The longtime adaptation, as seen by an increasing population size is demonstrated to be related to the convexity of the offspring probability. We explain how the models behaviour is a mathematical reflection of Darwin's concept of adaptation of profitable variations.

cond-mat.stat-mech↗

arXiv2009

Mutual information in the Tangled Nature Model

We consider the concept of mutual information in ecological networks, and use this idea to analyse the Tangled Nature model of co-evolution. We show that this measure of correlation has two distinct behaviours depending on how we define the network in question: if we consider only the network of viable species this measure increases, whereas for the whole system it decreases. It is suggested that these are complimentary behaviours that show how ecosystems can become both more stable and better adapted.

q-bio.PE↗

arXiv2009

Origin of `end of aging' and sub-aging scaling behavior in glassy dynamics

Linear response functions of aging systems are routinely interpreted using the scaling variable $t_{\rm obs}/t_{\rm w}^μ$,where $t_{\rm w}$ is the time at which the field conjugated to the response is turned on or off, and where $t_{\rm obs}$ is the `observation' time elapsed from the field change. The response curve obtained for different values of $t_w$ are usually collapsed using values of $μ$ slightly below one, a scaling behavior generally known as \emph{sub-aging}. Recent spin glass Thermoremanent Magnetization experiments have shown that the value of $μ$ is strongly affected by the form of the initial cooling protocol (Rodriguez et al., Phys. Rev. Lett. 91, 037203, 2003), and even more importantly, (Kenning et al., Phys. Rev. Lett. 97, 057201, 2006) that the $t_{\rm w}$ dependence of the response curves vanishes altogether in the limit $t_{\rm obs} \gg t_{\rm w}$. The latter result shows that the widely used $t_{\rm obs}/t_{\rm w}^μ$ scaling of linear response data cannot be generally valid, and casts some doubt on the theoretical significance of the exponent $μ$. In this work, a common mechanism is proposed for the origin of both sub-aging and end of aging behavior in glassy dynamics. The mechanism combines real and configuration space properties of the state produced by the initial thermal quench which initiates the aging process.

cond-mat.stat-mech↗

arXiv2008

Intermittent relaxation in hierarchical energy landscapes

We numerically simulate a thermalization process in an energy landscape with hierarchically organized metastable states. The initial configuration is chosen to have a large energy excess, relative to the thermal equilibrium value at the running temperature. We show that the initial energy surplus is dissipated in a series of intermittent bursts, or quakes, whose rate decreases as the inverse of the age of the system. In addition, one observes energy fluctuations with a zero centered Gaussian distribution. These pertain to the pseudo equilibrium dynamics within a single metastable state, and do not contribute to the energy dissipation. The derivative of the thermal energy with respect to the logarithm of time is asymptotically constant, and comprises a temperature independent part, and a part with an Arrhenius temperature dependence. The findings closely mirror recent numerical simulation results obtained for microscopic glassy models. For these models, record-sized energy fluctuations have been claimed to trigger intermittent events during low temperature thermalization. In the present model record-sized fluctuations are by construction needed to trigger changes from one metastable state to another. This property thus suffices to explain the statistical property of intermittent energy flow in complex metastable systems.

cond-mat.stat-mech↗

arXiv2007

Linear response subordination to intermittent energy release in off-equilibrium aging dynamics

The interpretation of experimental and numerical data describing off-equilibrium aging dynamics crucially depends on the connection between spontaneous and induced fluctuations. The hypothesis that linear response fluctuations are statistically subordinated to irreversible outbursts of energy, so-called quakes, leads to predictions for averages and fluctuations spectra of physical observables in reasonable agreement with experimental results [see e.g. Sibani et al., Phys. Rev. B74:224407, 2006]. Using simulational data from a simple but representative Ising model with plaquette interactions, direct statistical evidence supporting the hypothesis is presented and discussed in this work. A strict temporal correlation between quakes and intermittent magnetization fluctuations is demonstrated. The external magnetic field is shown to bias the pre-existent intermittent tails of the magnetic fluctuation distribution, with little or no effect on the Gaussian part of the latter. Its impact on energy fluctuations is shown to be negligible. Linear response is thus controlled by the quakes and inherits their temporal statistics. These findings provide a theoretical basis for analyzing intermittent linear response data from aging system in the same way as thermal energy fluctuations, which are far more difficult to measure.

