Rain, Power Laws, and Advection

Fractal rain distributions and chaotic advection

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 ...

Power-laws and Non-Power-laws in Dark Matter Halos

Simulated dark matter profiles are often modelled as a ‘NFW’ density profile rather than a single power law. Recently, attention has turned to the rather rigorous power-law behaviour exhibited by the ‘pseudo phase-space density’ of the dark matter halo, which is defined dimensionally in terms of the local density and velocity dispersion of the dark matter particles. The non-power-law behaviour ...

Power laws

Introduction Conclusions References

The power of power laws and an

Although already defined in 1926 by A. Lotka, power laws are becoming more and more important since they have been found valid in social networks such as the Internet. In this paper we prove some unique properties of power laws. We show that they characterise functions with the scale-free property (also called self-similarity property) as well as functions with the product property. They also h...

Self-Similarity and Power Laws