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We investigate how the kinetic energy acquired by a dense granular system driven by an external vibration depends on the input energy. Our focus is on the dependence of the granular behavior on two main parameters: frequency and vibration amplitude. We find that there exists an optimal forcing frequency, at which the system reaches the maximal kinetic energy: if the input energy is increased beyond such a threshold, the system dissipates more and more energy and recovers a colder and more viscous state. Quite surprisingly, the nonmonotonic behavior is found for vibration amplitudes which are sufficiently small to keep the system always in contact with the driving oscillating plate. Studying dissipative properties of the system, we unveil a striking difference between this nonmonotonic behavior and a standard resonance mechanism. This feature is also observed at the microscopic scale of the single-grain dynamics and can be interpreted as an instance of negative specific heat. An analytically solvable model based on a generalized forced-damped oscillator well reproduces the observed phenomenology, illustrating the role of the competing effects of forcing and dissipation.

The elaboration of reliable forecasting in the first hours after large shocks, very useful for the postseismic management, is strongly affected by the huge incompleteness of seismic catalogs. The deficit of observed events, in the first part of aftershock sequences, can be naturally attributed to different mechanisms such as the inefficiency of the seismic network as well as the overlap of seismic records. In this study we show that short‐term aftershock incompleteness can be explained only in terms of the second mechanism whereas it is only weakly affected by the quality of the instrumental coverage. Indeed, we show that larger deviations from the Gutenberg‐Richter law and the Omori‐Utsu law can be found in regions with a higher seismic network efficiency. We use these results to develop an incomplete Epidemic‐Type Aftershock Sequence model able to reproduce statistical features in time and magnitude of recorded aftershocks.

The frictional properties of disordered systems are affected by external perturbations. These perturbations usually weaken the system by reducing the macroscopic friction coefficient. This friction reduction is of particular interest in the case of disordered systems composed of granular particles confined between two plates, as this is a simple model of seismic fault. Indeed, in the geophysical context frictional weakening could explain the unexpected weakness of some faults, as well as earthquake remote triggering. In this manuscript we review recent results concerning the response of confined granular systems to external perturbations, considering the different mechanisms by which the perturbation could weaken a system, the relevance of the frictional reduction to earthquakes, as well as discussing the intriguing scenario whereby the weakening is not monotonic in the perturbation frequency, so that a re-entrant transition is observed, as the system first enters a fluidized state and then returns to a frictional state., Comment: 15 pages, 12 figures

Pattern recognition is a fundamental neuronal process which enables a cortical system to interpret visual stimuli. How the brain learns to recognize patterns is, however, an unsolved problem. The frequently employed method of back propagation excels at this task but has been found to be unbiological in many aspects. In this Rapid Communication we achieve pattern recognition tasks in a biologically, fully consistent framework. We consider a neuronal network exhibiting avalanche dynamics, as observed experimentally, and implement negative feedback signals. These are chemical signals, such as dopamine, which mediate synaptic plasticity and sculpt the network to achieve certain tasks. The system is able to distinguish horizontal and vertical lines with high accuracy, as well as to perform well at the more complicated task of handwritten digit recognition. Resulting from the learning mechanism, spatially separate activity regions emerge, as observed in the primary visual cortex using functional magnetic resonance imaging techniques. The results therefore suggest that negative feedback signals offer an explanation for the emergence of distinct activity areas in the visual cortex.

In recent years self organised critical neuronal models have provided insights regarding the origin of the experimentally observed avalanching behaviour of neuronal systems. It has been shown that dynamical synapses, as a form of short-term plasticity, can cause critical neuronal dynamics. Whereas long-term plasticity, such as hebbian or activity dependent plasticity, have a crucial role in shaping the network structure and endowing neural systems with learning abilities. In this work we provide a model which combines both plasticity mechanisms, acting on two different time-scales. The measured avalanche statistics are compatible with experimental results for both the avalanche size and duration distribution with biologically observed percentages of inhibitory neurons. The time-series of neuronal activity exhibits temporal bursts leading to 1/f decay in the power spectrum. The presence of long-term plasticity gives the system the ability to learn binary rules such as XOR, providing the foundation of future research on more complicated tasks such as pattern recognition., 8 pages, 7 figures

