We present a scaling Ansatz for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for (i) the effect of the finite size of the system, and (ii) the dependence of this distribution on the site occupancy probability p. We present...

We discuss recent findings suggesting that an inverse square probability density distribution P(ℓ)∼ℓ−2 of step lengths ℓ leads to an optimal random search strategy for organisms that can search efficiently for randomly located objects that can only be detected in the limited vicinity...

Recently it has been shown that the most efficient strategy for searching randomly located objects, when the sites are randomly distributed and can be revisited any number of times, leads to a power law distribution P(ℓ)=ℓ−μ of the flights ℓ, with μ=2. We show analytically that the...

We review the general search problem of how to find randomly located objects that can only be detected in the limited vicinity of a forager, and discuss its quantitative description using the theory of random walks. We illustrate Lévy flight foraging by comparison to Brownian random walks and...

We discuss the possible utility of statistical physics in elucidating some of the puzzling phenomena that seem to occur in the brains of patients affected with Alzheimer’s disease. Further, we report three specific results from this approach: (i) The size distribution of senile plaques appears...

Inspired by work of both Widom and Mandelbrot, we analyze the Computstat database comprising all publicly traded United States manufacturing companies in the years 1974–1993. We find that the distribution of company size remains stable for the 20 years we study, i.e., the mean value and...