Related papers: Power-law size distributions in geoscience revisit…
We find that watersheds in real and artificial landscapes can be strongly affected by small, local perturbations like landslides or tectonic motions. We observe power-law scaling behavior for both the distribution of areas enclosed by the…
Energy landscape approaches have become increasingly popular for analysing a wide variety of chemical physics phenomena. Basic to many of these applications has been the inherent structure mapping, which divides up the potential energy…
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…
Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here we attempt to describe it using an AC threshold…
One of the first steps to understand and forecast economic downturns is identifying their frequency distribution, but it remains uncertain. This problem is common in phenomena displaying power-law-like distributions. Power laws play a…
Physical systems characterized by stick-slip dynamics often display avalanches. Regardless of the diversity of their microscopic structure, these systems are governed by a power-law distribution of avalanche size and duration. Here we focus…
The $b$-value in the Gutenberg-Richter (GR) law contains information that is essential for evaluating earthquake hazard and predicting the occurrence of large earthquakes. Estimates of $b$ are often based on seismic events whose magnitude…
Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…
Two models of binary fragmentation are introduced in which a time dependent transition size produces two regions of fragment sizes above and below the transition size. In the models we consider a fixed rate of fragmentation for the largest…
Nonlinear dissipative systems in the state of self-organized criticality release energy sporadically in avalanches of all sizes, such as in earthquakes, auroral substorms, solar and stellar flares, soft gamma-ray repeaters, and pulsar…
The statistical property of the calm times, i.e., time intervals between successive earthquakes with arbitrary values of magnitude, is studied by analyzing the seismic time series data in California and Japan. It is found that the calm…
We propose a dynamical mechanism for a scale dependent error growth rate, by the introduction of a class of hierarchical models. The coupling of time scales and length scales is motivated by atmospheric dynamics. This model class can be…
Since the times of Holtsmark (1911), statistics of fields in random environments have been widely studied, for example in astrophysics, active matter, and line-shape broadening. The power-law decay of the two-body interaction, of the form…
We analyze time evolution of statistical distributions of citations to scientific papers published in one year. While these distributions can be fitted by a power-law dependence we find that they are nonstationary and the exponent of the…
There is no agreement over which statistical distribution is most appropriate for modelling citation count data. This is important because if one distribution is accepted then the relative merits of different citation-based indicators, such…
We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of…
Hysteresis, the lag between the force and the response, is often associated with noisy, jerky motion which have recently been called ``avalanches''. The interesting question is why the avalanches come in such a variety of sizes: naively one…
Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis…
We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it…
Bayesian modelling and statistical text analysis rely on informed probability priors to encourage good solutions. This paper empirically analyses whether text in medical discharge reports follow Zipf's law, a commonly assumed statistical…