According to the acoustic fluidization hypothesis, elastic waves at a characteristic frequency form inside seismic faults even in the absence of an external perturbation. These waves are able to generate a normal stress which contrasts the confining pressure and promotes failure. Here, we study the mechanisms responsible for this wave activation via numerical simulations of a granular fault model. We observe the particles belonging to the percolating backbone, which sustains the stress, to perform synchronized oscillations over ellipticlike trajectories in the fault plane. These oscillations occur at the characteristic frequency of acoustic fluidization. As the applied shear stress increases, these oscillations become perpendicular to the fault plane just before the system fails, opposing the confining pressure, consistently with the acoustic fluidization scenario. The same change of orientation can be induced by external perturbations at the acoustic fluidization frequency. Published version

We experimentally investigate the fluidization of a granular material subject to mechanical vibrations by monitoring the angular velocity of a vane suspended in the medium and driven by an external motor. On increasing the frequency we observe a re-entrant transition, as a jammed system first enters a fluidized state, where the vane rotates with high constant velocity, and then returns to a frictional state, where the vane velocity is much lower. While the fluidization frequency is material independent, the viscosity recovery frequency shows a clear dependence on the material, that we rationalize by relating this frequency to the balance between dissipative and inertial forces in the system. Molecular dynamics simulations well reproduce the experimental data, confirming the suggested theoretical picture., Comment: 6 pages, 5 figures + supplemental material, accepted for publication in PRL

The b value of the Gutenberg - Richter distribution is estimated as a function of a threshold magnitude m_th and it is found to depend on m_th for magnitudes larger than the completeness magnitude m_c. We identify a magnitude interval [m_c;m_m] where b is a decreasing function of m_th followed by a regime of increasing b for large magnitudes. This is a common feature of experimental catalogues for different geographic areas. The increase at large m_th is explained in terms of an upper magnitude cut-off in experimental catalogues due to finite size effects. We develop a rigorous mathematical framework to relate the decrease of b in the intermediate regime to the functional form of the distribution of the b values. We propose two hypotheses: The first is that the spatial and temporal vari- ability of b leads to a b distribution peaked around its average value. The second is that mainshocks and aftershocks are distributed according to the Gutenberg-Richter law with different b values, leading to a bimodal distribution of b. Simulated Epidemic Type Aftershock Sequences (ETAS) catalogues, generated according to this hypothesis, exhibit the same magnitude distribution of experimental ones. In alternative we cannot exclude the b dependence on m caused by magnitudes not homogeneously evaluated in a seismic catalogue. In the latter scenario our results provide the correction terms to the estimated magnitudes.

Branching processes provide an accurate description of earthquake occurrence in the short term (days to a few weeks). Yet, the implementation of these models is not usually straightforward because of the difficulties in estimating the parameters. Indeed, log‐likelihood estimation involves a spatial integral that cannot be analytically evaluated and is difficult to implement in numerical codes. Here we present a novel technique that allows for an accurate, stable, and relatively fast parameter inversion procedure. We study the efficiency of this technique using synthetic epidemic‐type aftershock sequence catalogs with a set of parameters known a priori . Results show the efficiency of the novel technique and illustrate the limits of recently proposed approximations.

The recent upraise of interest in the dynamics of the brain resting activity opens a number of new and different questions. A fundamental one is related to the character of correlations of healthy large scale brain activity. These studies focus on the linear correlation of the spontaneous activity between brain sites. Here we present a different approach, instead to estimate the average linear correlation of activity between pairs of brain sites, we ask: what are average sequels in space and time of a big event (i.e., a thunder). By strobing these events we find that on average the activity variations with opposite sign are correlated in time, over a temporal scale of few seconds, exposing a critical balance between excitation and depression opposing forces. Fil: Lombardi, F.. ETH Zurich; Suiza Fil: Chialvo, Dante Renato. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Herrmann, H. J.. ETH Zurich; Suiza. Universidade Federal do Ceará; Brasil Fil: de Arcangelis, L.. Seconda Universita Degli Studi Di Napoli; Italia

We study the spatial distribution of earthquakes in temporal intervals before and after the occurrence of large shocks (mainshocks) in the magnitude range $$m \in [2,5]$$ for four different regional catalogs. We find that the spatial organization of pre-shock seismicity depends on the mainshock magnitude and is independent of the lower magnitude threshold. These properties are found to be a stable feature of regional catalogs and cannot be reproduced by Epidemic Type Aftershock Sequence models. Our findings suggest that the area fractured during the mainshock is encoded in the foreshock spatial organization and, therefore, enhance the prognostic value of foreshocks.

