5,717 research outputs found
A global take on congestion in urban areas
We analyze the congestion data collected by a GPS device company (TomTom) for
almost 300 urban areas in the world. Using simple scaling arguments and data
fitting we show that congestion during peak hours in large cities grows
essentially as the square root of the population density. This result, at odds
with previous publications showing that gasoline consumption decreases with
density, confirms that density is indeed an important determinant of
congestion, but also that we need urgently a better theoretical understanding
of this phenomena. This incomplete view at the urban level leads thus to the
idea that thinking about density by itself could be very misleading in
congestion studies, and that it is probably more useful to focus on the spatial
redistribution of activities and residences.Comment: 3 pages, 2 figure
Crossover from Scale-Free to Spatial Networks
In many networks such as transportation or communication networks, distance
is certainly a relevant parameter. In addition, real-world examples suggest
that when long-range links are existing, they usually connect to hubs-the well
connected nodes. We analyze a simple model which combine both these
ingredients--preferential attachment and distance selection characterized by a
typical finite `interaction range'. We study the crossover from the scale-free
to the `spatial' network as the interaction range decreases and we propose
scaling forms for different quantities describing the network. In particular,
when the distance effect is important (i) the connectivity distribution has a
cut-off depending on the node density, (ii) the clustering coefficient is very
high, and (iii) we observe a positive maximum in the degree correlation
(assortativity) which numerical value is in agreement with empirical
measurements. Finally, we show that if the number of nodes is fixed, the
optimal network which minimizes both the total length and the diameter lies in
between the scale-free and spatial networks. This phenomenon could play an
important role in the formation of networks and could be an explanation for the
high clustering and the positive assortativity which are non trivial features
observed in many real-world examples.Comment: 4 pages, 6 figures, final versio
Transitions in spatial networks
Networks embedded in space can display all sorts of transitions when their
structure is modified. The nature of these transitions (and in some cases
crossovers) can differ from the usual appearance of a giant component as
observed for the Erdos-Renyi graph, and spatial networks display a large
variety of behaviors. We will discuss here some (mostly recent) results about
topological transitions, `localization' transitions seen in the shortest paths
pattern, and also about the effect of congestion and fluctuations on the
structure of optimal networks. The importance of spatial networks in real-world
applications makes these transitions very relevant and this review is meant as
a step towards a deeper understanding of the effect of space on network
structures.Comment: Corrected version and updated list of reference
Betweenness Centrality in Large Complex Networks
We analyze the betweenness centrality (BC) of nodes in large complex
networks. In general, the BC is increasing with connectivity as a power law
with an exponent . We find that for trees or networks with a small loop
density while a larger density of loops leads to . For
scale-free networks characterized by an exponent which describes the
connectivity distribution decay, the BC is also distributed according to a
power law with a non universal exponent . We show that this exponent
must satisfy the exact bound . If the scale
free network is a tree, then we have the equality .Comment: 6 pages, 5 figures, revised versio
A Path Integral Approach to Effective Non-Linear Medium
In this article, we propose a new method to compute the effective properties
of non-linear disordered media. We use the fact that the effective constants
can be defined through the minimum of an energy functional. We express this
minimum in terms of a path integral allowing us to use many-body techniques. We
obtain the perturbation expansion of the effective constants to second order in
disorder, for any kind of non-linearity. We apply our method to both cases of
strong and weak non-linearities. Our results are in agreement with previous
ones, and could be easily extended to other types of non-linear problems in
disordered systems.Comment: 7 page
Modeling the polycentric transition of cities
Empirical evidence suggest that most urban systems experience a transition
from a monocentric to a polycentric organisation as they grow and expand. We
propose here a stochastic, out-of-equilibrium model of the city which explains
the appearance of subcenters as an effect of traffic congestion. We show that
congestion triggers the unstability of the monocentric regime, and that the
number of subcenters and the total commuting distance within a city scale
sublinearly with its population, predictions which are in agreement with data
gathered for around 9000 US cities between 1994 and 2010.Comment: 11 pages, 12 figure
Self-Consistent Effective-Medium Approximations with Path Integrals
We study effective-medium approximations for linear composite media by means
of a path integral formalism with replicas. We show how to recover the
Bruggeman and Hori-Yonezawa effective-medium formulas. Using a replica-coupling
ansatz, these formulas are extended into new ones which have the same
percolation thresholds as that of the Bethe lattice and Potts model of
percolation, and critical exponents s=0 and t=2 in any space dimension d>= 2.
Like the Bruggeman and Hori-Yonezawa formulas, the new formulas are exact to
second order in the weak-contrast and dilute limits. The dimensional range of
validity of the four effective-medium formulas is discussed, and it is argued
that the new ones are of better relevance than the classical ones in dimensions
d=3,4 for systems obeying the Nodes-Links-Blobs picture, such as
random-resistor networks.Comment: 18 pages, 6 eps figure
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