Related papers: Aftershocks in Coherent-Noise Models

As exemplified by the Kuramoto model, large systems of coupled oscillators may undergo a transition to phase coherence with increasing coupling strength. It is shown that below the critical coupling strength for this transition such systems…

We propose a simple theory for the ``universal'' scaling law previously reported for the distributions of waiting times between earthquakes. It is based on a largely used benchmark model of seismicity, which just assumes no difference in…

We propose a new physically-based ``multifractal stress activation'' model of earthquake interaction and triggering based on two simple ingredients: (i) a seismic rupture results from activated processes giving an exponential dependence on…

A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence $\Xi$, and discuss in some detail a general…

We report in details the observations of structures in coupled map lattice during its chaotic evolution, both in one and two dimension, driven by identical noise on each site (by a structure we mean a group of neighboring lattice-sites for…

The analysis of the classical and mirror triads of the sequence of earthquakes has been carried out in order to find the equations of evolution of foreshocks and aftershocks. The differential equation with cubic (quadratic) nonlinearity has…

We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical…

A review of the statistical properties of earthquakes is provided, centered mainly in the work of the author (apologies for that). We explain the scaling law for the recurrence-time distributions, its universal character for stationary…

We study the frictional behavior of small contacts as those realized in the atomic force microscope and other experimental setups, in the framework of generalized Prandtl-Tomlinson models. Particular attention is paid to mechanisms that…

Spatio-temporal correlations of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes are extensively studied by means of numerical computer simulations. Particular attention is paid to clarifying how the statistical…

We analyze 21 aftershock sequences of California to test for evidence of space-time diffusion. Aftershock diffusion may result from stress diffusion and is also predicted by any mechanism of stress weakening. Here, we test an alternative…

We study the decoherence of a one-particle system, whose classical correpondent is chaotic, when it evolves coupled to a weak quenched environment. This is done by analytical evaluation of the Loschmidt Echo, (i.e. the revival of a…

We analyze the memory in volatility by studying volatility return intervals, defined as the time between two consecutive fluctuations larger than a given threshold, in time periods following stock market crashes. Such an aftercrash period…

Classical chaotic dynamics is characterized by the exponential sensitivity to initial conditions. Quantum mechanics, however, does not show this feature. We consider instead the sensitivity of quantum evolution to perturbations in the…

We present a new kind of critical stochastic finite-time-singularity, relying on the interplay between long-memory and extreme fluctuations. We illustrate it on the well-established epidemic-type aftershock (ETAS) model for aftershocks,…

We study the statistical properties of recurrence times in the self-excited Hawkes conditional Poisson process, the simplest extension of the Poisson process that takes into account how the past events influence the occurrence of future…

We investigate the sequence of great earthquakes over the past century. To examine whether the earthquake record includes temporal clustering, we identify aftershocks and remove those from the record. We focus on the recurrence time,…

In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of gaussian profiles localized at random…

Analysis of the Sumatra-Andaman earthquake on 26.12.2004 (M = 9) has allowed us to identify two non- trivial properties of the dynamics of aftershocks. First, the strongest aftershock (M = 7.2) was likely triggered by the round-the-world…

We investigate the effects of a time-correlated noise on an extended chaotic system. The chosen model is the Lorenz'96, a kind of "toy" model used for climate studies. Through the analysis of the system's time evolution and its time and…