342 research outputs found
Analytic model for the ballistic adsorption of polydisperse mixtures
We study the ballistic adsorption of a polydisperse mixture of spheres onto a
line. Within a mean-field approximation, the problem can be analytically solved
by means of a kinetic equation for the gap distribution. In the mean-field
approach, the adsorbed substrate as approximated as composed by {\em effective}
particles with the {\em same} size, equal to the average diameter of the
spheres in the original mixture. The analytic solution in the case of binary
mixtures agrees quantitatively with direct Monte Carlo simulations of the
model, and qualitatively with previous simulations of a related model in .Comment: 6 pages, RevTex, includes 2 PS figures. Phys. Rev. E (in press
On the numerical study of percolation and epidemic critical properties in networks
The static properties of the fundamental model for epidemics of diseases allowing immunity (susceptible-infected-removed model) are known to be derivable by an exact mapping to bond percolation. Yet when performing numerical simulations of these dynamics in a network a number of subtleties must be taken into account in order to correctly estimate the transition point and the associated critical properties. We expose these subtleties and identify the different quantities which play the role of criticality detector in the two dynamics.Postprint (author's final draft
Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects
The largest eigenvalue of a network's adjacency matrix and its associated
principal eigenvector are key elements for determining the topological
structure and the properties of dynamical processes mediated by it. We present
a physically grounded expression relating the value of the largest eigenvalue
of a given network to the largest eigenvalue of two network subgraphs,
considered as isolated: The hub with its immediate neighbors and the densely
connected set of nodes with maximum -core index. We validate this formula
showing that it predicts with good accuracy the largest eigenvalue of a large
set of synthetic and real-world topologies. We also present evidence of the
consequences of these findings for broad classes of dynamics taking place on
the networks. As a byproduct, we reveal that the spectral properties of
heterogeneous networks built according to the linear preferential attachment
model are qualitatively different from those of their static counterparts.Comment: 18 pages, 13 figure
Anomalous scaling in the Zhang model
We apply the moment analysis technique to analyze large scale simulations of
the Zhang sandpile model. We find that this model shows different scaling
behavior depending on the update mechanism used. With the standard parallel
updating, the Zhang model violates the finite-size scaling hypothesis, and it
also appears to be incompatible with the more general multifractal scaling
form. This makes impossible its affiliation to any one of the known
universality classes of sandpile models. With sequential updating, it shows
scaling for the size and area distribution. The introduction of stochasticity
into the toppling rules of the parallel Zhang model leads to a scaling behavior
compatible with the Manna universality class.Comment: 4 pages. EPJ B (in press
Zero temperature Glauber dynamics on complex networks
We study the Glauber dynamics at zero temperature of spins placed on the
vertices of an uncorrelated network with a power-law degreedistribution.
Application of mean-field theory yields as main prediction that for symmetric
disordered initial conditions the mean time to reach full order is finite or
diverges as a logarithm of the system size N, depending on the exponent of the
degree distribution. Extensive numerical simulations contradict these results
and clearly show that the mean-field assumption is not appropriate to describe
this problem.Comment: 20 pages, 10 figure
Temporal percolation in activity driven networks
We study the temporal percolation properties of temporal networks by taking
as a representative example the recently proposed activity driven network model
[N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical
framework based on a mapping to hidden variables networks, we provide
expressions for the percolation time marking the onset of a giant connected
component in the integrated network. In particular, we consider both the
generating function formalism, valid for degree uncorrelated networks, and the
general case of networks with degree correlations. We discuss the different
limits of the two approach, indicating the parameter regions where the
correlated threshold collapses onto the uncorrelated case. Our analytical
prediction are confirmed by numerical simulations of the model. The temporal
percolation concept can be fruitfully applied to study epidemic spreading on
temporal networks. We show in particular how the susceptible-infected- removed
model on an activity driven network can be mapped to the percolation problem up
to a time given by the spreading rate of the epidemic process. This mapping
allows to obtain addition information on this process, not available for
previous approaches
Immunization of complex networks
Complex networks such as the sexual partnership web or the Internet often
show a high degree of redundancy and heterogeneity in their connectivity
properties. This peculiar connectivity provides an ideal environment for the
spreading of infective agents. Here we show that the random uniform
immunization of individuals does not lead to the eradication of infections in
