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Power-law type distributions are extensively found when studying the behaviour of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult…
The numerical experiments of turbulence conducted by Gotoh et al. are analyzed precisely with the help of the formulae for the scaling exponents of velocity structure function and for the probability density function (PDF) of velocity…
In this paper a composite model for earthquake rupture initiation and propagation is proposed. The model includes aspects of damage mechanics, fiber-bundle models, and slider-block models. An array of elements is introduced in analogy to…
Earthquakes are produced by the propagation of rapid slip along tectonic faults. The propagation dynamics is governed by a balance between elastic stored energy in the surrounding rock, and dissipated energy at the propagating tip of the…
Power spectrum of the distributed chaos can be represented by a weighted superposition of the exponential functions which is converged to a stretched exponential $\propto \exp-(k/k_{\beta})^{\beta }$. An asymptotic theory has been developed…
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the…
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…
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…
We introduce a new model for an earthquake fault system that is composed of non-interacting simple lattice models with different levels of damage denoted by $q$. The undamaged lattice models ($q=0$) have Gutenberg-Richter scaling with a…
Earthquakes occur because of abrupt slips on faults due to accumulated stress in the Earth's crust. Because most of these faults and their mechanisms are not readily apparent, deterministic earthquake prediction is difficult. For effective…
A two-dimensional earthquake model that consists of a single block resting upon a slowly moving rough surface and connected by two springs to rigid supports is studied. Depending on the elastic anisotropy and the friction force three…
The two-fractal overlap model of earthquake shows that the contact area distribution of two fractal surfaces follows power law decay in many cases and this agrees with the Guttenberg-Richter power law. Here, we attempt to predict the large…
Hysteresis loops and the associated avalanche statistics of spin systems, such as the random-field Ising and Edwards-Anderson spin-glass models, have been extensively studied. A particular focus has been on self-organized criticality,…
One of the classic data mining tasks is to discover bursts, time intervals, where events occur at abnormally high rate. In this paper we revisit Kleinberg's seminal work, where bursts are discovered by using exponential distribution with a…
The complete part of the earthquake frequency-magnitude distribution (FMD), above completeness magnitude mc, is well described by the Gutenberg-Richter law. The parameter mc however varies in space due to the seismic network configuration,…
This entry in the Encyclopedia of Complexity and Systems Science, Springer present a summary of some of the concepts and calculational tools that have been developed in attempts to apply statistical physics approaches to seismology. We…
We consider a family of one-dimensional diffusions, in dynamical Wiener mediums, which are random perturbations of the Ornstein-Uhlenbeck diffusion process. We prove quenched and annealed convergences in distribution and under weighted…
We introduce a Self-affine Asperity Model (SAM) for the seismicity that mimics the fault friction by means of two fractional Brownian profiles (fBm) that slide one over the other. An earthquake occurs when there is an overlap of the two…
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…
We perform a computational study of a variant of the ``train'' model for earthquakes [PRA 46, 6288 (1992)], where we assume a static friction that is a stochastic function of position rather than being velocity dependent. The model consists…