23,261 research outputs found
Singular diffusion and criticality in a confined sandpile
We investigate the behavior of a two-state sandpile model subjected to a
confining potential in one and two dimensions. From the microdynamical
description of this simple model with its intrinsic exclusion mechanism, it is
possible to derive a continuum nonlinear diffusion equation that displays
singularities in both the diffusion and drift terms. The stationary-state
solutions of this equation, which maximizes the Fermi-Dirac entropy, are in
perfect agreement with the spatial profiles of time-averaged occupancy obtained
from model numerical simulations in one as well as in two dimensions.
Surprisingly, our results also show that, regardless of dimensionality, the
presence of a confining potential can lead to the emergence of typical
attributes of critical behavior in the two-state sandpile model, namely, a
power-law tail in the distribution of avalanche sizes.Comment: 5 pages, 5 figure
Critical properties of an aperiodic model for interacting polymers
We investigate the effects of aperiodic interactions on the critical behavior
of an interacting two-polymer model on hierarchical lattices (equivalent to the
Migadal-Kadanoff approximation for the model on Bravais lattices), via
renormalization-group and tranfer-matrix calculations. The exact
renormalization-group recursion relations always present a symmetric fixed
point, associated with the critical behavior of the underlying uniform model.
If the aperiodic interactions, defined by s ubstitution rules, lead to relevant
geometric fluctuations, this fixed point becomes fully unstable, giving rise to
novel attractors of different nature. We present an explicit example in which
this new attractor is a two-cycle, with critical indices different from the
uniform model. In case of the four-letter Rudin-Shapiro substitution rule, we
find a surprising closed curve whose points are attractors of period two,
associated with a marginal operator. Nevertheless, a scaling analysis indicates
that this attractor may lead to a new critical universality class. In order to
provide an independent confirmation of the scaling results, we turn to a direct
thermodynamic calculation of the specific-heat exponent. The thermodynamic free
energy is obtained from a transfer matrix formalism, which had been previously
introduced for spin systems, and is now extended to the two-polymer model with
aperiodic interactions.Comment: 19 pages, 6 eps figures, to appear in J. Phys A: Math. Ge
Large cities are less green
We study how urban quality evolves as a result of carbon dioxide emissions as
urban agglomerations grow. We employ a bottom-up approach combining two
unprecedented microscopic data on population and carbon dioxide emissions in
the continental US. We first aggregate settlements that are close to each other
into cities using the City Clustering Algorithm (CCA) defining cities beyond
the administrative boundaries. Then, we use data on emissions at a
fine geographic scale to determine the total emissions of each city. We find a
superlinear scaling behavior, expressed by a power-law, between
emissions and city population with average allometric exponent
across all cities in the US. This result suggests that the high productivity of
large cities is done at the expense of a proportionally larger amount of
emissions compared to small cities. Furthermore, our results are substantially
different from those obtained by the standard administrative definition of
cities, i.e. Metropolitan Statistical Area (MSA). Specifically, MSAs display
isometric scaling emissions and we argue that this discrepancy is due to the
overestimation of MSA areas. The results suggest that allometric studies based
on administrative boundaries to define cities may suffer from endogeneity bias
Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations
We study the distributions of traveling length l and minimal traveling time t
through two-dimensional percolation porous media characterized by long-range
spatial correlations. We model the dynamics of fluid displacement by the
convective movement of tracer particles driven by a pressure difference between
two fixed sites (''wells'') separated by Euclidean distance r. For strongly
correlated pore networks at criticality, we find that the probability
distribution functions P(l) and P(t) follow the same scaling Ansatz originally
proposed for the uncorrelated case, but with quite different scaling exponents.
We relate these changes in dynamical behavior to the main morphological
difference between correlated and uncorrelated clusters, namely, the
compactness of their backbones. Our simulations reveal that the dynamical
scaling exponents for correlated geometries take values intermediate between
the uncorrelated and homogeneous limiting cases
Fracturing the optimal paths
Optimal paths play a fundamental role in numerous physical applications
ranging from random polymers to brittle fracture, from the flow through porous
media to information propagation. Here for the first time we explore the path
that is activated once this optimal path fails and what happens when this new
path also fails and so on, until the system is completely disconnected. In fact
numerous applications can be found for this novel fracture problem. In the
limit of strong disorder, our results show that all the cracks are located on a
single self-similar connected line of fractal dimension .
For weak disorder, the number of cracks spreads all over the entire network
before global connectivity is lost. Strikingly, the disconnecting path
(backbone) is, however, completely independent on the disorder.Comment: 4 pages,4 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
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