We propose a new model of the steep power law state of luminous black hole X-ray binaries. The model uses the fact that at high luminosities, radiation pressure dominated accretion discs become effectively optically thin. The gas temperature therefore rises sharply inwards, producing local saturated Compton spectra with rapidly increasing peak energy. These spectra sum together to form a steep ...

The power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these seemingly unrelated systems share great similarity. Through a detailed analysis of natural language texts and simulation experiments based on the proposed ‘Hierar...

WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. Fi...

A major objective of science is to provide a fundamental understanding of natural phenomena. In “the old kind of science” this was done primarily by using partial differential equations. Boundary and initial value conditions were specified and solutions were obtained either analytically or numerically. However, many phenomena in geology are complex and statistical in nature and thus require alt...

In neurons, power-law behavior with different scaling exponents has been reported at many different levels, including fluctuations in membrane potentials, synaptic transmission up to neuronal network dynamics. Unfortunately in most cases the source of this non-linear feature remains controversial. Here we have analyzed the dynamics of spontaneous quantal release at hippocampal synapses and char...

The effect of day-night variations was evaluated in both a female and a male population of healthy subjects. A total of 239 subjects were included in this study, of which 119 male and 120 female. 24 hour Holter recordings were used to analyze heart rate variability. Power spectral indices (total power, low and high frequency power) were calculated together with the nonlinear indices fractal dim...

The West-Brown-Enquist universal growth curve has been mapped on the power law function with the time-dependent scaling factor and exponent representing the temporal fractal dimension of the growth of species like mammals, birds, fish, crustaceans, regardless of taxon, cellular metabolic rate and body size. The results obtained permit formulation of three important rules governing the biologica...

Localized rain events have been found to follow power-law distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws can be generated by treating raindrops as passive tracers advected by the velocity field of a two-dimensional system of point vortices [R. Dickman, PRL 90, 108701 (2003)]. Here ...

This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequ...

The Ardabil geothermal area is located in the northwest of Iran, which hosts several hot springs. It is situated mostly around the Sabalan Mountain. The Sabalan geothermal area is now under investigation for the geothermal electric power generation. It is characterized by its high thermal gradient and high heat flow. In this study, our aim is to determine the fractal parameter and top and botto...