cond-mat.stat-mech↗

arXiv2007

Thermal shifts and intermittent linear response of aging systems

At time $t$ after an initial quench, an aging system responds to a perturbation turned on at time $ t_{\rm w} < t$ in a way mainly depending on the number of intermittent energy fluctuations, so-called quakes, which fall within the observation interval $(t_{\rm w},t]$ [Sibani et al. Phys. Rev. B, 74, 224407 and Eur. J. of Physics B, 58,483-491, 2007]. The temporal distribution of the quakes implies a functional dependence of the average response on the ratio $t/t_{\rm w}$. Further insight is obtained imposing small temperature steps, so-called $T$-shifts. The average response as a function of $t/t_{\rm w,eff}$, where $t_{\rm w,eff}$ is the effective age, is similar to the response of a system aged isothermally at the final temperature. Using an Ising model with plaquette interactions, the applicability of analytic formulae for the average isothermal magnetization is confirmed. The $T$-shifted aging behavior of the model is described using effective ages. Large positive shifts nearly reset the effective age. Negative $T$-shifts offer a more detailed probe of the dynamics. Assuming the marginal stability of the `current' attractor against thermal noise fluctuations, the scaling form $t_{\rm w,eff} = t_{\rm w}^x$, and the dependence of the exponent $x$ on the aging temperatures before and after the shift are theoretically available. The predicted form of $x$ has no adjustable parameters. Both the algebraic scaling of the effective age and the form of the exponent agree with the data. The simulations thus confirm the crucial rôle of marginal stability in glassy relaxation.

cond-mat.stat-mech↗

arXiv2007

Linear response in aging glassy systems, intermittency and the Poisson statistics of record fluctuations

We study the intermittent behavior of the energy decay and linear magnetic response of a glassy system during isothermal aging after a deep thermal quench using the Edward-Anderson spin glass model as a paradigmatic example. The large intermittent changes in the two observables are found to occur in a correlated fashion and through irreversible bursts, `quakes', which punctuate reversible and equilibrium-like fluctuations of zero average. The temporal distribution of the quakes it found to be a Poisson distribution with an average growing logarithmically on time, indicating that the quakes are triggered by record sized fluctuations. As the drift of an aging system is to a good approximation subordinated to the quakes, simple analytical expressions (Sibani et al. Phys Rev B 74, 224407, 2006) are available for the time and age dependence of the average response and average energy. These expressions are shown to capture the time dependencies of the EA simulation results. Finally, we argue that whenever the changes of the linear response function and of its conjugate autocorrelation function follow from the same intermittent events a fluctuation-dissipation-like relation can arise between the two in off-equilibrium aging.

cond-mat.stat-mech↗

arXiv2006

Intermittent quakes and record dynamics in the thermoremanent magnetization of a spin-glass

A novel method for analyzing the intermittent behavior of linear response data in aging systems is presented and applied to spin-glass thermoremanent magnetization (TRM) (Rodriguez et al. Phys. Rev. Lett. 91, 037203, 2003). The probability density function (PDF) of magnetic fluctuations is shown to have an asymmetric exponential tail, demonstrating that the demagnetization process is carried by intermittent, significant, spin rearrangements or \emph{quakes}. These quakes are most pronounced shortly after the field removal, $t/t_w \approx 1$ and in the non-equilibrium aging regime $t/t_w >>1$. For a broad temperature range, we study the dependence of the TRM decay rate on $t$, the time since the initial quench and on $t_w$, the time at which the magnetic field is cut. The $t$ and $t_w$ dependence of the rate is extracted numerically from the data and described analytically using the assumption that the linear response is subordinated to the intermittent process which spasmodically release the initial imbalances created by the quench.

