48,964 research outputs found
Chaos and a Resonance Mechanism for Structure Formation in Inflationary Models
We exhibit a resonance mechanism of amplification of density perturbations in
inflationary mo-dels, using a minimal set of ingredients (an effective
cosmological constant, a scalar field minimally coupled to the gravitational
field and matter), common to most models in the literature of inflation. This
mechanism is based on the structure of homoclinic cylinders, emanating from an
unstable periodic orbit in the neighborhood of a saddle-center critical point,
present in the phase space of the model. The cylindrical structure induces
oscillatory motions of the scales of the universe whenever the orbit visits the
neighborhood of the saddle-center, before the universe enters a period of
exponential expansion. The oscillations of the scale functions produce, by a
resonance mechanism, the amplification of a selected wave number spectrum of
density perturbations, and can explain the hierarchy of scales observed in the
actual universe. The transversal crossings of the homoclinic cylinders induce
chaos in the dynamics of the model, a fact intimately connected to the
resonance mechanism occuring immediately before the exit to inflation.Comment: 4 pages. This essay received an Honorable Mention from the Gravity
Research Foundation, 1998-Ed. To appear in Mod. Phys. Lett.
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
Numerical study of a model for non-equilibrium wetting
We revisit the scaling properties of a model for non-equilibrium wetting
[Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the
critical exponents and providing a complete scaling scheme. Moreover, we
investigate a special point in the phase diagram, where the model exhibits a
roughening transition related to directed percolation. We argue that in the
vicinity of this point evaporation from the middle of plateaus can be
interpreted as an external field in the language of directed percolation. This
analogy allows us to compute the crossover exponent and to predict the form of
the phase transition line close to its terminal point.Comment: 8 pages, 8 figure
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
Equivalence between different classical treatments of the O(N) nonlinear sigma model and their functional Schrodinger equations
In this work we derive the Hamiltonian formalism of the O(N) non-linear sigma
model in its original version as a second-class constrained field theory and
then as a first-class constrained field theory. We treat the model as a
second-class constrained field theory by two different methods: the
unconstrained and the Dirac second-class formalisms. We show that the
Hamiltonians for all these versions of the model are equivalent. Then, for a
particular factor-ordering choice, we write the functional Schrodinger equation
for each derived Hamiltonian. We show that they are all identical which
justifies our factor-ordering choice and opens the way for a future
quantization of the model via the functional Schrodinger representation.Comment: Revtex version, 17 pages, substantial change
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