arXiv subjects

Alvaro Corral

Publications and source records attributed to Alvaro Corral.

50 records · Page 3Linked to original sources

arXiv2004

Comment on "Do Earthquakes Exhibit Self-Organized Criticality?"

It is shown that earthquakes do not know how large they will become, at least from the information collected at seismic catalogs. In other words, the magnitude is independent on previous magnitudes as well as on the waiting time between previous earthquakes. In contrast, the time to the next event does depend on the magnitude. Also it is argued that SOC systems do not necessarily shown a Poisson-type behavior in time, and SOC does not exclude the possibility of some degree of prediction.

cond-mat.other↗

arXiv2004

Correlations and invariance of seismicity under renormalization-group transformations

The effect of transformations analogous to those of the real-space renormalization group are analyzed for the temporal occurrence of earthquakes. The distribution of recurrence times turns out to be invariant under such transformations, for which the role of the correlations between the magnitudes and the recurrence times are fundamental. A general form for the distribution is derived imposing only the self-similarity of the process, which also yields a scaling relation between the Gutenberg-Richter b-value, the exponent characterizing the correlations, and the recurrence-time exponent. This approach puts the study of the structure of seismicity in the context of critical phenomena.

cond-mat.stat-mech↗

arXiv2004

Universal local versus unified global scaling laws in the statistics of seismicity

The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the rescaled recurrence-time probability densities show a power-law behavior for long times, with a universal exponent about (minus) 2.2. Another decreasing power law governs short times, but with an exponent that may change from one area to another. This is in contrast with a spatially independent, time-homogenized version of Bak et al's procedure, which seems to present a universal scaling behavior.

cond-mat.other↗

arXiv2003

Time-Decreasing Hazard and Increasing Time until the Next Earthquake

Contrary to common belief, as the time since the last earthquake in a certain region increases, the risk of occurrence of another earthquake diminishes. As a consequence, the expected waiting time to the next event increases with the elapsed time, in other words, the event moves away to the future faster than we move. This paradoxical phenomenon is found in regions as diverse (from a tectonic point of view) as California, Japan, New Zealand, Spain or the British Islands, as well as in worldwide scales. This behaviour shows a surprising regularity, since in all the cases it is well described by the same universal scaling functions. This universality suggests the existence of a common simple physical mechanism in the earthquake generation process.

cond-mat↗

arXiv2003

Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes

Scaling analysis reveals striking regularities in earthquake occurrence. The time between any one earthquake and that following it is random, but it is described by the same universal-probability distribution for any spatial region and magnitude range considered. When time is expressed in rescaled units, set by the averaged seismic activity, the self-similar nature of the process becomes apparent. The form of the probability distribution reveals that earthquakes tend to cluster in time, beyond the duration of aftershock sequences. Furthermore, if aftershock sequences are analysed in an analogous way, yet taking into account the fact that seismic activity is not constant but decays in time, the same universal distribution is found for the rescaled time between events.

cond-mat↗

arXiv2003

Calculation of the transition matrix and of the occupation probabilities for the states of the Oslo sandpile model

The Oslo sandpile model, or if one wants to be precise, ricepile model, is a cellular automaton designed to model experiments on granular piles displaying self-organized criticality. We present an analytic treatment that allows the calculation of the transition probabilities between the different configurations of the system; from here, using the theory of Markov chains, we can obtain the stationary occupation distribution, which tell us that the phase space is occupied with probabilities that vary in many orders of magnitude from one state to another. Our results show how the complexity of this simple model is built as the number of elements increases, and allows, for a given system size, the exact calculation of the avalanche size distribution and other properties related to the profile of the pile.

cond-mat.stat-mech↗

arXiv2003

Local Distributions and Rate Fluctuations in a Unified Scaling Law for Earthquakes

A recently proposed unified scaling law for interoccurrence times of earthquakes [P. Bak et al., Phys. Rev. Lett. {\bf 88}, 178501 (2002)] is analyzed, both theoretically and with data from Southern California. We decompose the corresponding probability density into local-instantaneous distributions, which scale with the rate of earthquake occurrence. The fluctuations of the rate, characterizing the non-stationarity of the process, show a doubly power-law distribution and are fundamental to determine the overall behavior, described by a double power law as well.

cond-mat↗

arXiv2002

Anomalous Transport in Conical Granular Piles

Experiments on 2+1-dimensional piles of elongated particles are performed. Comparison with previous experiments in 1+1 dimensions shows that the addition of one extra dimension to the dynamics changes completely the avalanche properties, appearing a characteristic avalanche size. Nevertheless, the time single grains need to cross the whole pile varies smoothly between several orders of magnitude, from a few seconds to more than 100 hours. This behavior is described by a power-law distribution, signaling the existence of scale invariance in the transport process.

cond-mat↗

arXiv2000

Self-organized Networks of Competing Boolean Agents

A model of Boolean agents competing in a market is presented where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority. After a long time interval, the poorest player's strategy is changed randomly, and the process is repeated. Eventually the network evolves to a stationary but intermittent state where random mutation of the worst strategy can change the behavior of the entire network, often causing a switch in the dynamics between attractors of vastly different lengths.

cond-mat.stat-mech↗

arXiv1999

Avalanche Merging and Continuous Flow in a Sandpile Model

A dynamical transition separating intermittent and continuous flow is observed in a sandpile model, with scaling functions relating the transport behaviors between both regimes. The width of the active zone diverges with system size in the avalanche regime but becomes very narrow for continuous flow. The change of the mean slope, Delta z, on increasing the driving rate, r, obeys Delta z ~ r^{1/theta}. It has nontrivial scaling behavior in the continuous flow phase with an exponent theta given, paradoxically, only in terms of exponents characterizing the avalanches theta = (1+z-D)/(3-D).

cond-mat.stat-mech↗

arXiv1997

Long-Tailed Trapping Times and Levy Flights in a Self-Organized Critical Granular System

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lévy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

cond-mat↗

arXiv1997

Self-Organized Criticality Induced by Diversity

We have studied the collective behavior of a population of integrate-and-fire oscillators. We show that diversity, introduced in terms of a random distribution of natural periods, is the mechanism that permits to observe self-organized criticality (SOC) in the long time regime. As diversity increases the system undergoes several transitions from a supercritical regime to a subcritical one, crossing the SOC region. Although there are resemblances with percolation, we give proofs that criticality takes place for a wide range of values of the control parameter instead of a single value.

cond-mat↗

arXiv1996

Symmetries and Fixed Point Stability of Stochastic Differential Equations Modeling Self-Organized Criticality

A stochastic nonlinear partial differential equation is built for two different models exhibiting self-organized criticality, the Bak, Tang, and Wiesenfeld (BTW) sandpile model and the Zhang's model. The dynamic renormalization group (DRG) enables to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

cond-mat↗

arXiv1995

On Synchronization in a Lattice Model of Pulse-Coupled Oscillators

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that ensures, in a general context, the existence of a fully synchronized regime. This condition turns out to be the same than the obtained for the globally coupled population. When the condition is not completely satisfied we find different spatial structures. This also gives some hints about self-organized criticality.

cond-mat↗