Related papers: Size-frequency distribution and the large deviatio…
Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can…
We study the statistical properties of time distribution of seimicity in California by means of a new method of analysis, the Diffusion Entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a…
A globally driven self-organized critical model of earthquakes with conservative dynamics has been studied. An open but moving boundary condition has been used so that the origin (epicenter) of every avalanche (earthquake) is at the center…
We critically examine how well the evolution of large-scale density perturbations is followed in cosmological $N$-body simulations. We first run a large volume simulation and perform a mode-by-mode analysis in three-dimensional Fourier…
Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we…
Fluctuations in diversity and extinction sizes are discussed and compared for two different, individual-based models of biological coevolution. Both models display power-law distributions for various quantities of evolutionary interest,…
Characteristic versus critical features of earthquakes are studied on the basis of the Olami-Feder-Christensen model. It is found that the local recurrence-time distribution exhibits a sharp $\delta$-function-like peak corresponding to…
Macroscopic fluctuation theory has shown that a wide class of non-equilibrium stochastic dynamical systems obey a large deviation principle, but except for a few one-dimensional examples these large deviation principles are in general not…
The long-term erosion of steep landscapes is punctuated by dramatic erosional events that can remove significant amount of sediments within a time-scale shorter than a seismic cycle. However, the role of such large erosional events on…
In this paper, we expand and generalize the findings presented in our previous work on the law of large numbers and the large deviation principle for Poisson processes with uniform catastrophes. We study three distinct scalings: sublinear…
It has been shown [Phys. Rev. E 84, 022101 (2011); Chaos 22, 023123 (2012)] that earthquakes of magnitude $M$ greater or equal to 7 are globally correlated. Such correlations were identified by studying the variance $\kappa_1$ of natural…
We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDF) of event locations to improve the spatial information content of seismic catalogs. The method reduces the size of seismic…
The concept of proper time, which is different from universal time, has been introduced into the physics of earthquakes. The global activity of strong earthquakes was chosen as the object of study. We consider the sequence of earthquakes as…
Slow earthquakes differ from regular earthquakes in their slower moment release and size distribution dominated by smaller events. However, the physical origin of these slow earthquake statistics remains controversial. In this work, we…
Extending the central concept of recurrence times for a point process to recurrent events in space-time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events. Linking record…
We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of…
The dynamic energy balance is essential for earthquake studies. The energy balance approach is one of the most famous developments in fracture mechanics. To interpret seismological data, crack models and sliding on a frictional surface…
Laboratory earthquakes exhibit characteristics of a low dimensional random attractor with a dimension similar to that of natural slow earthquakes. A model of stochastic differential equations based on rate and state-dependent friction…
Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior, such as Gutenberg-Richter scaling and the relation between large and small events, which is the basis for various forecasting…
A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…