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We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed…
A system is in a self-organized critical state if the distribution of some measured events (avalanche sizes, for instance) obeys a power law for as many decades as it is possible to calculate or measure. The finite-size scaling of this…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
The scaling behavior of the thermoelectric transport properties in disordered systems is studied in the energy region near the metal-insulator transition. Using an energy-dependent conductivity $\sigma$ obtained experimentally, we extend…
Topological defects dominate the deformation response of materials in processes ranging from quantum turbulence to crystal plasticity. We calculate the probability distribution function for the fluctuations in velocity $v$, using scaling…
In this study we are testing whether the power law slopes ($\alpha_F$, $\alpha_E$) of fluxes $(F)$, fluences or energies $(E)$ are universal in their size distributions, $N(F) \propto F^{-\alpha_F}$ and $N(E) \propto E^{-\alpha_E}$, in…
The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic…
Using the phenomenological expression for the level spacing distribution with only one parameter, $0 \leq \beta \leq \infty$, covering all regimes of chaos and complexity in a quantum system, we show that transport properties of the…
The self-diffusion coefficient of a granular gas in the homogeneous cooling state is analyzed near the shearing instability. Using mode-coupling theory, it is shown that the coefficient diverges logarithmically as the instability is…
Avalanches whose sizes and durations are distributed as power laws appear in many contexts. Here, we show that there is a hidden peril in thresholding continuous times series --either from empirical or synthetic data-- for the detection of…
In the present work, it is developed a formalism to deal with the macroscopic study of the astrophysical systems, which is based on the consideration of the exponential self-similarity scaling laws that these systems exhibit during the…
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…
We present a detailed study of the statistics of a system of diffusing aggregating particles with a steady monomer source. We emphasise the case of low spatial dimensions where strong diffusive fluctuations invalidate the mean-field…
Numerous systems ranging from deformation of materials to earthquakes exhibit bursty dynamics, which consist of a sequence of events with a broad event size distribution. Very often these events are observed to be temporally correlated or…
This paper presents a novel, safe control architecture (SCA) for controlling an important class of systems: safety-critical systems. Ensuring the safety of control decisions has always been a challenge in automatic control. The proposed SCA…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…
Recent studies have shown that adaptive networks driven by simple local rules can organize into "critical" global steady states, providing another framework for self-organized criticality (SOC). We focus on the important convergence to…
The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not…
We investigate thermal avalanche dynamics in amorphous solids using elastoplastic models with local activation rules and no external driving. Dynamical heterogeneities, quantified through persistence measurements and the associated…
We reexamine the dynamics of the Olami, Feder and Christensen (OFC) model. We show that, depending on the dissipation, it exhibits two different behaviors and that it can or cannot show self - organized - criticality (SOC) and/or…