Particle nucleation remains one of the most intriguing steps in the process of particle formation in flames. Although stacking/clustering of polycyclic aromatic hydrocarbons (PAHs) has been identified as a key step in the nucleation process, uncertainties remain about the size of the PAHs undergoing clustering, the organisation of the PAHs in the forming clusters and the factors affecting the relative amounts of order and disorder present in the texture organisation. A molecular dynamics approach is presented to study the influence of the molecular weight and structure of PAHs on the nucleation and coagulation processes and on the morphology of the formed clusters. Two different types of macromolecules have been analysed: pericondensed aromatic hydrocarbons (PCAHs) and aromatic aliphatic linked hydrocarbons (AALHs), known to be present in flame environments depending on flame temperature, equivalence ratio and fuel chemical structure. Clustering of six organic molecules has been analysed at two extreme temperatures, namely 500 K and 1500 K. The six molecules have been chosen on the basis of their molecular weight (pyrene and coronene) and molecular structure (single molecules, covalent-bonded dimers and covalent-bonded trimers). Nucleation of single pyrene molecules is negligible at low temperature and practically absent at high temperature. Conversely, nucleation of single coronene molecules involves 33% of the initial molecules at low temperature. Molecules within the clusters are highly mobile at flame temperatures and just 5% of the initial molecules are in clusters. The presence of covalent bonds among the aromatic sub-units improves clustering and growth, both for pyrene and coronene sub-units. Looking at the structure and the fractal dimensionality of the formed clusters, an enhancement of the disorder of the clusters is observed in the case of the AALHs (dimers and trimers) with an increased number of molecules not arranged in parallel planes. The same behaviour is found for the higher temperature.

Ongoing cortical activity consists of sequences of synchronized bursts, named neuronal avalanches, whose size and duration are power law distributed. These features have been observed in a variety of systems and conditions, at all spatial scales, supporting scale invariance, universality and therefore criticality. However, the mechanisms leading to burst triggering, as well as the relationship between bursts and quiescence, are still unclear. The analysis of temporal correlations constitutes a major step towards a deeper understanding of burst dynamics. Here, we investigate the relation between avalanche sizes and quiet times, as well as between sizes of consecutive avalanches recorded in cortex slice cultures. We show that quiet times depend on the size of preceding avalanches and, at the same time, influence the size of the following one. Moreover we evidence that sizes of consecutive avalanches are correlated. In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively. Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity., Scientific Reports, 6, ISSN:2045-2322

Recent experiments have detected a novel form of spontaneous neuronal activity both in vitro and in vivo: neuronal avalanches. The statistical properties of this activity are typical of critical phenomena, with power laws characterizing the distributions of avalanche size and duration. A critical behaviour for the spontaneous brain activity has important consequences on stimulated activity and learning. Very interestingly, these statistical properties can be altered in significant ways in epilepsy and by pharmacological manipulations. In particular, there can be an increase in the number of large events anticipated by the power law, referred to herein as dragon-king avalanches. This behaviour, as verified by numerical models, can originate from a number of different mechanisms. For instance, it is observed experimentally that the emergence of a critical behaviour depends on the subtle balance between excitatory and inhibitory mechanisms acting in the system. Perturbing this balance, by increasing either synaptic excitation or the incidence of depolarized neuronal up-states causes frequent dragon-king avalanches. Conversely, an unbalanced GABAergic inhibition or long periods of low activity in the network give rise to sub-critical behaviour. Moreover, the existence of power laws, common to other stochastic processes, like earthquakes or solar flares, suggests that correlations are relevant in these phenomena. The dragon-king avalanches may then also be the expression of pathological correlations leading to frequent avalanches encompassing all neurons. We will review the statistics of neuronal avalanches in experimental systems. We then present numerical simulations of a neuronal network model introducing within the self-organized criticality framework ingredients from the physiology of real neurons, as the refractory period, synaptic plasticity and inhibitory synapses. The avalanche critical behaviour and the role of dragon-king avalanches will be discussed in relation to different drives, neuronal states and microscopic mechanisms of charge storage and release in neuronal networks.

