Universal relaxation function in nonextensive systems

We have derived the dipolar relaxation function for a cluster model whose volume distribution was obtained from the generalized maximum Tsallis nonextensive entropy principle. The power law exponents of the relaxation function are simply related to a global fractal parameter $\alpha$ and for large time to the entropy nonextensivity parameter $q$. For intermediate times the relaxation follows a stretched exponential behavior. The asymptotic power law behaviors both in the time and the frequency domains coincide with those of the Weron generalized dielectric function derived from an extension of the Levy central limit theorem. They are in full agreement with the Jonscher universality principle. Moreover our model gives a physical interpretation of the mathematical parameters of the Weron stochastic theory and opens new paths to understand the ubiquity of self-similarity and power laws in the relaxation of large classes of materials in terms of their fractal and nonextensive properties.Comment: Two figures. Submitted for publicatio

Self-organized criticality and directed percolation

A sandpile model with stochastic toppling rule is studied. The control parameters and the phase diagram are determined through a MF approach, the subcritical and critical regions are analyzed. The model is found to have some similarities with directed percolation, but the existence of different boundary conditions and conservation law leads to a different universality class, where the critical state is extended to a line segment due to self-organization. These results are supported with numerical simulations in one dimension. The present model constitute a simple model which capture the essential difference between ordinary nonequilibrium critical phenomena, like DP, and self-organized criticality.Comment: 9 pages, 10 eps figs, revtex, submitted to J. Phys.

Phase Transition in Liquid Drop Fragmentation

A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software enables us to automatically count and size up to tens of thousands of tiny droplets with a smallest detectable volume of approximately 0.02 nl. Upon varying the gas pressure, a critical value is found where the size-distribution becomes a pure power-law, a fact that is indicative of a phase transition. Away from this transition, the resulting size distributions are well described by Fisher's model at coexistence. It is found that the sign of the surface correction term changes sign, and the apparent power-law exponent tau has a steep minimum, at criticality, as previously reported in Nuclear Multifragmentation studies [1,2]. We argue that the observed transition is not percolative, and introduce the concept of dominance in order to characterize it. The dominance probability is found to go to zero sharply at the transition. Simple arguments suggest that the correlation length exponent is nu=1/2. The sizes of the largest and average fragments, on the other hand, do not go to zero but behave in a way that appears to be consistent with recent predictions of Ashurst and Holian [3,4].Comment: 10 pages, 11 figures. LaTeX (revtex4) with psfig/epsfi