780 research outputs found
Epidemic Incidence in Correlated Complex Networks
We introduce a numerical method to solve epidemic models on the underlying
topology of complex networks. The approach exploits the mean-field like rate
equations describing the system and allows to work with very large system
sizes, where Monte Carlo simulations are useless due to memory needs. We then
study the SIR epidemiological model on assortative networks, providing
numerical evidence of the absence of epidemic thresholds. Besides, the time
profiles of the populations are analyzed. Finally, we stress that the present
method would allow to solve arbitrary epidemic-like models provided that they
can be described by mean-field rate equations.Comment: 5 pages, 4 figures. Final version published in PR
Local versus Global Knowledge in the Barabasi-Albert scale-free network model
The scale-free model of Barabasi and Albert gave rise to a burst of activity
in the field of complex networks. In this paper, we revisit one of the main
assumptions of the model, the preferential attachment rule. We study a model in
which the PA rule is applied to a neighborhood of newly created nodes and thus
no global knowledge of the network is assumed. We numerically show that global
properties of the BA model such as the connectivity distribution and the
average shortest path length are quite robust when there is some degree of
local knowledge. In contrast, other properties such as the clustering
coefficient and degree-degree correlations differ and approach the values
measured for real-world networks.Comment: Revtex format. Final version appeared in PR
Properties of highly clustered networks
We propose and solve exactly a model of a network that has both a tunable
degree distribution and a tunable clustering coefficient. Among other things,
our results indicate that increased clustering leads to a decrease in the size
of the giant component of the network. We also study SIR-type epidemic
processes within the model and find that clustering decreases the size of
epidemics, but also decreases the epidemic threshold, making it easier for
diseases to spread. In addition, clustering causes epidemics to saturate
sooner, meaning that they infect a near-maximal fraction of the network for
quite low transmission rates.Comment: 7 pages, 2 figures, 1 tabl
Weak Solutions to a Nonuniformly Elliptic PDE System in the Harmonic Regime
We study the existence of weak solutions to a nonlinear strongly coupled
parabolic–elliptic PDEs arising in the heating induction-conduction process of steel
hardening. In this setting, our major concern is to consider the case when the electric
conductivity is nonuniformly elliptic which, together with a right hand side in L1 in
the energy balance equation, yields to a difficult theoretical situation. The existence
result gives a weak solution to a similar PDEs system where the energy balance
equation has been perturbed by a measure term.Ministerio de EconomĂa y Competitividad MTM2010-16401Junta de AndalucĂa FQM-31
Topology and correlations in structured scale-free networks
We study a recently introduced class of scale-free networks showing a high
clustering coefficient and non-trivial connectivity correlations. We find that
the connectivity probability distribution strongly depends on the fine details
of the model. We solve exactly the case of low average connectivity, providing
also exact expressions for the clustering and degree correlation functions. The
model also exhibits a lack of small world properties in the whole parameters
range. We discuss the physical properties of these networks in the light of the
present detailed analysis.Comment: 10 pages, 9 figure
Steady-State Dynamics of the Forest Fire Model on Complex Networks
Many sociological networks, as well as biological and technological ones, can
be represented in terms of complex networks with a heterogeneous connectivity
pattern. Dynamical processes taking place on top of them can be very much
influenced by this topological fact. In this paper we consider a paradigmatic
model of non-equilibrium dynamics, namely the forest fire model, whose
relevance lies in its capacity to represent several epidemic processes in a
general parametrization. We study the behavior of this model in complex
networks by developing the corresponding heterogeneous mean-field theory and
solving it in its steady state. We provide exact and approximate expressions
for homogeneous networks and several instances of heterogeneous networks. A
comparison of our analytical results with extensive numerical simulations
allows to draw the region of the parameter space in which heterogeneous
mean-field theory provides an accurate description of the dynamics, and
enlights the limits of validity of the mean-field theory in situations where
dynamical correlations become important.Comment: 13 pages, 9 figure
Class of correlated random networks with hidden variables
We study a class models of correlated random networks in which vertices are
characterized by \textit{hidden variables} controlling the establishment of
edges between pairs of vertices. We find analytical expressions for the main
topological properties of these models as a function of the distribution of
hidden variables and the probability of connecting vertices. The expressions
obtained are checked by means of numerical simulations in a particular example.