We study the elasticity behaviour at the sol-gel transition with a percolation dynamic model via computer simulations on a square lattice. From the fluctuations in the center-of-mass motion of the percolating cluster we determine the critical behaviour of the macroscopic elastic constant of the gel phase, growing above the gel point with a critical exponent mu similar or equal to 2.7 +/- 0.1. We also study time autocorrelation functions and find that the relaxation times diverge, as the percolation threshold is approached from below, with a critical exponent s similar or equal to 1.9 +/- 0.1.

Context. Experimental observations indicate that flares and CMEs are often associated, even if the precise relationship between the two phenomena is a still hot and open question. Aims. We present a study of the statistical properties of solar flare and CME temporal organisation, in order to enlighten differences in the mechanisms at the basis of their occurrence. Methods. We analyse experimental catalogs and compare the occurrence rate of flares and CME with the sunspot number. We also perform numerical simulations of simple stochastic models to be compared with experimental data. Results. We find that the CME and flare occurrence rates are related, respectively, linearly and quadratically to the level of solar activity. Conclusions. This behaviour could be understood in terms of correlations among flares: the occurrence of a flare, by perturbing the magnetic configuration, may eventually trigger further flares. This interpretation is supported by the existence of Omori sequences of after-flares following more energetic flares.

The unexpected weakness of some faults has been attributed to the emergence of acoustic waves that promote failure by reducing the confining pressure through a mechanism known as acoustic fluidization, also proposed to explain earthquake remote triggering. Here we validate this mechanism via the numerical investigation of a granular fault model system. We find that the stick-slip dynamics is affected only by perturbations applied at a characteristic frequency corresponding to oscillations normal to the fault, leading to gradual dynamical weakening as failure is approaching. Acoustic waves at the same frequency spontaneously emerge at the onset of failure in the absence of perturbations, supporting the relevance of acoustic fluidization in earthquake triggering. Published version

Neuronal avalanches measured in vitro and in vivo in different cortical networks consistently exhibit power law behaviour for the size and duration distributions with exponents typical for a mean field self-organized branching process. These exponents are also recovered in neuronal network simulations implementing various neuronal dynamics on different network topologies. They can therefore be considered a very robust feature of spontaneous neuronal activity. Interestingly, this scaling behaviour is also observed on regular lattices in finite dimensions, which raises the question about the origin of the mean field behavior observed experimentally. In this study we provide an answer to this open question by investigating the effect of activity dependent plasticity in combination with the neuronal refractory time in a neuronal network. Results show that the refractory time hinders backward avalanches forcing a directed propagation. Hebbian plastic adaptation plays the role of sculpting these directed avalanche patterns into the topology of the network slowly changing it into a branched structure where loops are marginal., Scientific Reports, 6, ISSN:2045-2322

Aftershocks are the most striking evidence of earthquake interactions and the physical mechanisms at the origin of their occurrence are still intensively debated. Novel insights stem from recent results on the influence of the faulting style on the aftershock organisation in magnitude and time. Our study shows that the size of the aftershock zone depends on the fault geometry. We find that positive correlations among parameters controlling aftershock occurrence in time, energy and space are a stable feature of seismicity independently of magnitude range and geographic areas. We explain the ensemble of experimental findings by means of a description of the Earth Crust as an heterogeneous elastic medium coupled with a Maxwell viscoelastic asthenosphere. Our results show that heterogeneous stress distribution in an elastic layer combined with a coupling to a viscous flow are sufficient ingredients to describe the physics of aftershock triggering.

The brain exhibits a wide variety of spatiotemporal patterns of neuronal activity recorded using functional magnetic resonance imaging as the so-called blood-oxygenated-level–dependent (BOLD) signal. An active area of work includes efforts to best describe the plethora of these patterns evolving continuously in the brain. Here we explore the third-moment statistics of the brain BOLD signals in the resting state as a proxy to capture extreme BOLD events. We find that the brain signal exhibits typically nonzero skewness, with positive values for cortical regions and negative values for subcortical regions. Furthermore, the combined analysis of structural and functional connectivity demonstrates that relatively more connected regions exhibit activity with high negative skewness. Overall, these results highlight the relevance of recent results emphasizing that the spatiotemporal location of the relatively large-amplitude events in the BOLD time series contains relevant information to reproduce a number of features of the brain dynamics during resting state in health and disease. Fil: Amor, T. A.. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina Fil: Russo, R.. Università Degli Studi Di Napoli Federico Ii; Italia Fil: Diez, I.. Cruces University Hospital; España Fil: Bharath, P.. VA West Los Angeles Medical Center; Estados Unidos Fil: Zirovich, P.. VA West Los Angeles Medical Center; Estados Unidos Fil: Stramaglia, S.. Universita Degli Studi Di Bari; Italia. Basque Center for Applied Mathematics; España Fil: Cortes, J. M.. Cruces University Hospital; España. The Basque Foundation for Science; España. University of the Basque Country; España Fil: de Arcangelis, L.. Seconda Universita Degli Studi Di Napoli; Italia Fil: Chialvo, Dante Renato. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentina

