2,114 research outputs found
Analytical approach to directed sandpile models on the Apollonian network
We investigate a set of directed sandpile models on the Apollonian network,
which are inspired on the work by Dhar and Ramaswamy (PRL \textbf{63}, 1659
(1989)) for Euclidian lattices. They are characterized by a single parameter
, that restricts the number of neighbors receiving grains from a toppling
node. Due to the geometry of the network, two and three point correlation
functions are amenable to exact treatment, leading to analytical results for
the avalanche distributions in the limit of an infinite system, for .
The exact recurrence expressions for the correlation functions are numerically
iterated to obtain results for finite size systems, when larger values of
are considered. Finally, a detailed description of the local flux properties is
provided by a multifractal scaling analysis.Comment: 7 pages in two-column format, 10 illustrations, 5 figure
Targeted Recovery as an Effective Strategy against Epidemic Spreading
We propose a targeted intervention protocol where recovery is restricted to
individuals that have the least number of infected neighbours. Our recovery
strategy is highly efficient on any kind of network, since epidemic outbreaks
are minimal when compared to the baseline scenario of spontaneous recovery. In
the case of spatially embedded networks, we find that an epidemic stays
strongly spatially confined with a characteristic length scale undergoing a
random walk. We demonstrate numerically and analytically that this dynamics
leads to an epidemic spot with a flat surface structure and a radius that grows
linearly with the spreading rate.Comment: 6 pages, 5 figure
A worldwide model for boundaries of urban settlements
The shape of urban settlements plays a fundamental role in their sustainable
planning. Properly defining the boundaries of cities is challenging and remains
an open problem in the Science of Cities. Here, we propose a worldwide model to
define urban settlements beyond their administrative boundaries through a
bottom-up approach that takes into account geographical biases intrinsically
associated with most societies around the world, and reflected in their
different regional growing dynamics. The generality of the model allows to
study the scaling laws of cities at all geographical levels: countries,
continents, and the entire world. Our definition of cities is robust and holds
to one of the most famous results in Social Sciences: Zipf's law. According to
our results, the largest cities in the world are not in line with what was
recently reported by the United Nations. For example, we find that the largest
city in the world is an agglomeration of several small settlements close to
each other, connecting three large settlements: Alexandria, Cairo, and Luxor.
Our definition of cities opens the doors to the study of the economy of cities
in a systematic way independently of arbitrary definitions that employ
administrative boundaries
Dynamics in the Fitness-Income plane: Brazilian states vs World countries
In this paper we introduce a novel algorithm, called Exogenous Fitness, to calculate the Fitness of subnational entities and we apply it to the states of Brazil. In the last decade, several indices were introduced to measure the competitiveness of countries by looking at the complexity of their export basket. Tacchella et al (2012) developed a non-monetary metric called Fitness. In this paper, after an overview about Brazil as a whole and the comparison with the other BRIC countries, we introduce a new methodology based on the Fitness algorithm, called Exogenous Fitness. Combining the results with the Gross Domestic Product per capita (GDPp), we look at the dynamics of the Brazilian states in the Fitness-Income plane. Two regimes are distinguishable: one with high predictability and the other with low predictability, showing a deep analogy with the heterogeneous dynamics of the World countries. Furthermore, we compare the ranking of the Brazilian states according to the Exogenous Fitness with the ranking obtained through two other techniques, namely Endogenous Fitness and Economic Complexity Index
Non-Local Product Rules for Percolation
Despite original claims of a first-order transition in the product rule model
proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies
indicate that this percolation model, in fact, displays a continuous
transition. The distinctive scaling properties of the model at criticality,
however, strongly suggest that it should belong to a different universality
class than ordinary percolation. Here we introduce a generalization of the
product rule that reveals the effect of non-locality on the critical behavior
of the percolation process. Precisely, pairs of unoccupied bonds are chosen
according to a probability that decays as a power-law of their Manhattan
distance, and only that bond connecting clusters whose product of their sizes
is the smallest, becomes occupied. Interestingly, our results for
two-dimensional lattices at criticality shows that the power-law exponent of
the product rule has a significant influence on the finite-size scaling
exponents for the spanning cluster, the conducting backbone, and the cutting
bonds of the system. In all three cases, we observe a continuous variation from
ordinary to (non-local) explosive percolation exponents.Comment: 5 pages, 4 figure
How dense can one pack spheres of arbitrary size distribution?
We present the first systematic algorithm to estimate the maximum packing
density of spheres when the grain sizes are drawn from an arbitrary size
distribution. With an Apollonian filling rule, we implement our technique for
disks in 2d and spheres in 3d. As expected, the densest packing is achieved
with power-law size distributions. We also test the method on homogeneous and
on empirical real distributions, and we propose a scheme to obtain
experimentally accessible distributions of grain sizes with low porosity. Our
method should be helpful in the development of ultra-strong ceramics and high
performance concrete.Comment: 5 pages, 5 figure
IMDB network revisited: unveiling fractal and modular properties from a typical small-world network
We study a subset of the movie collaboration network, imdb.com, where only
adult movies are included. We show that there are many benefits in using such a
network, which can serve as a prototype for studying social interactions. We
find that the strength of links, i.e., how many times two actors have
collaborated with each other, is an important factor that can significantly
influence the network topology. We see that when we link all actors in the same
movie with each other, the network becomes small-world, lacking a proper
modular structure. On the other hand, by imposing a threshold on the minimum
number of links two actors should have to be in our studied subset, the network
topology becomes naturally fractal. This occurs due to a large number of
meaningless links, namely, links connecting actors that did not actually
interact. We focus our analysis on the fractal and modular properties of this
resulting network, and show that the renormalization group analysis can
characterize the self-similar structure of these networks.Comment: 12 pages, 9 figures, accepted for publication in PLOS ON
Transverse instability of dunes
The simplest type of dune is the transverse one, which propagates with
invariant profile orthogonally to a fixed wind direction. Here we show
numerically and with a linear stability analysis that transverse dunes are
unstable with respect to along-axis perturbations in their profile and decay on
the bedrock into barchan dunes. Any forcing modulation amplifies exponentially
with growth rate determined by the dune turnover time. We estimate the distance
covered by a transverse dune before fully decaying into barchans and identify
the patterns produced by different types of perturbation.Comment: 4 pages, 3 figures; To appear in Physical Review Letter
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