Related papers: Fractal Fluctuations and Statistical Normal Distri…
Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed by vorticity fluctuations only,…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
Atmospheric flows exhibit cantorian fractal space-time fluctuations signifying long-range spatiotemporal correlations. A recently developed cell dynamical system model shows that such non-local connections are intrinsic to quantum-like…
Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that…
City-size distributions follow an approximate power law in various countries despite high volatility in relative city sizes over time. Our empirical evidence for the United States and Japan indicates that the scaling law stems from a…
Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…
Recent developments in extracting and processing biological and clinical data are allowing quantitative approaches to studying living systems. High-throughput sequencing, expression profiles, proteomics, and electronic health records are…
Within the point vortex model, we compute the probability distribution function of the velocity fluctuations induced by same-signed vortices scattered within a disk according to a fractal distribution of distances to origin $\sim…
Using numerical simulations and scaling theory we study the dynamics of the world-wide Web from the growth rules recently proposed in Ref. [1] with appropriate parameters. We demonstrate that the emergence of power-law behavior of the out-…
A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical…
Power law-like size distributions are ubiquitous in astrophysical instabilities. There are at least four natural effects that cause deviations from ideal power law size distributions, which we model here in a generalized way: (1) a physical…
The variability of temporal (or spatial) fluctuations of any variable is represented in conventional statistical theory by the relative dispersion equal to the standard deviation divided by the mean . The Relative Dispersion decreases with…
Financial markets can be seen as complex systems in non-equilibrium steady state, one of whose most important properties is the distribution of price fluctuations. Recently, there have been assertions that this distribution is qualitatively…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
We develop a statistical analytical model that predicts the occurrence frequency distributions and parameter correlations of avalanches in nonlinear dissipative systems in the state of a slowly-driven self-organized criticality (SOC)…
This is a brief introduction to fractals, multifractals and wavelets in an accessible way, in order that the founding ideas of those strange and intriguing newcomers to science as fractals may be communicated to a wider public. Fractals are…
The behavior of stock market returns over a period of 1-60 days has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are…
Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific…
We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its…