Avalanche Mixing of Granular Solids

Mixing of two fractions of a granular material in a slowly rotating two-dimensional drum is considered. The rotation is around the axis of the upright drum. The drum is filled partially, and mixing occurs only at a free surface of the material. We propose a simple theory of the mixing process which describes a real experiment surprisingly well. A geometrical approach without appealing to ideas of self-organized criticality is used. The dependence of the mixing time on the drum filling is calculated. The mixing time is infinite in the case of the half-filled drum. We describe singular behaviour of the mixing near this critical point.Comment: 9 pages (LaTeX) and 2 Postscript figures, to be published in Europhys. Let

Complex networks created by aggregation

We study aggregation as a mechanism for the creation of complex networks. In this evolution process vertices merge together, which increases the number of highly connected hubs. We study a range of complex network architectures produced by the aggregation. Fat-tailed (in particular, scale-free) distributions of connections are obtained both for networks with a finite number of vertices and growing networks. We observe a strong variation of a network structure with growing density of connections and find the phase transition of the condensation of edges. Finally, we demonstrate the importance of structural correlations in these networks.Comment: 12 pages, 13 figure

Evolution of a sandpile in a thick flow regime

We solve a one-dimensional sandpile problem analytically in a thick flow regime when the pile evolution may be described by a set of linear equations. We demonstrate that, if an income flow is constant, a space periodicity takes place while the sandpile evolves even for a pile of only one type of particles. Hence, grains are piling layer by layer. The thickness of the layers is proportional to the input flow of particles $r_0$ and coincides with the thickness of stratified layers in a two-component sandpile problem which were observed recently. We find that the surface angle $\theta$ of the pile reaches its final critical value ($\theta_f$) only at long times after a complicated relaxation process. The deviation ($\theta_f - \theta$) behaves asymptotically as $(t/r_{0})^{-1/2}$. It appears that the pile evolution depends on initial conditions. We consider two cases: (i) grains are absent at the initial moment, and (ii) there is already a pile with a critical slope initially. Although at long times the behavior appears to be similar in both cases, some differences are observed for the different initial conditions are observed. We show that the periodicity disappears if the input flow increases with time.Comment: 14 pages, 7 figure

Language as an Evolving Word Web

Human language can be described as a complex network of linked words. In such a treatment, each distinct word in language is a vertex of this web, and neighboring words in sentences are connected by edges. It was recently found (Ferrer and Sol\'e) that the distribution of the numbers of connections of words in such a network is of a peculiar form which includes two pronounced power-law regions. Here we treat language as a self-organizing network of interacting words. In the framework of this concept, we completely describe the observed Word Web structure without fitting.Comment: 4 pages revtex, 2 figure