arXiv subjects
Publications and source records attributed to Oscar Sotolongo-Costa.
This paper is devoted to show the advantages of introducing a geometric viewpoint and a non extensive formulation in the description of apparently unrelated phenomena: combustion and earthquakes. Here, it is shown how the introduction of a fragmentation analysis based on that formulation leads to find a common point for description of these phenomena
We consider the phenomenon of Bose-Einstein condensation in a random growing directed network. The network grows by the addition of vertices and edges. At each time step the network gains a vertex with probabilty $p$ and an edge with probability $1-p$. The new vertex has a fitness $(a,b)$ with probability $f(a,b)$. A vertex with fitness $(a,b)$, in-degree $i$ and out-degree $j$ gains a new incoming edge with rate $a(i+1)$ and an outgoing edge with rate $b(j+1)$. The Bose-Einstein condensation occurs as a function of fitness distribution $f(a,b)$.
By using the maximum entropy principle, with Tsallis entropy, we obtain an explicit dependence for energy distribution of earthquakes. This function describes very well the observations in a wide range of energies, where other distribution functions fail. We assume that the fragments filling the gap between the fault planes play an active role in the triggering of earthquakes. The energy distribution function is related to the size distribution function of these fragments.
By using the maximum entropy principle with Tsallis entropy and under the assumption that the gouge plays an active role in the triggering of earthquakes, we obtain a functional dependence for energy distribution function for earthquakes which fits very well with observations in the region of small energies. This distribution function is related to the size distribution function of fragments in the gouge.
Experiments in which thick clay plates and glass rods are fractured have revealed different behavior of fragment mass distribution function in the small and large fragment regions. In this paper we explain this behavior using non-extensive Tsallis statistics and show how the crossover between the two regions is caused by the change in the fragments' dimensionality during the fracture process. We obtain a physical criterion for the position of this crossover and an expression for the change in the power law exponent between the small and large fragment regions. These predictions are in good agreement with the experiments on thick clay plates
By using the maximum entropy principle with Tsallis entropy we obtain a fragment size distribution function which undergoes a transition to scaling. This distribution function reduces to those obtained by other authors using Shannon entropy. The treatment is easily generalisable to any process of fractioning with suitable constraints.
The precise determination of the universality classes in self-organized critical phenomena (SOC) is still an unsolved problem. Different SOC models like sandpile, linear interface depinning, and the Barkhausen effect have been investigated independently. In the present work we demonstrate that these models can all be mapped into a linear interface depinning model driven at constant rate. The model is found to belong to the universality class of constant force linear interface depinning above the depinning transition, with an upper critical dimension d_c=4. Results are compared with numerical simulations, experiments, and previous theoretical works reported in the literature. In this way we demonstrate a precise connection between different SOC models which display the same universal beha
The dynamics of critical slope self-organized critical models is studied, using a previous mapping into a linear interface depinning model dragged at one end. The model is solved obtaining the complete set of scaling exponents. Some results are supported by previous RG developed for constant force linear interface depinning models but others, like the linear dependency of the susceptibility with system size, are intrinsic of this model which belongs to a different universality class. The comparison of our results with numerical simulations of ricepile and vortexpile models reported in the literature reveals that, as in the constant force case, there are two universality classes corresponding to random and periodic pinning.
The dynamics of an elastic interface profile h(x,t) under a driving force increasing at rate c, a restored force -epsilon h, and disorder is investigated. Using perturbation theory and functional renormalization group the phase diagram and the scaling exponents, up to the first order in 4-d, are obtained. The model is found to be critical in the double limit epsilon->0$ and c/epsilon->0$ and belongs to a different universality class as that of constant force models. It is shown that undirected sandpile models with stochastic rules and linear interface models with extremal dynamics belong to this new universality class.
The existence of self-organized criticality in the Barkhausen effect and its analogy with sandpile models is investigated. It is demonstrated that a model recently introduced to describe the dynamics of a domain wall [Cizeau et al, Phys. Rev. Lett. 79, 4669 (1997)] belongs to the universality class of undirected Abelian sandpile models. In this way it is shown that the Barhausen effect can be taken as an experimental observation of self-organized critical phenomena.
The dynamics of a domain wall in magnetostrictive materials is investigated. The domain wall is modeled by a d-dimensional interface moving in a d+1-dimensional environment. Long-range demagnetization effects and quenched disorder are considered, while the external magnetic field is increased at constant rate. Exact expressions for the average interface velocity and susceptibility are obtained, resulting that the system is critical when the demagnetization constant and the average interface velocity vanishes. The critical exponents are computed to O(4-d). Our predictions are compared with numerical simulations and Barkhausen noise measurements reported in the literature.
Aging in complex systems is studied via the sandpile model. Relaxation of avalanches in sandpiles is observed to depend on the time elapsed since the begining of the relaxation. Levy behavior is observed in the distribution of characteristic times. In this way, aging and self-organized criticality appear to be closely related.
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.
In the present work we present a fractal model for the beta relaxation in supercooled liquids. The macroscopic dynamics is obtained by superposition of relaxation of independent mesoscopic regions (cages). Scaling relations and exponents are assumed for the distribution of cage sizes and for the size dependent response of the independent cages. In this way we obtain some scaling relations for the average response, in the time and frequency domain. For a particular choice of the scaling exponents we obtain the scaling relations predicted by the MCT. The comparison with recent light scattering data reveals that the scaling exponents of the distribution of cage sizes are universal but the single cage relaxation depends on the detailed material structure
Ultrametric concepts are applied to the Bernoulli map, showing the adequateness of the non-Archimedean metrics to describe in a simple and direct way the chaotic properties of this map. Lyapunov exponent and Kolmogorov entropy appear to find a simpler explanation. A p-adic time emerges as a natural consequence of the ultrametric properties of the map.
Avalanches in sandpiles are represented throughout a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches resemble more to experimental results than other models using cellular automata simulations. Apparent discrepancies between experiments are reconciled. Critical behavior is here expressed troughout the critical properties of percolation phenomena.