Related papers: Fractal Fluctuations and Statistical Normal Distri…
In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…
Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within…
One of the standardized features of financial data is that log-returns are uncorrelated, but absolute log-returns or their squares namely the fluctuating volatility are correlated and is characterized by heavy tailed in the sense that some…
We compare the properties of transmission across one-dimensional finite samples which are associated with two types of "quantum diffusion", one related to a classical chaotic dynamics, the other to a multifractal energy spectrum. We…
Atmospheric flows exhibit fractal fluctuations and inverse power law form for power spectra indicating an eddy continuum structure for the selfsimilar fluctuations. A general systems theory for fractal fluctuations developed by the author…
We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power-law profile, as opposed to a fractal model, can account for the observed power-law galaxy-galaxy correlations. We…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
Continuous periodogram power spectral analysis of daily incidence of acute myocardial infarction (AMI) reported at a leading hospital for cardiology in Pune, India for the two-year period June 1992 to May 1994 show that the power spectra…
The global energy fluctuations of a low density gas granular gas in the homogeneous cooling state near its clustering instability are studied by means of molecular dynamics simulations. The relative dispersion of the fluctuations is shown…
The notion of fractality, in the context of positive-valued probability distributions, is conventionally associated with the class of Paretian probability laws. In this research we show that the Paretian class is merely one out of six…
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
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…
The complex spatiotemporal patterns of atmospheric flows resulting from the cooperative existence of fluctuations ranging in size from millimeters to thousands of kilometers are found to exhibit long-range spatial and temporal correlations…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
Three-dimensional fractal models on grids of 200**3 pixels are generated from the inverse Fourier transform of noise with a power law cutoff, exponentiated to give a log normal distribution of density. The fractals are clipped at various…
The fracture strength distribution of materials is often described in terms of the Weibull law which can be derived by using extreme value statistics if elastic interactions are ignored. Here, we consider explicitly the interplay between…
The `plate tectonics' is an observed fact and most models of earthquake incorporate that through the frictional dynamics (stick-slip) of two surfaces where one surface moves over the other. These models are more or less successful to…
The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each…
In this paper, a simple dynamical model in which fractal networks are formed by self-organized critical (SOC) dynamics is proposed; the proposed model consists of growth and collapse processes. It has been shown that SOC dynamics are…
The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data…