Related papers: Aftershocks and fluctuating diffusivity
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…
We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker-Planck equation, we can obtain a…
We consider the Olami-Feder-Christensen (OFC) model on a square two-dimensional lattice with open boundary conditions. The model exhibits self-organized criticality and explains the Gutenberg-Richter law observed for earthquakes. A…
The paper is based on the report read by the author on October 24, 2018 at the meeting of the Scientific Council of the Institute of Earth Physics of the Russian Academy of Sciences. The report was dedicated to the 150th anniversary of the…
We report an empirical determination of the probability density functions P(r) of the number r of earthquakes in finite space-time windows for the California catalog, over fixed spatial boxes 5 x 5 km^2 and time intervals dt =1, 10, 100 and…
After a large earthquake, the likelihood of successive strong aftershocks needs to be estimated. Exploiting similarities with critical phenomena, we introduce a scaling law for the decay in time following a main shock of the expected number…
When a chaotic, ergodic Hamiltonian system with $N$ degrees of freedom is subject to sufficiently rapid periodic driving, its energy evolves diffusively. We derive a Fokker-Planck equation that governs the evolution of the system's…
Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal…
In the renewal processes, if the waiting time probability density function is a tempered power-law distribution, then the process displays a transition dynamics; and the transition time depends on the parameter $\lambda$ of the exponential…
We present an analytical solution and numerical tests of the epidemic-type aftershock (ETAS) model for aftershocks, which describes foreshocks, aftershocks and mainshocks on the same footing. The occurrence rate of aftershocks triggered by…
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…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
A recently proposed unified scaling law for interoccurrence times of earthquakes [P. Bak et al., Phys. Rev. Lett. {\bf 88}, 178501 (2002)] is analyzed, both theoretically and with data from Southern California. We decompose the…
The dynamical behavior of the currency exchange rate after its large-scale catastrophe is discussed through a case study of the rate of Russian rubles to US dollars after its crash in 2014. It is shown that, similarly to the case of the…
Three fundamental laws of the physics of earthquakes, bearing the names of their discoverers Omori, Gutenberg, Richter and Bath, are widely used in original, review, monographic, and encyclopedic literature. In this paper, we have tried to…
We study analytically and by numerical simulations the statistics of the aftershocks generated after large avalanches in models of interface depinning that include viscoelastic relaxation effects. We find in all the analyzed cases that the…
Strong frequency dependence is unlikely in diffusive or over-damped systems. When exceptions do occur, such as in the case of stochastic resonance, it signals an interesting underlying phenomenon. We find that such a case appears in the…
The dynamics of initial long-wavelength excitations of the Fermi-Pasta-Ulam-Tsingou chain has been the subject of intense investigations since the pioneering work of Fermi and collaborators. We have recently found a new regime where the…
We study the formation and the evolution of velocity distribution tails for systems with long-range interactions. In the thermal bath approximation, the evolution of the distribution function of a test particle is governed by a…
The relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high-frequency data sets of the Shanghai Stock Exchange Composite (SSEC) index. Compared with previous relevant work, we have defined main…