29 research outputs found
Scaling behavior of the conserved transfer threshold process
We analyze numerically the critical behavior of an absorbing phase transition
in the conserved transfer threshold process. We determined the steady state
scaling behavior of the order parameter as a function of both, the control
parameter and an external field, conjugated to the order parameter. The
external field is realized as a spontaneous creation of active particles which
drives the system away from criticality. The obtained results yields that the
conserved transfers threshold process belongs to the universality class of
absorbing phase transitions in a conserved field.Comment: 6 pages, 8 figures, accepted for publication in Phys. Rev.
Growing community networks with local events
The study of community networks has attracted considerable attention
recently. In this paper, we propose an evolving community network model based
on local processes, the addition of new nodes intra-community and new links
intra- or inter-community. Employing growth and preferential attachment
mechanisms, we generate networks with a generalized power-law distribution of
nodes' degrees.Comment: 9 pages, 2 figures, Latex Styl
The Network of Scientific Collaborations within the European Framework Programme
We use the emergent field of Complex Networks to analyze the network of
scientific collaborations between entities (universities, research
organizations, industry related companies,...) which collaborate in the context
of the so-called Framework Programme. We demonstrate here that it is a
scale--free network with an accelerated growth, which implies that the creation
of new collaborations is encouraged. Moreover, these collaborations possess
hierarchical modularity. Likewise, we find that the information flow depends on
the size of the participants but not on geographical constraints.Comment: 13 pages, 6 figure
Frequency of occurrence of numbers in the World Wide Web
The distribution of numbers in human documents is determined by a variety of
diverse natural and human factors, whose relative significance can be evaluated
by studying the numbers' frequency of occurrence. Although it has been studied
since the 1880's, this subject remains poorly understood. Here, we obtain the
detailed statistics of numbers in the World Wide Web, finding that their
distribution is a heavy-tailed dependence which splits in a set of power-law
ones. In particular, we find that the frequency of numbers associated to
western calendar years shows an uneven behavior: 2004 represents a `singular
critical' point, appearing with a strikingly high frequency; as we move away
from it, the decreasing frequency allows us to compare the amounts of existing
information on the past and on the future. Moreover, while powers of ten occur
extremely often, allowing us to obtain statistics up to the huge 10^127,
`non-round' numbers occur in a much more limited range, the variations of their
frequencies being dramatically different from standard statistical
fluctuations. These findings provide a view of the array of numbers used by
humans as a highly non-equilibrium and inhomogeneous system, and shed a new
light on an issue that, once fully investigated, could lead to a better
understanding of many sociological and psychological phenomena.Comment: 5 pages, 4 figure
Kawasaki-type Dynamics: Diffusion in the kinetic Gaussian model
In this article, we retain the basic idea and at the same time generalize
Kawasaki's dynamics, spin-pair exchange mechanism, to spin-pair redistribution
mechanism, and present a normalized redistribution probability. This serves to
unite various order-parameter-conserved processes in microscopic, place them
under the control of a universal mechanism and provide the basis for further
treatment. As an example of the applications, we treated the kinetic Gaussian
model and obtained exact diffusion equation. We observed critical slowing down
near the critical point and found that, the critical dynamic exponent z=1/nu=2
is independent of space dimensionality and the assumed mechanism, whether
Glauber-type or Kawasaki-type.Comment: accepted for publication in PR
Principles of statistical mechanics of random networks
We develop a statistical mechanics approach for random networks with
uncorrelated vertices. We construct equilibrium statistical ensembles of such
networks and obtain their partition functions and main characteristics. We find
simple dynamical construction procedures that produce equilibrium uncorrelated
random graphs with an arbitrary degree distribution. In particular, we show
that in equilibrium uncorrelated networks, fat-tailed degree distributions may
exist only starting from some critical average number of connections of a
vertex, in a phase with a condensate of edges.Comment: 14 pages, an extended versio
Study of the multi-species annihilating random walk transition at zero branching rate - cluster scaling behavior in a spin model
Numerical and theoretical studies of a one-dimensional spin model with
locally broken spin symmetry are presented. The multi-species annihilating
random walk transition found at zero branching rate previously is investigated
now concerning the cluster behaviour of the underlying spins. Generic power law
behaviors are found, besides the phase transition point, also in the active
phase with fulfillment of the hyperscaling law. On the other hand scaling laws
connecting bulk- and cluster exponents are broken - a possibility in no
contradiction with basic scaling assumptions because of the missing absorbing
phase.Comment: 7 pages, 6 figures, final form to appear in PRE Nov.200
Phase transition and selection in a four-species cyclic Lotka-Volterra model
We study a four species ecological system with cyclic dominance whose
individuals are distributed on a square lattice. Randomly chosen individuals
migrate to one of the neighboring sites if it is empty or invade this site if
occupied by their prey. The cyclic dominance maintains the coexistence of all
the four species if the concentration of vacant sites is lower than a threshold
value. Above the treshold, a symmetry breaking ordering occurs via growing
domains containing only two neutral species inside. These two neutral species
can protect each other from the external invaders (predators) and extend their
common territory. According to our Monte Carlo simulations the observed phase
transition is equivalent to those found in spreading models with two equivalent
absorbing states although the present model has continuous sets of absorbing
states with different portions of the two neutral species. The selection
mechanism yielding symmetric phases is related to the domain growth process
whith wide boundaries where the four species coexist.Comment: 4 pages, 5 figure
Travel and tourism: Into a complex network
It is discussed how the worldwide tourist arrivals, about 10% of world's
domestic product, form a largely heterogeneous and directed complex network.
Remarkably the random network of connectivity is converted into a scale-free
network of intensities. The importance of weights on network connections is
brought into discussion. It is also shown how strategic positioning
particularly benefit from market diversity and that interactions among
countries prevail on a technological and economic pattern, questioning the
backbones of traveling driving forces
Epidemic processes with immunization
We study a model of directed percolation (DP) with immunization, i.e. with
different probabilities for the first infection and subsequent infections. The
immunization effect leads to an additional non-Markovian term in the
corresponding field theoretical action. We consider immunization as a small
perturbation around the DP fixed point in d<6, where the non-Markovian term is
relevant. The immunization causes the system to be driven away from the
neighbourhood of the DP critical point. In order to investigate the dynamical
critical behaviour of the model, we consider the limits of low and high first
infection rate, while the second infection rate remains constant at the DP
critical value. Scaling arguments are applied to obtain an expression for the
survival probability in both limits. The corresponding exponents are written in
terms of the critical exponents for ordinary DP and DP with a wall. We find
that the survival probability does not obey a power law behaviour, decaying
instead as a stretched exponential in the low first infection probability limit
and to a constant in the high first infection probability limit. The
theoretical predictions are confirmed by optimized numerical simulations in 1+1
dimensions.Comment: 12 pages, 11 figures. v.2: minor correction