Related papers: Random stress and Omori's law
The Gutenberg-Richter power law distribution of earthquake sizes is one of the most famous example illustrating self-similarity. It is well-known that the Gutenberg-Richter distribution has to be modified for large seismic moments, due to…
Most materials exhibit creep memory under the action of a constant load. The memory behavior is governed by Andrade's creep law, which also has an inherent connection with the Omori-Utsu law of earthquake aftershocks. Both empirical laws…
This paper presents an analysis on the distribution of periods between consecutive reversals of the Earth's magnetic field. The analysis includes the randomness of polarities, whether the data corresponding to different periods belong to a…
We present a simple model of earthquakes on a pre-existing hierarchical fault network. The system self-organizes on long time scales in a stationary state with a power law Gutenberg-Richter distribution of earthquake sizes. The largest…
In this article, we proposed an inverse Lindley distribution and studied its fundamental properties such as quantiles, mode, stochastic ordering and entropy measure. The proposed distribution is observed to be a heavy-tailed distribution…
The statistics of Lagrangian pair dispersion in a homogeneous isotropic flow is investigated by means of direct numerical simulations. The focus is on deviations from Richardson eddy-diffusivity model and in particular on the strong…
We study a stochastic process defined by the interaction strength for the return to the mean and a stochastic term proportional to the magnitude of the variable. Its steady-state distribution is the Inverse Gamma distribution, whose…
In this paper, we study some aspects on random analysis on the L\'eevy stochastic processes with margins following generalized hyperbolic distributions generated by gamma laws. In particular we study the boundedness of its total variations…
We investigate the properties of relative dispersion of Lagrangian particles in a global-ocean simulation resolving both inertia-gravity waves (IGW) and meso and submesoscale (M/SM) turbulence. More specifically, we test if the dispersion…
Multiple types of fluctuations impact the collective dynamics of power grids and thus challenge their robust operation. Fluctuations result from processes as different as dynamically changing demands, energy trading, and an increasing share…
A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda…
A recent model predicting Omori's law giving the number of aftershocks per unit time following an earthquake involves a differential equation analogous to the Friedmann equation of cosmology. The before-shock phase is analogous to an…
We introduce a modification of the OFC earthquake model [Phys. Rev. Lett. 68, 1244 (1992)] in order to improve resemblance with the Burridge and Knopoff mechanical model and with possible laboratory experiments. A constant force continually…
A new non-parametric statistic is introduced for the characterization of deviations from power laws. It is tested on the distribution of seismic energies given by the Gutenberg-Richter law. Based on the two first statistical log-moments, it…
We study chaos and L\'evy flights in the general gravitational three-body problem. We introduce new metrics to characterize the time evolution and final lifetime distributions, namely Scramble Density $\mathcal{S}$ and the LF index…
We show analytically that the answer to the question, "The longer it has been since the last earthquake, the longer the expected time till the next ?" depends crucially on the statistics of the fluctuations in the interval times between…
The statistical property of acoustic emission (AE) events from a plunged granular bed is analyzed by means of actual time and natural time analyses. These temporal analysis methods allow us to investigate the details of AE events that…
It is well known that a random multiplicative process with weak additive noise generates a power-law probability distribution. It has recently been recognized that this process exhibits another type of power law: the moment of the…
Preconception-free analyses of the inclusive invariant transverse-momentum distribution data taken from the measurements of Au+Au collisions at $\sqrt{s_{NN}}=130$ GeV and $\sqrt{s_{NN}}=200$ GeV have been performed. It is observed that the…
In this paper, the process of shear deformation of the medium formed by the cubic grains is investigated experimentally. It is demonstrated that the deformation process is intermittent and accompanied by the radiation of acoustic…