A q-state frustrated Potts model is introduced which generalizes the Kasteleyn-Fortuin formalism to frustrated systems. For q = 2 the Ising spin is recovered. For q = 1 it gives the frustrated percolation model, which combines frustration and connectivity features and might be relevant to systems like gels of glasses. The solution on a decorated lattice shows that a line of critical temperatures T(p)(q) appears when frustration is introduced. T(p)(q) is the percolation temperature where the clusters used in the Swendsen and Wang dynamics diverge. The critical behaviour at T(p)(q) is found to be the same as the ferromagnetic q/2 state Potts model, implying the universality class of the ferromagnetic 1/2 state Potts model for frustrated percolation.

We study the BTW-height model of self-organized criticality on a square lattice with some long range connections giving to the lattice the character of small world network. We find that as function of the fraction $p$ of long ranged bonds the power law of the avalanche size and lifetime distribution changes following a crossover scaling law with crossover exponents 2/3 and 1 for size and lifetime respectively., 7 figures

Solar flares stem from the reconnection of twisted magnetic field lines in the solar photosphere. The energy and waiting time distributions of these events follow complex patterns that have been carefully considered in the past and that bear some resemblance with earthquakes and stockmarkets. Here we explore in detail the tangling motion of interacting flux tubes anchored in the plasma and the energy ejections resulting when they recombine. The mechanism for energy accumulation and release in the flow is reminiscent of self-organized criticality. From this model we suggest the origin for two important and widely studied properties of solar flare statistics, including the time-energy correlations. We first propose that the scale-free energy distribution of solar flares is largely due to the twist exerted by the vorticity of the turbulent photosphere. Second, the long-range temporal and time-energy correlations appear to arise from the tube-tube interactions. The agreement with satellite measurements is encouraging., 24 pages, 8 figures

This chapter introduces a minimal model for gelling systems and examines the dynamic behavior by means of numerical simulations. At the gelation transition, a viscous liquid transforms to an elastic disordered solid. This corresponds to the formation of a spanning structure that makes the system able to bear stress. In polymer systems, the structure formation is due to chemical bonding, producing a polymerization process. The gelling system typically displays critical power law behavior in the viscoelastic response and slow dynamics. The relaxation functions show, at long times, a stretched exponential decay, and at the gel point the relaxation process becomes critically slow. This suggests a unifying picture for gelation phenomena, connecting classical gelation and recent results on colloidal systems. By varying the model parameters, the slow dynamics present a crossover from the classical polymer gelation to dynamics more typical of colloidal systems, with a glassy regime that is interpreted in terms of effective clusters.

Spontaneous brain activity has been recently characterized by avalanche dynamics with critical features for systems in vitro and in vivo. In this contribution we present a review of experimental results on neuronal avalanches in cortex slices, together with numerical results from a neuronal model implementing several physiological properties of living neurons. Numerical data reproduce experimental results for avalanche statistics. The temporal organization of avalanches can be characterized by the distribution of waiting times between successive avalanches. Experimental measurements exhibit a non-monotonic behaviour, not usually found in other natural processes. Numerical simulations provide evidence that this behaviour is a consequence of the alternation between states of high and low activity, leading to a balance between excitation and inhibition controlled by a single parameter. During these periods both the single neuron state and the network excitability level, keeping memory of past activity, are tuned by homoeostatic mechanisms. Interestingly, the same homoeostatic balance is detected for neuronal activity at the scale of the whole brain. We finally review the learning abilities of this neuronal network. Learning occurs via plastic adaptation of synaptic strengths by a non-uniform negative feedback mechanism. The system is able to learn all the tested rules and the learning dynamics exhibits universal features as a function of the strength of plastic adaptation. Any rule could be learned provided that the plastic adaptation is sufficiently slow.

