Related papers: Energy Distribution in Earthquakes: A Non-Extensiv…
This paper extends the existing fractional Hawkes process to better model mainshock-aftershock sequences of earthquakes. The fractional Hawkes process is a self-exciting point process model with temporal decay kernel being a Mittag-Leffler…
The flux of turbulent kinetic energy from large to small spatial scales is measured in a small domain B of varying size R. The probability distribution function of the flux is obtained using a time-local version of Kolmogorov's four-fifths…
Potential energy stored during the inter-seismic period by tectonic loading around faults is released during earthquakes as radiated energy, heat and fracture energy. The latter is of first importance since it controls the nucleation,…
The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of…
In this paper, we used the Global Catalog of the National Earthquake Information Center US Geological Survey (NEIC USGS) for analysis of the magnitude-frequency distribution of earthquakes. We selected the unimodal part of the distribution…
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,…
It is possible to derive the maximum entropy principle from thermodynamic stability requirements. Using as a starting point the equilibrium probability distribution, currently used in non-extensive thermostatistics, it turns out that the…
Statistical mechanics reveals that the properties of a macroscopic physical system emerge as an average over an ensemble of statistically independent microscopic subsystems, each occupying a specific microstate. In the study of quantum…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
This article extends the non-extensive entropy of Tsallis and uses this entropy to model an energy producing system in an absorbing heat bath. This modified non-extensive entropy is superficially identical to the one proposed by Tsallis,…
We study the nonextensive thermodynamics for open systems. On the basis of the maximum entropy principle, the dual power-law q-distribution functions are re-deduced by using the dual particle number definitions and assuming that the…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
We extend the canonical Gibbs distribution, originally formulated for systems at equilibrium, to systems driven out of equilibrium. The stochastic dynamics of a small system are described by a probability distribution over discrete energy…
We present a novel approach for resolving modes of rupture directivity in large populations of earthquakes. A seismic spectral decomposition technique is used to first produce relative measurements of radiated energy for earthquakes in a…
We consider a general stochastic branching process, which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of…
We applied the Tsallis statistics with the conventional expectation value to a system of free particles, adopting the equilibrium temperature which is often called the physical temperature. The entropic parameter $q$ in the Tsallis…
The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
We investigated turbulence-like behavior in the geomagnetic field using ground-based magnetic observatory data across China. Through analysis of spatial and temporal structure functions, we find power-law scaling consistent with…
It has been proposed that the number of tropical cyclones as a function of the energy they release is a decreasing power-law function, up to a characteristic energy cutoff determined by the spatial size of the ocean basin in which the storm…