Related papers: Universal Earthquake-Occurrence Jumps, Correlation…
Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through action of the…
We study analytically the order statistics of a time series generated by the successive positions of a symmetric random walk of n steps with step lengths of finite variance \sigma^2. We show that the statistics of the gap d_{k,n}=M_{k,n}…
The emergence of a power-law distribution for the energy released during an earthquake is investigated in several models. Generic features are identified which are based on the self-affine behavior of the stress field prior to an event.…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
We study the spreading of information in a wide class of quantum systems, with variable-range interactions. We show that, after a quench, it generally features a double structure, whose scaling laws are related to a set of universal…
The statistics of recurrence times in broad areas have been reported to obey universal scaling laws, both for single homogeneous regions (Corral, 2003) and when averaged over multiple regions (Bak et al.,2002). These unified scaling laws…
In the present paper we have conducted studies on seismological properties using worldwide data of deep earthquakes (depth larger than 70 km), considering events with magnitude $m \geq 4.5$. We have addressed the problem under the…
Earthquakes and solar flares are phenomena involving huge and rapid releases of energy characterized by complex temporal occurrence. By analysing available experimental catalogs, we show that the stochastic processes underlying these…
We report an empirical determination of the probability density functions $P_{\text{data}}(r)$ of the number $r$ of earthquakes in finite space-time windows for the California catalog. We find a stable power law tail $P_{\text{data}}(r)…
Time series are characterized by complex memory and/or distribution patterns. In this letter we show that models obeying to different statistics may equally reproduce some pattern of a time series. In particular we discuss the difference…
Scale-invariant avalanches -- with events of all sizes following power-law distributions -- are considered critical. Above the upper critical dimension of four, the mean-field solution with a robust $3/2$ size exponent describes the…
Self-similarity indicates that large and small earthquakes share the same physics, where all variables scale with rupture length $L$. Here I show that rupture tip acceleration during the start of dynamic rupture (break-out phase) is also…
The statistical properties of time intervals between significant earthquakes are found to be described by the Zipf-Mandelbrot-Tsallis-type distribution.
Natural earthquake fault systems are highly non-homogeneous. The inhomogeneities occur be- cause the earth is made of a variety of materials which hold and dissipate stress differently. In this work, we study scaling in earthquake fault…
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…
We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi- ports can connect not to their nearest…
We report the analysis of the statistics of the phase fluctuations in the coda of earthquakes recorded during a temporary experiment deployed at Pinyon Flats Observatory, California. The practical measurement of the phase is discussed and…
We make an extensive numerical study of a two dimensional nonconservative model proposed by Olami-Feder-Christensen to describe earthquake behavior. By analyzing the distribution of earthquake sizes using a multiscaling method, we find…
The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed…