Fracture and second-order phase transitions

Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring at the collapse of the system. The model is analyzed using a probabilistic approach suited to smooth fluctuations. The branching ratio shows a behavior analogous to the magnetization in known magnetic systems with 2nd-order phase transitions. We obtain a universal critical exponent $\beta\approx 0.5$ independent of the probability distribution used to assign the strengths of individual fibers.Comment: 5 pages, 5 figures, APS style, submitted for publicatio

Modified Renormalization Strategy for Sandpile Models

Following the Renormalization Group scheme recently developed by Pietronero {\it et al}, we introduce a simplifying strategy for the renormalization of the relaxation dynamics of sandpile models. In our scheme, five sub-cells at a generic scale $b$ form the renormalized cell at the next larger scale. Now the fixed point has a unique nonzero dynamical component that allows for a great simplification in the computation of the critical exponent $z$. The values obtained are in good agreement with both numerical and theoretical results previously reported.Comment: APS style, 9 pages and 3 figures. To be published in Phys. Rev.

A Minimalist Model of Characteristic Earthquakes

In a spirit akin to the sandpile model of self-organized criticality, we present a simple statistical model of the cellular-automaton type which produces an avalanche spectrum similar to the characteristic-earthquake behavior of some seismic faults. This model, that has no parameter, is amenable to an algebraic description as a Markov Chain. This possibility illuminates some important results, obtained by Monte Carlo simulations, such as the earthquake size-frequency relation and the recurrence time of the characteristic earthquake.Comment: 9 pages, 4 figure

Aging in coherent noise models and natural time

Event correlation between aftershocks in the coherent noise model is studied by making use of natural time, which has recently been introduced in complex time-series analysis. It is found that the aging phenomenon and the associated scaling property discovered in the observed seismic data are well reproduced by the model. It is also found that the scaling function is given by the $q$-exponential function appearing in nonextensive statistical mechanics, showing power-law decay of event correlation in natural time.Comment: 4 pages and 5 figure

O uso de poleiros para a atração de aves frugívoras em áreas degradadas da Floresta Estacional Semidecidual.

Organizado por Patricia Póvoa de Mattos, Celso Garcia Auer, Rejane Stumpf Sberze, Katia Regina Pichelli e Paulo César Botosso