cond-mat.dis-nn↗

arXiv2006

Aging and intermittency in a p-spin model of a glass

We numerically analyze the statistics of the heat flow between an aging system and its thermal bath, following a method proposed and tested for a spin-glass model in a recent Letter (P. Sibani and H.J. Jensen, Europhys. Lett.69, 563 (2005)). The present system, which lacks quenched randomness, consists of Ising spins located on a cubic lattice, with each plaquette contributing to the total energy the product of the four spins located at its corners. Similarly to our previous findings, energy leaves the system in rare but large, so called intermittent, bursts which are embedded in reversible and equilibrium-like fluctuations of zero average. The intermittent bursts, or quakes, dissipate the excess energy trapped in the initial state at a rate which falls off with the inverse of the age. This strongly heterogeneous dynamical picture is explained using the idea that quakes are triggered by energy fluctuations of record size, which occur independently within a number of thermalized domains. From the temperature dependence of the width of the reversible heat fluctuations we surmise that these domains have an exponential density of states. Finally, we show that the heat flow consists of a temperature independent term and a term with an Arrhenius temperature dependence. Microscopic dynamical and structural information can thus be extracted from numerical intermittency data. This type of analysis seems now within the reach of time resolved micro-calorimetry techniques.

cond-mat.stat-mech↗

arXiv2005

Mesoscopic fluctuations and intermittency in aging dynamics

The configurational de-correlation in an aging system is attributed to irreversible intermittent rearrangements, which are described as a Poisson process with average $\propto \ln(1 + t/t_w)$, where $t$ is the observation time and $t_w$ is the age [P. Sibani and H.J. Jensen, Europhys. Lett. 69, 2005]. On this basis, we obtain a simple model for the off-equilibrium aging behavior of the autocorrelation: the average autocorrelation decays algebraically, and its shifted and rescaled probability density function (PDF) has a Gumbel-like shape which approaches a Gaussian at large times and becomes sharp in the thermodynamic limit. The model properties are tested against simulations of the Edwards-Anderson spin glass, and are in reasonable agreement with other available data.

cond-mat.soft↗

arXiv2005

Record dynamics and the observed temperature plateau in the magnetic creep rate of type II superconductors

We use Monte Carlo simulations of a coarse grained three dimensional model to demonstrate that the experimentally observed approximate temperature independence of the magnetic creep rate for a broad range of temperatures may be explained in terms of record dynamics, {\it viz.} the dynamical properties of the times at which a stochastic fluctuating signal establishes records.

cond-mat.supr-con↗

arXiv2005

Extremal noise events, intermittency and Log-Poisson statistics in non-equilibrium aging of complex systems

We review the close link between intermittent events ('quakes') and extremal noise fluctuations which has been advocated in recent numerical and theoretical work. From the idea that record-breaking noise fluctuations trigger the quakes, an approximate analytical description of non-equilibrium aging as a Poisson process with logarithmic time arguments can be derived. Theoretical predictions for measurable statistical properties of mesoscopic fluctuations are emphasized, and supporting numerical evidence is included from simulations of short-ranged Ising spin-glass models, of the ROM model of vortex dynamics in type II superconductors, and of the Tangled Nature model of biological evolution.

