arXiv subjects

Albert Diaz-Guilera

Publications and source records attributed to Albert Diaz-Guilera.

43 records · Page 3Linked to original sources

arXiv1998

Dynamical properties of the Zhang model of Self-Organized Criticality

Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for $d=2,3$ with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored and their critical exponents computed. Among other results, it is shown that the three dimensional exponents do not coincide with the Bak, Tang, and Wiesenfeld (abelian) model and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide as it is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from Renormalization Group arguments is also briefly addressed.

cond-mat.stat-mech↗

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↗

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↗

arXiv1994

Dynamic Renormalization Group Approach to Self-Organized Critical Phenomena

Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that they both belong to the same universality class, in agreement with computer simulations. The asymptotic values of the critical exponents are estimated up to one loop order from a systematic expansion of a nonlinear equation in the number of coupling constants.

cond-mat↗

arXiv1993

Nonlinear Stochastic Differential Equations and Self-Organized Criticality

Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a hydrodynamic description. We study two models with different noise correlations which make all the nonlinear contribution to be equally relevant below the upper critical dimension. The asymptotic values of the critical exponents are estimated from a systematic expansion in the number of coupling constants by means of the dynamic renormalization group.

cond-mat↗