In an effort to understand unusual power-law spectral slopes observed in some hypercompact HII regions, we consider the radio continuum energy distribution from an ensemble of spherical clumps. An analytic expression for the free-free emission from a single spherical clump is derived. The radio continuum slope (with Fν ∝ ν ) is governed by the population of clump optical depths N(τ), such that ...

– Personal income distribution in the USA has a well-defined two-class structure. The majority of population (97–99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs (“thermal”) distribution, whereas the upper class (1–3% of population) has a Pareto power-law (“superthermal”) distribution. By analyzing income data for 1983–2001, we show that the “thermal” part is sta...

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 that remain unexplained. A recently developed theory finds that the interplay between (i) one of the most universal ingredients, namely stochastic proportional...

There are two fair ways to distribute particles in boxes. The first way is to divide the particles equally between the boxes. The second way, which is calculated here, is to score fairly the particles between the boxes. The obtained power law distribution function yields an uneven distribution of particles in boxes. It is shown that the obtained distribution fits well to sociological phenomena,...

Dynamics of exploratory behaviour of rats and home base establishment is investigated. Time series of instantaneous speed of rats was computed from their position during exploration. The probability distribution function (PDF) of the speed obeys a power law distribution with exponents ranging from 2.1 to 2.32. The PDF of the recurrence time of large speed also exhibits a power law, P(τ) ~ τ(⁻β)...