Ongoing brain activity results from the mutual interaction of hundred billions non-linear units and represents a significant part of the overall brain activity. Although its complex dynamics has been widely investigated, a large number of fundamental questions are still open, many of them concerning its temporal structure. Why does a certain population of neurons fires synchronously? Are these synchronized bursts following each other randomly or are they correlated according to some organizing principle? Far from addressing the fundamental problem of its functions, in the present article we focus on the problem of temporal correlations of ongoing cortical activity. We first overview the major features of its temporal structure and review recent experimental results, with particular emphasis on alternative approaches inspired in the theory of stochastic processes; then we introduce a neuronal network model inspired in self organized criticality and compare numerical results with experimental findings., The European Physical Journal Special Topics, 223 (11), ISSN:1951-6355, ISSN:1951-6401

We investigate the slow dynamics in gelling systems by means of MonteCarlo simulations on the cubic lattice of a minimal statistical mechanics model. By opportunely varying some model parameter we are able to describe a crossover from the chemical gelation behaviour to dynamics more typical of colloidal systems. The results suggest a novel connection linking classical gelation, as originally described by Flory, to more recent results on colloidal systems., 7 pages, 4 figures

Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behaviour. Avalanche activity can be modelled within the self-organized criticality framework, including threshold firing, refractory period and activity-dependent synaptic plasticity. The size and duration distributions confirm that the system acts in a critical state, whose scaling behaviour is very robust. Next, we discuss the temporal organization of neuronal avalanches. This is given by the alternation between states of high and low activity, named up and down states, leading to a balance between excitation and inhibition controlled by a single parameter. During these periods both the single neuron state and the network excitability level, keeping memory of past activity, are tuned by homeostatic mechanisms. Finally, we verify if a system with no characteristic response can ever learn in a controlled and reproducible way. Learning in the model occurs via plastic adaptation of synaptic strengths by a non-uniform negative feedback mechanism. Learning is a truly collective process and the learning dynamics exhibits universal features. Even complex rules can be learned provided that the plastic adaptation is sufficiently slow.

An increase in the number of smaller magnitude events, retrospectively named foreshocks, is often observed before large earthquakes. We show that the linear density probability of earthquakes occurring before and after small or intermediate mainshocks displays a symmetrical behavior, indicating that the size of the area fractured during the mainshock is encoded in the foreshock spatial organization. This observation can be used to discriminate spatial clustering due to foreshocks from the one induced by aftershocks and is implemented in an alarm-based model to forecast m > 6 earthquakes. A retrospective study of the last 19 years Southern California catalog shows that the daily occurrence probability presents isolated peaks closely located in time and space to the epicenters of five of the six m > 6 earthquakes. We find daily probabilities as high as 25% (in cells of size 0.04 × 0.04deg 2), with significant probability gains with respect to standard models. © 2012 Macmillan Publishers Limited. All rights reserved.

Neuronal avalanches, measured in vitro and in vivo, exhibit a robust critical behavior. Their temporal organization hides the presence of correlations. Here we present experimental measurements of the waiting time distribution between successive avalanches in the rat cortex in vitro. This exhibits a nonmonotonic behavior not usually found in other natural processes. Numerical simulations provide evidence that this behavior is a consequence of the alternation between states of high and low activity, named up and down states, leading to a balance between excitation and inhibition controlled by a single parameter. During these periods, both the single neuron state and the network excitability level, keeping memory of past activity, are tuned by homeostatic mechanisms.

Stochastic branching models provide a good description of some aspects of the temporal organization in seismicity. Generally, they assume that magnitudes are independent of history, as in the widely used Epidemic Type Aftershock Sequence (ETAS) model. Here, we consider a recent epidemic-like model where time-magnitude and magnitude-magnitude correlations are introduced via a dynamical scaling (DS) hypothesis, namely, the magnitude difference between earthquakes fixes the time scale for correlations. We also consider a variation of the ETAS model where the c parameter of the Omori law is not fixed but depends on the parent magnitude. We develop a novel procedure to maximize the log likelihood of the different models. This method is based on a Monte Carlo sampling in the parameter space with a variable step size during the evolution to converge to the given accuracy. The log likelihood indicates that the DS model provides the best fit for the major California sequences and the whole catalog, setting as lower magnitude thresholds M(c) >= 3.5. For M(c) = 3, the best fit is obtained by a model with c depending on both the parent magnitude and goes into M(c) as in the generalized Omori law. The better performance of the DS model with respect to the ETAS model is attributed to correlations in magnitudes.

