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This paper presents an analysis of the distribution of the time $\tau$ between two consecutive events in a stationary point process. The study is motivated by the discovery of a unified scaling law for $\tau$ for the case of seismic events.…
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
This paper investigates exponential mixing of the invariant measure for randomly forced nonlinear Schr\"{o}dinger equation, with damping and random noise localized in space. Our study emphasizes the crucial role of exponential asymptotic…
Simulating dynamic rupture propagation is challenging due to the uncertainties involved in the underlying physics of fault slip, stress conditions, and frictional properties of the fault. A trial and error approach is often used to…
We find the static displacement, stress, strain and the modified Columb failure stress produced in an elastic medium by a finite size rectangular fault after its dislocation with uniform stress drop but a non uniform dislocation on the…
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing…
Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal, quasistatic limit. In all cases the distribution of avalanche sizes follows a…
Study of charged particle multiplicity distribution in high energy interactions of particles helps in revealing the dynamics of particle production and the underlying statistical patterns, which these distributions follow. Several…
A Predictor-Corrector strategy is employed for the numerical simulation of the one-dimensional Burridge-Knopoff model of earthquakes. This approach is totally explicit and allows to reproduce the main features of the model. The results…
In confined plasmas, a localized fluctuation in a marginal or weakly damped region will propagate and generate an avalanche if it exceeds a threshold. In this letter, a new model for turbulence spreading based on subcritical instability in…
Testing earthquake forecasts is essential to obtain scientific information on forecasting models and sufficient credibility for societal usage. We aim at enhancing the testing phase proposed by the Collaboratory for the Study of Earthquake…
For earthquake-resistant design, engineering seismologists employ time-history analysis for nonlinear simulations. The nonstationary stochastic method previously developed by Pousse et al. (2006) has been updated. This method has the…
We use an analogy with the statistical mechanics of gas to build the statistical mechanics of granular media. The case of an isotropic disordered packing of equal spheres submitted to an isotropic stress is considered. We use the assumption…
The recently introduced Minimalist Model [Vazquez- Prada et al., 2002] of characteristic earthquakes provides a simple representation of the seismicity originated in a sin- gle fault. Here, we first characterize the properties of this model…
We propose a branching process based on a dynamical scaling hypothesis relating time and mass. In the context of earthquake occurrence, we show that experimental power laws in size and time distribution naturally originate solely from this…
The epidemic-type aftershock sequence model (ETAS) is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power law decay ~1/t^{1+\theta} of seismicity after an earthquake) and…
The probability distribution of the magnitude can be modeled by an exponential distribution according to the Gutenberg-Richter relation. Two alternatives are the truncated exponential distribution (TED) and the cut-off exponential…
The `plate tectonics' is an observed fact and most models of earthquake incorporate that through the frictional dynamics (stick-slip) of two surfaces where one surface moves over the other. These models are more or less successful to…
In environmental science applications, extreme events frequently exhibit a complex spatio-temporal structure, which is difficult to describe flexibly and estimate in a computationally efficient way using state-of-art parametric…