Related papers: Anomalous diffusion of volcanic earthquakes
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
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…
We analyze the statistics of water droplet avalanches in a continuously driven system. Distributions are obtained for avalanche size, lifetime, and time between successive avalanches, along with power spectra and return maps. For low flow…
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…
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…
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,…
In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian…
In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a randomly forced particle which collides inelastically with a boundary can undergo inelastic collapse and come to rest in a finite time. Here we discuss the survival…
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,…
A review of the statistical properties of earthquakes is provided, centered mainly in the work of the author (apologies for that). We explain the scaling law for the recurrence-time distributions, its universal character for stationary…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination…
Large scale molecular dynamics (MD) simulations are performed to study and to model the ejecta production from the dynamic fragmentation of shock-loaded metals under melt conditions. A generic 3D crystal in contact with vacuum containing…
Due to the unitary evolution, quantum walks display different dynamical features from that of classical random walks. In contrast to this expectation, in this work, we show that extreme events can arise in unitary dynamics and its…
The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations…
In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…
The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexiglas block is followed using a high resolution fast camera. We show that the fracture front dynamics is governed by local and irregular…
The fractional Fokker-Planck equation for subdiffusion in time-dependent force fields is derived from the underlying continuous time random walk. Its limitations are discussed and it is then applied to the study of subdiffusion under the…
We investigate Brownian motion with diffusivity alternately fluctuating between fast and slow states. We assume that sojourn-time distributions of these two states are given by exponential or power-law distributions. We develop a theory of…