5,509 research outputs found
Motion in gauge theories of gravity
A description of motion is proposed, adapted to the composite bundle
interpretation of Poincar\'e Gauge Theory. Reference frames, relative positions
and time evolution are characterized in gauge-theoretical terms. The approach
is illustrated by an appropriate formulation of the familiar example of orbital
motion induced by Schwarzschild spacetime.Comment: 24 pages, 6 figures, revised version with minor change
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
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
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
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
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
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
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