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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 review the present status of our research and understanding regarding the dynamics and the statistical properties of earthquakes, mainly from a statistical physical viewpoint. Emphasis is put both on the physics of friction and fracture,…
Following the observations of the self-similarity in various length scales in the roughness of the fractured solid surfaces, we propose here a new model for the earthquake. We demonstrate rigorously that the contact area distribution…
We have developed a model that describes the major characteristics of a rupture, ranging from regular earthquakes (EQs) to slow slip events (SSEs), including episodic tremor and slip (ETS). Previous model predictions, while accurate, are…
Motivated by the fact that empirical time series of earthquakes exhibit long-range correlations in space and time and the Gutenberg-Richter distribution of magnitudes, we propose a simple fault model that can account for these types of…
This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that…
Event counts are a powerful diagnostic for earthquake analysis. We report on a bimodal distribution of earthquake event counts in the U.S. since 2013. The new peak is about a magnitude M1 with a distribution very similar to that of induced…
We discuss various statistical distributions of earthquake numbers. Previously we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson,…
Spatiotemporal properties of seismicity are investigated for a worldwide (WW) catalog and for Southern California in the stationary case (SC), showing a nearly universal scaling behavior. Distributions of distances between consecutive…
We address several questions on the behavior of a numerical model recently introduced to study seismic phenomena, that includes relaxation in the plates as a key ingredient. We make an analysis of the scaling of the largest events with…
The interevent time distribution characterizes the temporal occurrence in seismic catalogs. Universal scaling properties of this distribution have been evidenced for entire catalogs and seismic sequences. Recently, these universal features…
We study slowly pulling block-spring models in random media. Second-order phase transitions exist in a model pulled by a constant force in the case of velocity-strengthening friction. If external forces are slowly increased, nearly critical…
The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global statistical characteristics and underlying physical mechanisms are…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
Recently, Portelli et al (2003) have semi-numerically obtained a functional form of the probability distribution of fluctuations in the total energy flow in a model for fluid turbulence. This follows earlier work suggesting that…
An efficient method for inferring Manning's $n$ coefficients using water surface elevation data was presented in Sraj et al. (2014) focusing on a test case based on data collected during the $T\=ohoku$ earthquake and tsunami. Polynomial…
The time and size distribution of the waves of topplings in the Abelian sandpile model are expressed as the first arrival at the origin distribution for a scale invariant, time inhomogeneous Fokker-Planck equation. Assuming a linear…
A statistical model for describing the scaling of the distribution of inter-event times is described. By considering the diverse region seismicity (natural and induced) at different scale levels the self-similarity of the distribution has…
Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete…
The class of $\alpha$-stable distributions received much interest for modelling impulsive phenomena occur in engineering, economics, insurance, and physics. The lack of non-analytical form for probability density function is considered as…