12,046 research outputs found
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
Time of avalanche mixing of granular materials in a half filled rotated drum
The avalanche mixing of granular solids in a slowly rotated 2D upright drum
is studied. We demonstrate that the account of the difference between
the angle of marginal stability and the angle of repose of the granular
material leads to a restricted value of the mixing time for a half
filled drum. The process of mixing is described by a linear discrete difference
equation. We show that the mixing looks like linear diffusion of fractions with
the diffusion coefficient vanishing when is an integer part of .
Introduction of fluctuations of supresses the singularities of
and smoothes the dependence .Comment: 4 pages revtex (twocolumn, psfig), 2 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 and coincides with the
thickness of stratified layers in a two-component sandpile problem which were
observed recently. We find that the surface angle of the pile reaches
its final critical value () only at long times after a complicated
relaxation process. The deviation () behaves asymptotically
as . 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
A parity conserving dimer model with infinitely many absorbing states
We propose and study a model where, for the first time, two aspects are
present: parity conservation and infinitely many absorbing states. Whereas
steady-state simulations show that the static critical behaviour is not
affected by the presence of multiple absorbing configurations, the influence of
the initial state associated with the presence of slowly decaying memory
effects is clearly displayed in time dependent simulations. We report results
of a detailed investigation of the dependence of critical spreading exponents
on the initial particle density.Comment: 4 pages, 3 figures.p
Degree-dependent intervertex separation in complex networks
We study the mean length of the shortest paths between a vertex of
degree and other vertices in growing networks, where correlations are
essential. In a number of deterministic scale-free networks we observe a
power-law correction to a logarithmic dependence, in a wide range of network
sizes. Here is the number of vertices in the network, is the
degree distribution exponent, and the coefficients and depend on a
network. We compare this law with a corresponding dependence obtained
for random scale-free networks growing through the preferential attachment
mechanism. In stochastic and deterministic growing trees with an exponential
degree distribution, we observe a linear dependence on degree, . We compare our findings for growing networks with those for
uncorrelated graphs.Comment: 8 pages, 3 figure
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