We discuss a family of clusters C corresponding to the region whose boundary is formed by a fractional Brownian path y(i) and by the moving average function yn(i)≡1n∑k=0n−1y(i−k). Our model generates fractal directed patterns showing spatio-temporal complexity, and we demonstrate that...

When a mixture of small and large grains is poured between two vertical slabs, the mixture spontaneously stratifies in alternating layers of small and large grains. We describe a possible mechanism and we develop a model that reproduces stratification of the large and small grains in alternating...

Angell and his collaborators have underscored the importance of studying water under all extremes of pressure—squeezing to high pressures and stretching to negative pressures. Here we review recent results of molecular dynamics simulations of two models of liquid water, the extended simple...

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...

We present an overview of recent research applying ideas of statistical physics to try to better understand puzzles regarding economic fluctuations. One of these puzzles is how to describe outliers, phenomena that lie outside of patterns of statistical regularity. We review evidence consistent...

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...

The behavior of thermodynamic and dynamic properties of liquid water at atmospheric pressure in the temperature range between the lower limit of supercooling (TH≈235K) and the onset of the glassy state at Tg has been the focus of much research, and many questions remain about the properties of...

We study the scaling properties of noise reduced Eden clusters in three and four dimensions for variant B in the strip geometry. We find that the width W for large times behaves as a(s)g(Lsd−1), where L is the width of the strip, s the noise reduction parameter, d the dimension of space, and...

Asymptotic forms for the expected number of distinct sites visited by an n-step random walk, being calculable for many random walks, have been used in a number of analyses of physical models. We describe three recent extensions of the problem, the first replacing the single random walker by...