Related papers: Lacunarity Exponents
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
We have studied the localization of waves in a one-dimensional lattice consisting of impurities where the spacing between consecutive impurities can take certain values with given probabilities. In general, such a distribution of impurities…
The maintenance of diversity, the `commonness of rarity', and compositional turnover are ubiquitous features of species-rich communities. Through a minimal model, we consider how these features reflect the interplay between environmental…
It is well understood that various alternatives are available within EM theory for the definitions of energy density, momentum transfer, EM stress-energy tensor, and so forth. Although the various options are all compatible with the basic…
Plastic yield of amorphous solids occurs by power law distributed slip avalanches whose universality is still debated. Determination of the power law exponents from experiments and molecular dynamics simulations is hampered by limited…
In branching process theory, linear-fractional distributions are commonly used to model individual reproduction, especially when the goal is to obtain more explicit formulas than those derived under general model assumptions. In this…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions…
We consider dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation and pair distribution function of the disk…
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…
Stressed soft materials commonly present viscoelastic signatures in the form of power-law or exponential decay. Understanding the origins of such rheologic behaviors is crucial to find proper technological applications. Using an elastic…
In this work, the short-time dynamics of simple liquid is explored both analytically and numerically with the focus on the interplay between the density fluctuations in a volume surrounding a chosen particle and its random walk motion. The…
A formalism is introduced to describe a number of physical processes that may break down the coherence of a matter wave over a characteristic length scale l. In a second-quantized description, an appropriate master equation for a set of…
The opacity of typical objects in the world results in occlusion --- an important property of natural scenes that makes inference of the full 3-dimensional structure of the world challenging. The relationship between occlusion and low-level…
We review how dark matter is distributed in our local neighbourhood from an observational and theoretical perspective. We will start by describing first the dark matter halo of our own galaxy and in the Local Group. Then we proceed to…
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…
Estimates of the number and potential energy of molecules, aerosols, cloud droplets, insects, birds, planes and satellites in the atmosphere yield a distribution which is for potential energies below 10^2 kBT described by the Boltzmann…
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…
Branched flow is an interesting phenomenon that can occur in diverse systems. It is usually linear in the sense that the flow does not alter the medium properties. Branched flow of light on thin films was recently discovered. A question of…