Related papers: Order parameter fluctuations in natural time and b…
I introduce a simple continuous probability theory based on the Ginzburg-Landau equation that provides for the first time a common analytical basis to relate and describe the main features of two seemingly different phenomena of…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
Characteristic versus critical features of earthquakes are studied on the basis of the Olami-Feder-Christensen model. It is found that the local recurrence-time distribution exhibits a sharp $\delta$-function-like peak corresponding to…
Dynamical systems in nature such as fluid flows, heart beat patterns, rainfall variability, stock market price fluctuations, etc. exhibit selfsimilar fractal fluctuations on all scales in space and time. Power spectral analyses of fractal…
A new non-parametric statistic is introduced for the characterization of deviations from power laws. It is tested on the distribution of seismic energies given by the Gutenberg-Richter law. Based on the two first statistical log-moments, it…
We show that hyperscaling and finite-size scaling imply that the probability distribution of the order parameter in finite size critical systems exhibit data collapse. We consider the examples of equilibrium critical systems, and a…
Crustal deformation due to the 2016 earthquake sequence in Kumamoto, Japan, that culminated in a preceding earthquake of magnitude M6.5 and a subsequent M7.3 earthquake 28 hours later, caused stress perturbation on and around the causative…
We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data…
Recently (arXiv:0910.2870), we have derived a fluctuation theorem for systems in thermodynamic equilibrium compatible with anomalous response functions, e.g. the existence of states with \textit{negative heat capacities} $C<0$. In this…
A statistical model for describing the scaling of the distribution of inter-event times is described. By considering the diverse region seismicity (natural and induced) at different scale levels the self-similarity of the distribution has…
For systems exhibiting a second-order phase transition with a spontaneously broken continuous O(N)-symmetry at low temperature, we give a criterion for judging at which temperature T_K long-range directional fluctuations of the order field…
We study fluctuations in a vertically oscillated layer of grains below the critical acceleration for the onset of ordered standing waves. As onset is approached, transient disordered waves with a characteristic length scale emerge and…
Consider Ginibre's ensemble of $N \times N$ non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance $\frac{1}{N}$. As $N \uparrow \infty$ the normalized counting measure of the…
It is a common belief that power-law distributed avalanches are inherently unpredictable. This idea affects phenomena as diverse as evolution, earthquakes, superconducting vortices, stock markets, etc; from atomic to social scales. It…
Forest fire models may be interpreted as a simple model for earthquake occurrence by translating trees and fire into stressed segments of a fault and their rupture, respectively. Here we adopt a twodimensional forest-fire model in…
The long-term behavior of a supercritical branching random walk can be described and analyzed with the help of Biggins' martingales, parametrized by real or complex numbers. The study of these martingales with complex parameters is a rather…
We numerically investigate the Olami-Feder-Christensen model for earthquakes in order to characterise its scaling behaviour. We show that ordinary finite size scaling in the model is violated due to global, system wide events. Nevertheless…
The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit…
The counterintuitive emergence of order from noise is a central phenomenon in science, ranging from pattern formation and synchronization to order-by-disorder in frustrated systems. While large-scale spatial self-organization induced by…
We analyzed the correlations among the parameters of the Reasenberg and Jones (1989) formula describing the aftershock rate after a mainshock as a function of time and magnitude, on the basis of parameter estimates made in previous works…