1,970 research outputs found
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
Two-level relationships and Scale-Free Networks
Through the distinction between ``real'' and ``virtual'' links between the
nodes of a graph, we develop a set of simple rules leading to scale-free
networks with a tunable degree distribution exponent. Albeit sharing some
similarities with preferential attachment, our procedure is both faster than a
na\"ive implementation of the Barab\'asi and Albert model and exhibits
different clustering properties. The model is thoroughly studied numerically
and suggests that reducing the set of partners a node can connect to is
important in seizing the diversity of scale-free structures
Semigroups of finite-dimensional random projections
In this paper we present a complete description of a stochastic semigroup of
finite-dimensional projections in Hilbert space. The geometry of such
semigroups is characterized by the asymptotic behavior of the widths of compact
subsets with respect to the subspaces generated by the semigroup operators.Comment: 13 page
Network model of human language
The phenomenon of human language is widely studied from various points of
view. It is interesting not only for social scientists, antropologists or
philosophers, but also for those, interesting in the network dynamics. In
several recent papers word web, or language as a graph has been investigated.
In this paper I revise recent studies of syntactical word web. I present a
model of growing network in which such processes as node addition, edge
rewiring and new link creation are taken into account. I argue, that this model
is a satisfactory minimal model explaining measured data.Comment: 10 pages, 1 fig, to appear in Physica
- …