Related papers: Probabilistic Fragmentation and Effective Power La…
We present a theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material. Experiments were performed on brown and white hen egg-shells under two different loading conditions: impact…
A theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material is presented. Experiments were performed on brown and white hen egg-shells under two different loading conditions:…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
We analyze in details the statistical significance of the claim by Bird [2002] of a power law distribution of plate areas covering the Earth and confirm that the power law with exponent 0.25 +- 0.05 is the most robust and parsimonious model…
Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the…
It has been repeatedly stated that maximum likelihood (ML) estimates of exponents of power-law distributions can only be reliably obtained for exponents smaller than minus one. The main argument that power laws are otherwise not…
We consider scattering exponents arising in small-angle scattering from power-law polydisperse surface and mass fractals. It is shown that a set of fractals, whose sizes are distributed according to a power-law, can change its fractal…
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…
A mechanism is proposed for the appearance of power law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law…
We introduce and solve a model that mimics the herding effect in financial markets when groups of agents share information. The number of agents in the model is growing and at each time step either (i) with probability $p$ an incoming agent…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence…
In the spirit of a classical results for Crump-Mode-Jagers processes, we prove a strong law of large numbers for homogenous fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we…
We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition…
We study the distribution of the occurrence of rare patterns in sufficiently mixing Gibbs random fields on the lattice $\mathbb{Z}^d$, $d\geq 2$. A typical example is the high temperature Ising model. This distribution is shown to converge…
Many physical processes result in very uneven, apparently random, distributions of matter, characterized by fluctuations of the local density over orders of magnitude. The density of matter in the sparsest regions can have a power-law…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
The dynamics of particle transport under the influence of localised high energy anomalies (explosions) is a complicated phenomena dependent on many physical parameters of both the particle and the medium it resides in. Here we present a…
We report the binomial multiplicative model for low impact energy fragmentation. Impact fragmentation experiments were performed for low impact energy region, and it was found that the weighted mean mass is scaled by the pseudo control…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…