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At least 451 records · Page 25Linked to original sources
arXiv1997

Random Neighbor Theory of the Olami-Feder-Christensen Earthquake Model

We derive the exact equations of motion for the random neighbor version of the Olami-Feder-Christensen earthquake model in the infinite-size limit. We solve them numerically, and compare with simulations of the model for large numbers of sites. We find perfect agreement. But we do not find any scaling or phase transitions, except in the conservative limit. This is in contradiction to claims by Lise & Jensen (Phys. Rev. Lett. 76, 2326 (1996)) based on approximate solutions of the same model. It indicates again that scaling in the Olami-Feder-Christensen model is only due to partial synchronization driven by spatial inhomogeneities. Finally, we point out that our method can be used also for other SOC models, and treat in detail the random neighbor version of the Feder-Feder model.

adap-org↗
arXiv1997

Self-Organized Criticality Driven by Deterministic Rules

We have investigated the essential ingredients allowing a system to show Self Organized Criticality (SOC) in its collective behavior. Using the Bak-Sneppen model of biological evolution as our paradigm, we show that the random microscopic rules of update can be effectively substituted with a chaotic map without changing the universality class. Using periodic maps SOC is preserved, but in a different universality class, as long as the spectrum of frequencies is broad enough.

cond-mat↗
arXiv1997

Aging Exponents in Self-Organized Criticality

In a recent Letter [Phys. Rev. Lett. 79, 889 (1997) and cond-mat/9702054] we have demonstrated that the avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical results for temporal correlations show a broad distribution with two distinct regimes separated by a time scale which is related to the age of the avalanche. This dynamical breaking of time-translational invariance results in a new critical exponent, $r$. Here we present results for $r$ from extensive numerical simulations of self-organized critical models in $d=1$ and 2. We find $r_{d=1}=0.45\pm 0.05$ and $r_{d=2}=0.23\pm 0.05$ for the Bak-Sneppen model, and our results suggest $r=1/4$ for the analytically tractable multi-trade model in both dimensions.

cond-mat.stat-mech↗
arXiv1997

Stationary Velocity Distributions in Traffic Flows

We introduce a traffic flow model that incorporates clustering and passing. We obtain analytically the steady state characteristics of the flow from a Boltzmann-like equation. A single dimensionless parameter, R=c_0v_0t_0 with c_0 the concentration, v_0 the velocity range, and 1/t_0 the passing rate, determines the nature of the steady state. When R<<1, uninterrupted flow with single cars occurs. When R>>1, large clusters with average mass ~ R^α form, and the flux is J ~ R^{-γ}. The initial distribution of slow cars governs the statistics. When P_0(v) ~ v^μ as v->0, the scaling exponents are γ=1/(μ+2), α=1/2 when μ>0, and α=(μ+1)/(μ+2) when μ<0.

cond-mat.stat-mech↗
arXiv1997

A Simple Model of Evolution with Variable System Size

A simple model of biological extinction with variable system size is presented that exhibits a power-law distribution of extinction event sizes. The model is a generalization of a model recently introduced by Newman (Proc. R. Soc. Lond. B265, 1605 (1996). Both analytical and numerical analysis show that the exponent of the power-law distribution depends only marginally on the growth rate $g$ at which new species enter the system and is equal to the one of the original model in the limit $g\to\infty$. A critical growth rate $g_c$ can be found below which the system dies out. Under these model assumptions stable ecosystems can only exist if the regrowth of species is sufficiently fast.

physics.bio-ph↗
arXiv1997

Towards a Simple Model of Compressible Alfvenic Turbulence

A simple model collisionless, dissipative, compressible MHD (Alfvenic) turbulence in a magnetized system is investigated. In contrast to more familiar paradigms of turbulence, dissipation arises from Landau damping, enters via nonlinearity, and is distributed over all scales. The theory predicts that two different regimes or phases of turbulence are possible, depending on the ratio of steepening to damping coefficient (m_1/m_2). For strong damping (|m_1/m_2|<1), a regime of smooth, hydrodynamic turbulence is predicted. For |m_1/m_2|>1, steady state turbulence does not exist in the hydrodynamic limit. Rather, spikey, small scale structure is predicted.

physics.plasm-ph↗
arXiv1997

Effect of the Output of the System in Signal Detection

We analyze the consequences that the choice of the output of the system has in the efficiency of signal detection. It is shown that the signal and the signal-to-noise ratio (SNR), used to characterize the phenomenon of stochastic resonance, strongly depend on the form of the output. In particular, the SNR may be enhanced for an adequate output.

