Different hierarchy of avalanches observed in the Bak-Sneppen evolution model

We introduce a new quantity, average fitness, into the Bak-Sneppen evolution model. Through the new quantity, a different hierarchy of avalanches is observed. The gap equation, in terms of the average fitness, is presented to describe the self-organization of the model. It is found that the critical value of the average fitness can be exactly obtained. Based on the simulations, two critical exponents, avalanche distribution and avalanche dimension, of the new avalanches are given.Comment: 5 pages, 3 figure

Unified Scaling Law for Earthquakes

We show that the distribution of waiting times between earthquakes occurring in California obeys a simple unified scaling law valid from tens of seconds to tens of years, see Eq. (1) and Fig. 4. The short time clustering, commonly referred to as aftershocks, is nothing but the short time limit of the general hierarchical properties of earthquakes. There is no unique operational way of distinguishing between main shocks and aftershocks. In the unified law, the Gutenberg-Richter b-value, the exponent -1 of the Omori law for aftershocks, and the fractal dimension d_f of earthquakes appear as critical indices.Comment: 4 pages, 4 figure

Spatial-temporal correlations in the process to self-organized criticality

A new type of spatial-temporal correlation in the process approaching to the self-organized criticality is investigated for the two simple models for biological evolution. The change behaviors of the position with minimum barrier are shown to be quantitatively different in the two models. Different results of the correlation are given for the two models. We argue that the correlation can be used, together with the power-law distributions, as criteria for self-organized criticality.Comment: 3 pages in RevTeX, 3 eps figure

Chaos in Sandpile Models

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Simulation results show that "weak chaos" exponent may be one of the characteristic exponents of the attractor of \textit{deterministic} models. We have shown that the (abelian) BTW sandpile model and the (non abelian) Zhang model posses different "weak chaos" exponents, so they may belong to different universality classes. We have also shown that \textit{stochasticity} destroys "weak chaos" exponents' effectiveness so it slows down the divergence of nearby configurations. Finally we show that getting off the critical point destroys this behavior of deterministic models.Comment: 5 pages, 6 figure

Self-organization of structures and networks from merging and small-scale fluctuations

We discuss merging-and-creation as a self-organizing process for scale-free topologies in networks. Three power-law classes characterized by the power-law exponents 3/2, 2 and 5/2 are identified and the process is generalized to networks. In the network context the merging can be viewed as a consequence of optimization related to more efficient signaling.Comment: Physica A: Statistical Mechanics and its Applications, In Pres

Intrinsic Variability and Field Statistics for the Vela Pulsar: 3. Two-Component Fits and Detailed Assessment of Stochastic Growth Theory

The variability of the Vela pulsar (PSR B0833-45) corresponds to well-defined field statistics that vary with pulsar phase, ranging from Gaussian intensity statistics off-pulse to approximately power-law statistics in a transition region and then lognormal statistics on-pulse, excluding giant micropulses. These data are analyzed here in terms of two superposed wave populations, using a new calculation for the amplitude statistics of two vectorially-combined transverse fields. Detailed analyses show that the approximately power-law and lognormal distributions observed are fitted well at essentially all on-pulse phases by Gaussian-lognormal and double-lognormal combinations, respectively. These good fits, plus the smooth but significant variations in fit parameters across the source, provide strong evidence that the approximately power-law statistics observed in the transition region are not intrinsic. Instead, the data are consistent with normal pulsar emission having lognormal statistics at all phases. This is consistent with generation in an inhomogeneous source obeying stochastic growth theory (SGT) and with the emission mechanism being purely linear (either direct or indirect). A nonlinear mechanism is viable only if it produces lognormal statistics when suitably ensemble-averaged. Variations in the SGT fit parameters with phase imply that the radiation is relatively more variable near the pulse edges than near the center, as found in earlier work. In contrast, Vela's giant micropulses come from a very restricted phase range and have power-law statistics with indices ($6.7 \pm 0.6$) not inconsistent with nonlinear wave collapse. These results imply that normal pulses have a different source and generation mechanism than giant micropulses, as suggested previously on other grounds.Comment: 10 pages and 14 figures. Accepted by Monthly Notices of the Royal Astronomical Society in April 200

Scaling of impact fragmentation near the critical point

We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition disagreed with that of percolation. However, the weighted mean mass of the fragments could be scaled using the pseudo-control parameter multiplicity. The data for highly fragmented samples included a cumulative fragment mass distribution that clearly obeyed a power-law. The exponent of this power-law was 0.5 and it was independent of sample size. The fragment mass distributions in this regime seemed to collapse into a unified scaling function using weighted mean fragment mass scaling. We also examined the behavior of higher order moments of the fragment mass distributions, and obtained multi-scaling exponents that agreed with those of the simple biased cascade model.Comment: 6 pages, 6 figure

Precise toppling balance, quenched disorder, and universality for sandpiles

A single sandpile model with quenched random toppling matrices captures the crucial features of different models of self-organized criticality. With symmetric matrices avalanche statistics falls in the multiscaling BTW universality class. In the asymmetric case the simple scaling of the Manna model is observed. The presence or absence of a precise toppling balance between the amount of sand released by a toppling site and the total quantity the same site receives when all its neighbors topple once determines the appropriate universality class.Comment: 5 Revtex pages, 4 figure

Critical States in a Dissipative Sandpile Model

A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is mean-field like. We discuss the role of infinite avalanches of dissipative models in periodic systems in determining the critical behaviour of same models in open systems.Comment: 4 pages (Revtex), 5 ps figures (included

A perturbative approach to the Bak-Sneppen Model

We study the Bak-Sneppen model in the probabilistic framework of the Run Time Statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing Self-Organized Criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a non-trivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in {\em avalanches} of activity power law distributed. In this letter we use the RTS approach to compute the value of $x_c$, the value of the avalanche exponent $\tau$ and the asymptotic distribution of minimal fitnesses.Comment: 4 pages, 3 figures, to be published on Physical Review Letter