We investigate a recently introduced seismic fault model where granular particles simulate fault gouge, performing a detailed analysis of the size distribution of slipping events. We show that the model reproduces the Gutenberg-Richter law characterising real seismic occurrence, independently of model parameters. The effect of system size, elastic constant of the external drive, thickness of the gouge, frictional and mechanical properties of the particles are considered. The distribution is also characterised by a bump at large slips, whose characteristic size is solely controlled by the ratio of the drive elastic constant and the system size. Large slips become less probable in the absence of fault gouge and tend to disappear for stiff drives. Copyright (C) EPLA, 2011

We use the method of damage spreading to study the time, t , taken for a spin at a distance r to be damaged for the first time in Ising models with heat-bath dynamics. We report time-dependent scaling exponents, d t ≃ 2.0 (1D), 2.52 (2D), 2.26 (3D) and (2.0) (4D), if we assume that t ∾ r dt . We also analyze our data assuming various forms of logarithmic corrections and we find that d t ∾ 2.25 or less (2D) and ∾2.0 (3D). We argue that it is extremely plausible that d t is equal to z , the dynamic critical exponent, and thus our estimate of z , in two dimensions is higher than the “consensus” value of 2.14, but we find good agreement in one, three and four dimensions with the exact and expected values.

The interevent time distribution characterizes the temporal occurrence in seismic catalogs. Universal scaling properties of this distribution have been evidenced for entire catalogs and seismic sequences. Recently, these universal features have been questioned and some criticisms have been raised. We investigate the existence of universal scaling properties by analyzing a Californian catalog and by means of numerical simulations of an epidemic-type model. We show that the interevent time distribution exhibits a universal behavior over the entire temporal range if four characteristic times are taken into account. The above analysis allows us to identify the scaling form leading to universal behavior and explains the observed deviations. Furthermore, it provides a tool to identify the dependence on the mainshock magnitude of the c parameter that fixes the onset of the power law decay in the Omori law., 3 figures

Context. The existence of time-energy correlations in flare occurrence is still an open and much debated problem. Aims. This study addresses the question whether statistically significant correlations are present between energies of successive flares as well as energies and waiting times. Methods. We analyze the GOES catalog with a statistical approach based on the comparison of the real catalog with a reshuffled one where energies are decorrelated. This analysis reduces the effect of background activity and is able to reveal the role of obscuration. Results. We show the existence of non-trivial correlations between waiting times and energies, as well as between energies of subsequent flares. More precisely, we find that flares close in time tend to have the second event with large energy. Moreover, after large flares the flaring rate significantly increases, together with the probability of other large flares. Conclusions. Results suggest that correlations between energies and waiting times are a physical property and not an effect of obscuration. These findings could give important information on the mechanisms for energy storage and release in the solar corona.

Clustering in time and space is a widely accepted feature of seismicity. Much more questionable is the existence of magnitude correlations. The standard approach to time-dependent seismic hazard generally assumes that magnitudes are independent and therefore, in principle, the next earthquake magnitude is unpredictable. We will show that an earthquake magnitude depends on previous ones: earthquakes occur with higher probability close, not only in time and space, but also in magnitude to previous events. Moreover, the magnitude difference fixes the characteristic temporal and spatial scale controlling correlations between events. As a consequence, the next earthquake tends to have a magnitude similar but smaller than the previous one. We will discuss a dynamical scaling relation between energy, time and space distance that reproduces the main statistical properties of experimental catalogs.

Networks of living neurons represent one of the most fascinating systems of modern biology. If the physical and chemical mechanisms at the basis of the functioning of a single neuron are quite well understood, the collective behavior of a system of many neurons is an extremely intriguing subject. Crucial ingredient of this complex behavior is the plasticity property of the network, namely the capacity to adapt and evolve depending on the level of activity. This plastic ability is believed, nowadays, to be at the basis of learning and memory in real brains. This fundamental problem in neurobiology has recently shown a number of features in common to other complex systems. These features mainly concern the morphology of the network, namely the spatial organization of the established connections, and a novel kind of neuronal activity. Experimental data have, in fact, shown that electrical information propagates in a cortex slice via an avalanche mode. Both features have been found in other problems in the context of the physics of complex systems and successful models have been developed to describe their behavior. In this contribution, we apply a statistical mechanical model to describe the complex activity in a neuronal network. The network is chosen to have a number of connections in long range, as found for neurons in vitro. The model implements the main physiological properties of living neurons and is able to reproduce recent experimental results. The numerical power spectra for electrical activity reproduces also the power law behavior measured in an EEG of man resting with the eyes closed.