cond-mat.dis-nn↗

arXiv2005

Comparing extremal and thermal Explorations of Energy Landscapes

Using a non-thermal local search, called Extremal Optimization (EO), in conjunction with a recently developed scheme for classifying the valley structure of complex systems, we analyze a short-range spin glass. In comparison with earlier studies using a thermal algorithm with detailed balance, we determine which features of the landscape are algorithm dependent and which are inherently geometrical. Apparently a characteristic for any local search in complex energy landscapes, the time series of successive energy records found by EO also is characterized approximately by a log-Poisson statistics. Differences in the results provide additional insights into the performance of EO. In contrast with a thermal search, the extremal search visits dramatically higher energies while returning to more widely separated low-energy configurations. Two important properties of the energy landscape are independent of either algorithm: first, to find lower energy records, progressively higher energy barriers need to be overcome. Second, the Hamming distance between two consecutive low-energy records is linearly related to the height of the intervening barrier.

cond-mat.dis-nn↗

arXiv2004

Intermittency, aging and record fluctuations

Aging in spin glasses is analyzed via the Probability Density Function (PDF) of the heat transfer between system and bath over a small time $δt$. The PDF contains a Gaussian part, describing reversible fluctuations, and an exponential tail caused by intermittent events. We find that the relative weight of these two parts depends, for fixed $δt$, on the ratio of the total sampling time to the age $t_w$. Fixing this ratio, the intensity of the intermittent events is proportional to $δt/t_w$ and independent of the temperature. The Gaussian part has a variance with the same temperature dependence as the variance of the equilibrium energy in a system with an exponential density of states. All these observations are explained assuming that, for any $t_w$, intermittent events are triggered by local energy fluctuations exceeding those previously occurred.

cond-mat.soft↗

arXiv2004

How a spin-glass remembers. Memory and rejuvenation from intermittency data: an analysis of temperature shifts

The memory and rejuvenation aspects of intermittent heat transport are explored theoretically and by numerical simulation for Ising spin glasses with short-ranged interactions. The theoretical part develops a picture of non-equilibrium glassy dynamics recently introduced by the authors. Invoking the concept of marginal stability, this theory links irreversible `intermittent' events, or `quakes' to thermal fluctuations of record magnitude. The pivotal idea is that the largest energy barrier $b(t_w,T)$ surmounted prior to $t_w$ by thermal fluctuations at temperature $T$ determines the rate $r_q \propto 1/t_w$ of the intermittent events occurring near $t_w$. The idea leads to a rate of intermittent events after a negative temperature shift given by $r_q \propto 1/t_w^{eff}$, where the `effective age' $t_w^{eff} \geq t_w$ has an algebraic dependence on $t_w$, whose exponent contains the temperatures before and after the shift. The analytical expression is verified by numerical simulations. Marginal stability suggests that a positive temperature shift $T \to T'$ could erase the memory of the barrier $b(t_w,T)$. The simulations show that the barrier $b(t_w,T') \geq b(t_w,T)$ controls the intermittent dynamics, whose rate is hence $r_q \propto 1/t_w$. Additional `rejuvenation' effects are also identified in the intermittency data for shifts of both signs.

cond-mat.stat-mech↗

arXiv2004

Evolution in complex systems

What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analysed to confirm this effect. The strain arises from local frustration. As the strain is released through "quakes", some system variable undergoes record statistics with accompanying log-Poisson statistics for the quake event times[4]. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology, and show how quantitative indications of ageing can be found.

cond-mat.stat-mech↗

arXiv2003

The energy landscape of aging systems--from a different angle

A novel method for glassy landscape exploration is presented which utilizes a time series of energy values collected during an isothermal relaxation after a thermal quench. A sub-series of increasingly rare events, or quakes, which are connected to an irreversible release of energy from the system, is used to identify entry and exit times for landscape valleys. The landscape of three dimensional spin glasses is studied from this angle for a number of lattice sizes and for a range of low temperatures. A simple picture emerges regarding the temperature and size dependence of (1) the energy barriers separating the valleys, (2) the lowest energy minimum within a valley, and (3) the distance between the configurations belonging to the lowest minima in neighboring valleys. The configuration changes following the quakes are analyzed in terms of connected clusters of flipped spins, and the size distribution of these clusters is presented.

cond-mat.stat-mech↗