all complex networks. Namely, networks with scale-free properties do not
acquire global immunity from major epidemic outbreaks even in the presence of
unrealistically high densities of randomly immunized individuals. The absence
of any critical immunization threshold is due to the unbounded connectivity
fluctuations of scale-free networks. Successful immunization strategies can be
developed only by taking into account the inhomogeneous connectivity properties
of scale-free networks. In particular, targeted immunization schemes, based on
the nodes' connectivity hierarchy, sharply lower the network's vulnerability to
epidemic attacks
Scaling of a slope: the erosion of tilted landscapes
We formulate a stochastic equation to model the erosion of a surface with
fixed inclination. Because the inclination imposes a preferred direction for
material transport, the problem is intrinsically anisotropic. At zeroth order,
the anisotropy manifests itself in a linear equation that predicts that the
prefactor of the surface height-height correlations depends on direction. The
first higher-order nonlinear contribution from the anisotropy is studied by
applying the dynamic renormalization group. Assuming an inhomogeneous
distribution of soil substrate that is modeled by a source of static noise, we
estimate the scaling exponents at first order in \ep-expansion. These
exponents also depend on direction. We compare these predictions with empirical
measurements made from real landscapes and find good agreement. We propose that
our anisotropic theory applies principally to small scales and that a
previously proposed isotropic theory applies principally to larger scales.
Lastly, by considering our model as a transport equation for a driven diffusive
system, we construct scaling arguments for the size distribution of erosion
``events'' or ``avalanches.'' We derive a relationship between the exponents
characterizing the surface anisotropy and the avalanche size distribution, and
indicate how this result may be used to interpret previous findings of
power-law size distributions in real submarine avalanches.Comment: 19 pages, includes 10 PS figures. J. Stat. Phys. (in press
Random walks in non-Poissoinan activity driven temporal networks
The interest in non-Markovian dynamics within the complex systems community has recently blossomed, due to a new wealth of time-resolved data pointing out the bursty dynamics of many natural and human interactions, manifested in an inter-event time between consecutive interactions showing a heavy-tailed distribution. In particular, empirical data has shown that the bursty dynamics of temporal networks can have deep consequences on the behavior of the dynamical processes running on top of them. Here, we study the case of random walks, as a paradigm of diffusive processes, unfolding on temporal networks generated by a non-Poissonian activity driven dynamics. We derive analytic expressions for the steady state occupation probability and first passage time distribution in the infinite network size and strong aging limits, showing that the random walk dynamics on non-Markovian networks are fundamentally different from what is observed in Markovian networks. We found a particularly surprising behavior in the limit of diverging average inter-event time, in which the random walker feels the network as homogeneous, even though the activation probability of nodes is heterogeneously distributed. Our results are supported by extensive numerical simulations. We anticipate that our findings may be of interest among the researchers studying non-Markovian dynamics on time-evolving complex topologies.Postprint (published version
Bosonic reaction-diffusion processes on scale-free networks
Reaction-diffusion processes can be adopted to model a large number of
dynamics on complex networks, such as transport processes or epidemic
outbreaks. In most cases, however, they have been studied from a fermionic
perspective, in which each vertex can be occupied by at most one particle.
While still useful, this approach suffers from some drawbacks, the most
important probably being the difficulty to implement reactions involving more
than two particles simultaneously. Here we introduce a general framework for
the study of bosonic reaction-diffusion processes on complex networks, in which
there is no restriction on the number of interacting particles that a vertex
can host. We describe these processes theoretically by means of continuous time
heterogeneous mean-field theory and divide them into two main classes: steady
state and monotonously decaying processes. We analyze specific examples of both
behaviors within the class of one-species process, comparing the results
(whenever possible) with the corresponding fermionic counterparts. We find that
the time evolution and critical properties of the particle density are
independent of the fermionic or bosonic nature of the process, while
differences exist in the functional form of the density of occupied vertices in
a given degree class k. We implement a continuous time Monte Carlo algorithm,
well suited for general bosonic simulations, which allow us to confirm the
analytical predictions formulated within mean-field theory. Our results, both
at the theoretical and numerical level, can be easily generalized to tackle
more complex, multi-species, reaction-diffusion processes, and open a promising
path for a general study and classification of this kind of dynamical systems
on complex networks.Comment: 15 pages, 7 figure
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