[1] We propose a fast method able to discriminate between Poissonian independent earthquakes and aftershocks. The method is based on the evaluation of the variability coefficient, defined as the ratio between the standard deviation and the average value of the interoccurrence time between two successive earthquakes. We apply this technique to the California and a properly constructed synthetic catalogue in order to estimate the level of background seismicity and identify seismic sequences. We then investigate the spatiotemporal organization of aftershocks focusing on the distributions of interevent times and interevent distances between two successive events. We find evidence for the existence of a characteristic spatial length scale, related to the size of the aftershock zone, whereas no typical timescale is detected.

We investigate the spatial distribution of aftershocks and we find that aftershock linear density exhibits a maximum, that depends on the mainshock magnitude, followed by a power law decay. The exponent controlling the asymptotic decay and the fractal dimensionality of epicenters clearly indicate triggering by static stress. The non monotonic behavior of the linear density and its dependence on the mainshock magnitude can be interpreted in terms of diffusion of static stress. This is supported by the power law growth with exponent $H\simeq 0.5$ of the average main-aftershock distance. Implementing static stress diffusion within a stochastic model for aftershock occurrence we are able to reproduce aftershock linear density spatial decay, its dependence on the mainshock magnitude and its evolution in time., Comment: 4 figures

Earthquakes are phenomena of great complexity, however some simple general laws govern the statistics of their occurrence. Some of these most important laws exhibit scale invariance, as the Gutenberg- Richter law and the Omori law. The origin of these scaling behaviours is not yet fully understood and a natural fondamental question concerns the existence of these features also in other complex phenomena. A direct inspection of experimental catalogues has shown that the stochastic processes underlying solar flare and earthquake occurrence have universal properties. Another intensively debated question is the ex- istence of correlations between magnitudes of subsequent earthquakes. Our recent analysis of the Southern California Catalogue has shown that non-zero magnitude correlations exist. A branching model based on a dynamical scaling hypothesis, relating magnitude to time, reproduces the hierarchical organization in time and magnitude of events and the observed magnitude correlations.

A crucial point in the debate on the feasibility of earthquake predictions is the dependence of an earthquake magnitude from past seismicity. Indeed, while clustering in time and space is widely accepted, much more questionable is the existence of magnitude correlations. The standard approach generally assumes that magnitudes are independent and therefore in principle unpredictable. Here we show the existence of clustering in magnitude: earthquakes occur with higher probability close in time, space, and magnitude to previous events. More precisely, the next earthquake tends to have a magnitude similar but smaller than the previous one. A dynamical scaling relation between magnitude, time, and space distances reproduces the complex pattern of magnitude, spatial, and temporal correlations observed in experimental seismic catalogs.

Experimental results have shown that the kinetics of bond formation in chemical crosslinking of gelatin solutions is strongly affected not only by gelatin and reactant concentrations but also by the solution pH. We present an extended numerical investigation of the phase diagram and of the kinetics of bond formation as a function of the pH, via Monte Carlo simulations of a lattice model for gelatin chains and reactant agent in solution. We find a reentrant phase diagram, namely gelation can be hindered either by loop formation, at low reactant concentrations, or by saturation of active sites of the chains via formation of single bonds with crosslinkers, at high reactant concentrations. The ratio of the characteristic times for the formation of the first and of the second bond between the crosslinker and an active site of a chain is found to depend on the reactant reactivity, in good agreement with experimental data., Comment: 8 pages, 8 figures

Through "damage spreading" numerical simulations, we study the Ising spin glass in three dimensions with ±J near-neighbour interactions. The results are compared to other simulation data; we conclude that the damage spreading method can provide good estimates of the transition temperatures in this type of system. A discussion is given of phase transitions in spin glasses in terms of the geometry of phase space.

The 3D ± J Ising spin glass has been shown in massive simulations by Ogielski to have strongly non-exponential relaxation between T g and the ferromagnetic ordering temperature T G . “Damage spreading” numerical data by Derrida and collaborators have indicated anomalous behaviour in a similar temperature range. The results from the two different types of simulation are compared and discussed in terms of the geometry of the phase space of the system; conclusions are drawn on the phase transitions in spin glasses.