Related papers: Levy Flights and Earthquakes
Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can…
A theoretical analysis of the earthquake prediction problem in space-time is presented. We find an explicit structure of the optimal strategy and its relation to the generalized error diagram. This study is a generalization of the…
Spatially extended chaotic systems with power-law decaying interactions are considered. Two coupled replicas of such systems synchronize to a common spatio-temporal chaotic state above a certain coupling strength. The synchronization…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…
A novel geomechanics concept is presented for studying the behavior of geomaterials and structures by capturing the underlying dynamics as realistically as possible for earthquake excitation applied in time domain. Enormous amount of…
This paper develops a novel method, based on hidden Markov models, to forecast earthquakes and applies the method to mainshock seismic activity in southern California and western Nevada. The forecasts are of the probability of a mainshock…
We present an overview of our ongoing studies of the rich dynamical behavior of the uniform, deterministic Burridge--Knopoff model of an earthquake fault. We discuss the behavior of the model in the context of current questions in…
A novel model of transport is proposed to explain power law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Levy process of…
We provide a general model for Brownian motions on metric graphs with interactions. In a general setting, for (sticky) Brownian propagations on edges, our model provides a characterization of lifetimes and holding times on vertices in terms…
A globally driven self-organized critical model of earthquakes with conservative dynamics has been studied. An open but moving boundary condition has been used so that the origin (epicenter) of every avalanche (earthquake) is at the center…
The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…
The paper is devoted to the relationship between the continuous Markovian description of Levy flights developed previously and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of…
Universal shape profiles in a variety of systems contain crucial information on the underlying dynamics. We develop such shape profiles for earthquakes as a stronger test of theory against observations. The earthquake analysis shows good…
Earthquakes are a complex spatiotemporal phenomenon, the underlying mechanism for which is still not fully understood despite decades of research and analysis. We propose and develop a network approach to earthquake events. In this network,…
Anomalous diffusion and L\'evy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate…
Terra Seismic can predict most major earthquakes (M6.2 or greater) at least 2 - 5 months before they will strike. Global earthquake prediction is based on determinations of the stressed areas that will start to behave abnormally before…
Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations…
We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large earthquakes. The model idealizes the loading of elastic energy in a seismic fault by the stochastic filling of a box. The emptying of the box…
Multiple scattering of light by resonant vapor is characterized by Levy-type superdiffusion with a step size distribution $P(x) \propto 1/x^{1+{\alpha}}$, with $0 < {\alpha} < 2$. The Levy parameter ${\alpha}$ was measured from $P(x)$,…
We present a new technique in order to quantify the dynamics of spatially extended systems. Using a test on the existence of unstable periodic orbits, we identify intermediate spatial scales, wherein the dynamics is characterized by maximum…