The general model is extended to describe a practical algorithm to generate
random networks with an \textit{a priori} specified correlation structure. We
also present an extension of the class, to map non-equilibrium growing networks
to networks with hidden variables that represent the time at which each vertex
was introduced in the system
Renormalization group approach to an Abelian sandpile model on planar lattices
One important step in the renormalization group (RG) approach to a lattice
sandpile model is the exact enumeration of all possible toppling processes of
sandpile dynamics inside a cell for RG transformations. Here we propose a
computer algorithm to carry out such exact enumeration for cells of planar
lattices in RG approach to Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett.
{\bf 59}, 381 (1987)] and consider both the reduced-high RG equations proposed
by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. {\bf 72}, 1690
(1994)] and the real-height RG equations proposed by Ivashkevich [Phys. Rev.
Lett. {\bf 76}, 3368 (1996)]. Using this algorithm we are able to carry out RG
transformations more quickly with large cell size, e.g. cell for
the square (sq) lattice in PVZ RG equations, which is the largest cell size at
the present, and find some mistakes in a previous paper [Phys. Rev. E {\bf 51},
1711 (1995)]. For sq and plane triangular (pt) lattices, we obtain the only
attractive fixed point for each lattice and calculate the avalanche exponent
and the dynamical exponent . Our results suggest that the increase of
the cell size in the PVZ RG transformation does not lead to more accurate
results. The implication of such result is discussed.Comment: 29 pages, 6 figure
A first-principles approach to electrical transport in atomic-scale nanostructures
We present a first-principles numerical implementation of Landauer formalism
for electrical transport in nanostructures characterized down to the atomic
level. The novelty and interest of our method lies essentially on two facts.
First of all, it makes use of the versatile Gaussian98 code, which is widely
used within the quantum chemistry community. Secondly, it incorporates the
semi-infinite electrodes in a very generic and efficient way by means of Bethe
lattices. We name this method the Gaussian Embedded Cluster Method (GECM). In
order to make contact with other proposed implementations, we illustrate our
technique by calculating the conductance in some well-studied systems such as
metallic (Al and Au) nanocontacts and C-atom chains connected to metallic (Al
and Au) electrodes. In the case of Al nanocontacts the conductance turns out to
be quite dependent on the detailed atomic arrangement. On the contrary, the
conductance in Au nanocontacts presents quite universal features. In the case
of C chains, where the self-consistency guarantees the local charge transfer
and the correct alignment of the molecular and electrode levels, we find that
the conductance oscillates with the number of atoms in the chain regardless of
the type of electrode. However, for short chains and Al electrodes the even-odd
periodicity is reversed at equilibrium bond distances.Comment: 14 pages, two-column format, submitted to PR
Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets
The spins of ten stellar black holes have been measured using the
continuum-fitting method. These black holes are located in two distinct classes
of X-ray binary systems, one that is persistently X-ray bright and another that
is transient. Both the persistent and transient black holes remain for long
periods in a state where their spectra are dominated by a thermal accretion
disk component. The spin of a black hole of known mass and distance can be
measured by fitting this thermal continuum spectrum to the thin-disk model of
Novikov and Thorne; the key fit parameter is the radius of the inner edge of
the black hole's accretion disk. Strong observational and theoretical evidence
links the inner-disk radius to the radius of the innermost stable circular
orbit, which is trivially related to the dimensionless spin parameter a_* of
the black hole (|a_*| < 1). The ten spins that have so far been measured by
this continuum-fitting method range widely from a_* \approx 0 to a_* > 0.95.
The robustness of the method is demonstrated by the dozens or hundreds of
independent and consistent measurements of spin that have been obtained for
several black holes, and through careful consideration of many sources of
systematic error. Among the results discussed is a dichotomy between the
transient and persistent black holes; the latter have higher spins and larger
masses. Also discussed is recently discovered evidence in the transient sources
for a correlation between the power of ballistic jets and black hole spin.Comment: 30 pages. Accepted for publication in Space Science Reviews. Also to
appear in hard cover in the Space Sciences Series of ISSI "The Physics of
Accretion onto Black Holes" (Springer Publisher). Changes to Sections 5.2,
6.1 and 7.4. Section 7.4 responds to Russell et al. 2013 (MNRAS, 431, 405)
who find no evidence for a correlation between the power of ballistic jets
and black hole spi
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