We have derived a model of the Kuiper belt luminosity function exhibited by a broken power-law size distribution. This model allows direct comparison of the observed luminosity function to the underlying size distribution. We discuss the importance of the radial distribution model in determining the break diameter. We determine a best-fit break-diameter of the Kuiper belt size-distribution of 3...

Whether there are universal laws or principles in complex systems is a fascinating and important question. Prof. John Casti uses the case of Normal Distribution (\bell curves") to illustrate that such universal principle is perhaps out there waiting to be discovered [1]. He suggests Zipf's law as a candidate for such universal principle. But as the author of one of the three publications to pro...

A study on the behavior of off-site AC power failure recovery times at three nuclear plant sites is presented. It is shown, that power law is appropriate for the representation of failure frequency-duration correlation function of off-site power failure events, based on simple assumptions about component failure and repair rates. It is also found that the annual maxima of power failure duration...

In this paper we investigate the similarity solutions of a plane mixed convection boundary layer flow near a semi-vertical plate, with a prescribed power law function of the distance from the leading edge for the temperature, that is embedded in a porous medium. We show the existence and uniqueness of convex and concave solutions for positive values of the power law exponent.

Many phenomenological models of the responses of simple cells in primary visual cortex have concluded that a cell's firing rate should be given by its input raised to a power greater than one. This is known as an expansive power-law nonlinearity. However, intracellular recordings have shown that a different nonlinearity, a linear-threshold function, appears to give a good prediction of firing r...

Power-law distributions are common, particularly in social physics. Here, we explore whether power-laws might arise as a consequence of a general variational principle for stochastic processes. We describe communities of ‘social particles’, where the cost of adding a particle to the community is shared equally between the particle joining the cluster and the particles that are already members o...

platinum extraction from different secondary sources has been experimentally tested by many researchers. in this article, dissolution of platinum in aqua-regia solution from two types of spent catalysts (reforming and nitric acid production) was kinetically studied. a variety of kinetic models for heterogeneous solid-liquid reactions, including homogeneous diffusion model, shrinking core model,...

It is shown that the distribution of word frequencies for randomly generated texts is very similar to Zipf's law observed in natural languages such as the English. The facts that the frequency of occurrence of a word is almost an inverse power law function of its rank and the exponent of this inverse power law is very close to 1 are largely due to the transformation from the word's length to it...

We report our efforts to constrain the form of the low-mass star and brown dwarf mass function via Bayesian inference. Recent surveys of M, L, and T dwarfs in the local solar neighborhood are an essential component of our study. Uncertainties in the age distribution of local field stars make reliable inference complicated. We adopt a wide range of plausible assumptions about the rate of galacti...

The power law of practice states that performance on a task improves as a power-law function of the number of times the task has been performed. In this article we describe recent work on a model of this effect. The model, called the chunking theory of /earning, is based on the notion of chunhing. A limited version of this model has been implemented within the XapsP production system architectu...