cond-mat↗
arXiv1997

Avalanches and Waves in the Abelian Sandpile Model

We numerically study avalanches in the two dimensional Abelian sandpile model in terms of a sequence of waves of toppling events. Priezzhev et al [PRL 76, 2093 (1996)] have recently proposed exact results for the critical exponents in this model based on the existence of a proposed scaling relation for the difference in sizes of subsequent waves, $Δs =s_{k}- s_{k+1}$, where the size of the previous wave $s_{k}$ was considered to be almost always an upper bound for the size of the next wave $s_{k+1}$. Here we show that the significant contribution to $Δs$ comes from waves that violate the bound; the average $<Δs(s_{k})>$ is actually negative and diverges with the system size, contradicting the proposed solution.

cond-mat.stat-mech↗
arXiv1997

Sandpile Model with Activity Inhibition

A new sandpile model is studied in which bonds of the system are inhibited for activity after a certain number of transmission of grains. This condition impels an unstable sand column to distribute grains only to those neighbours which have toppled less than m times. In this non-Abelian model grains effectively move faster than the ordinary diffusion (super-diffusion). A novel system size dependent cross-over from Abelian sandpile behaviour to a new critical behaviour is observed for all values of the parameter m.

cond-mat.stat-mech↗
arXiv1997

Self-Organized Criticality with Complex Scaling Exponents in the Train Model

The train model which is a variant of the Burridge-Knopoff earthquake model is investigated for a velocity-strengthening friction law. It shows self-organized criticality with complex scaling exponents. That is, the probability density function of the avalanche strength is a power law times a log-periodic function. Exact results (scaling exponent: $3/2+2πi/\ln 4$) are found for a nonlocal cellular automaton which approximates the overdamped train model. Further the influence of random static friction is discussed.

adap-org↗
arXiv1997

Jamming transition in a cellular automaton model for traffic flow

The cellular automaton model for traffic flow exhibits a jamming transition from a free-flow phase to a congested phase. In the deterministic case this transition corresponds to a critical point with diverging correlation length. In the presence of noise, however, no consistent picture has emerged up to now. We present data from numerical simulations which suggest the absence of critical behavior. The transition of the deterministic case is smeared out and one only observes the remnants of the critical point.

cond-mat.stat-mech↗
arXiv1997

Classifying Rational Densities Using Two One-Dimensional Cellular Automata

Given a (finite) string of zeros and ones, we report a way to determine if the number of ones is less than, greater than, or equal to a prescribed number by applying two sets of cellular automaton rules in succession. Thus, we solve the general density classification problem using cellular automaton.

adap-org↗
arXiv1997

Early-time critical dynamics of lattices of coupled chaotic maps

The early-time critical dynamics of continuous, Ising-like phase transitions is studied numerically for two-dimensional lattices of coupled chaotic maps. Emphasis is laid on obtaining accurate estimates of the dynamic critical exponents θ' and z. The critical points of five different models are investigated, varying the mode of update, the coupling, and the local map. Our results suggest that the nature of update is a relevant parameter for dynamic universality classes of extended dynamical systems, generalizing results obtained previously for the static properties. They also indicate that the universality observed for the static properties of Ising-like transitions of synchronously-updated systems does not hold for their dynamic critical properties.

adap-org↗
arXiv1997

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.

cond-mat.stat-mech↗
arXiv1999

Genetic algorithm dynamics on a rugged landscape

The genetic algorithm is an optimization procedure motivated by biological evolution and is successfully applied to optimization problems in different areas. A statistical mechanics model for its dynamics is proposed based on the parent-child fitness correlation of the genetic operators, making it applicable to general fitness landscapes. It is compared to a recent model based on a maximum entropy ansatz. Finally it is applied to modeling the dynamics of a genetic algorithm on the rugged fitness landscape of the NK model.

cond-mat.stat-mech↗
arXiv1998

Statistics of extinction and survival in Lotka-Volterra systems

We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a semiquantitative analysis of the phase-space structure, and extensive numerical simulations are performed to study the statistics of the extinctions. We find that the number of surviving species depends strongly on the statistical properties of the interaction matrix, and that the probability of survival is weakly correlated to specific initial conditions.

adap-org↗