12,024 research outputs found
Projections from Subvarieties
Let be an n-dimensional connected projective submanifold of
projective space. Let denote the projection from a
linear . Assuming that we have the induced
rational mapping . This article started as an
attempt to understand the structure of this mapping when has a lower
dimensional image. In this case of necessity we have is
nonempty. We have in this article studied a closely related question, which
includes many special cases including the case when the center of the
projection \pn q is contained in .
PROBLEM. Let be a proper connected k-dimensional projective submanifold
of an -dimensional projective manifold . Assume that . Let be a
very ample line bundle on such that is spanned by global
sections, where denotes the ideal sheaf of in . Describe the
structure of under the additional assumption that the image of
under the mapping associated to is lower dimensional
Fully dissipative relativistic lattice Boltzmann method in two dimensions
In this paper, we develop and characterize the fully dissipative Lattice
Boltzmann method for ultra-relativistic fluids in two dimensions using three
equilibrium distribution functions: Maxwell-J\"uttner, Fermi-Dirac and
Bose-Einstein. Our results stem from the expansion of these distribution
functions up to fifth order in relativistic polynomials. We also obtain new
Gaussian quadratures for square lattices that preserve the spatial resolution.
Our models are validated with the Riemann problem and the limitations of lower
order expansions to calculate higher order moments are shown. The kinematic
viscosity and the thermal conductivity are numerically obtained using the
Taylor-Green vortex and the Fourier flow respectively and these transport
coefficients are compared with the theoretical prediction from Grad's theory.
In order to compare different expansion orders, we analyze the temperature and
heat flux fields on the time evolution of a hot spot
Rigidity and intermediate phases in glasses driven by speciation
The rigid to floppy transitions and the associated intermediate phase in
glasses are studied in the case where the local structure is not fully
determined from the macroscopic concentration. The approach uses size
increasing cluster approximations and constraint counting algorithms. It is
shown that the location and the width of the intermediate phase and the
corresponding structural, mechanical and energetical properties of the network
depend crucially on the way local structures are selected at a given
concentration. The broadening of the intermediate phase is obtained for
networks combining a large amount of flexible local structural units and a high
rate of medium range order.Comment: 4 pages, 4 figure
Metastability and anomalous fixation in evolutionary games on scale-free networks
We study the influence of complex graphs on the metastability and fixation
properties of a set of evolutionary processes. In the framework of evolutionary
game theory, where the fitness and selection are frequency-dependent and vary
with the population composition, we analyze the dynamics of snowdrift games
(characterized by a metastable coexistence state) on scale-free networks. Using
an effective diffusion theory in the weak selection limit, we demonstrate how
the scale-free structure affects the system's metastable state and leads to
anomalous fixation. In particular, we analytically and numerically show that
the probability and mean time of fixation are characterized by stretched
exponential behaviors with exponents depending on the network's degree
distribution.Comment: 5 pages, 4 figures, to appear in Physical Review Letter
The Ising M-p-spin mean-field model for the structural glass: continuous vs. discontinuous transition
The critical behavior of a family of fully connected mean-field models with
quenched disorder, the Ising spin glass, is analyzed, displaying a
crossover between a continuous and a random first order phase transition as a
control parameter is tuned. Due to its microscopic properties the model is
straightforwardly extendable to finite dimensions in any geometry.Comment: 10 pages, 1 figure, 1 tabl
Physics with nonperturbative quantum gravity: radiation from a quantum black hole
We study quantum gravitational effects on black hole radiation, using loop
quantum gravity. Bekenstein and Mukhanov have recently considered the
modifications caused by quantum gravity on Hawking's thermal black-hole
radiation. Using a simple ansatz for the eigenstates the area, they have
obtained the intriguing result that the quantum properties of geometry affect
the radiation considerably, yielding a definitely non-thermal spectrum. Here,
we replace the simple ansatz employed by Bekenstein and Mukhanov with the
actual eigenstates of the area, computed using the loop representation of
quantum gravity. We derive the emission spectra, using a classic result in
number theory by Hardy and Ramanujan. Disappointingly, we do not recover the
Bekenstein-Mukhanov spectrum, but --effectively-- a Hawking's thermal spectrum.
The Bekenstein-Mukhanov result is therefore likely to be an artefact of the
naive ansatz, rather than a robust result. The result is an example of concrete
(although somewhat disappointing) application of nonperturbative quantum
gravity.Comment: 4 pages, latex-revtex, no figure
Beyond the Death of Linear Response: 1/f optimal information transport
Non-ergodic renewal processes have recently been shown by several authors to
be insensitive to periodic perturbations, thereby apparently sanctioning the
death of linear response, a building block of nonequilibrium statistical
physics. We show that it is possible to go beyond the ``death of linear
response" and establish a permanent correlation between an external stimulus
and the response of a complex network generating non-ergodic renewal processes,
by taking as stimulus a similar non-ergodic process. The ideal condition of
1/f-noise corresponds to a singularity that is expected to be relevant in
several experimental conditions.Comment: 4 pages, 2 figures, 1 table, in press on Phys. Rev. Let
Noise and Correlations in a Spatial Population Model with Cyclic Competition
Noise and spatial degrees of freedom characterize most ecosystems. Some
aspects of their influence on the coevolution of populations with cyclic
interspecies competition have been demonstrated in recent experiments [e.g. B.
Kerr et al., Nature {\bf 418}, 171 (2002)]. To reach a better theoretical
understanding of these phenomena, we consider a paradigmatic spatial model
where three species exhibit cyclic dominance. Using an individual-based
description, as well as stochastic partial differential and deterministic
reaction-diffusion equations, we account for stochastic fluctuations and
spatial diffusion at different levels, and show how fascinating patterns of
entangled spirals emerge. We rationalize our analysis by computing the
spatio-temporal correlation functions and provide analytical expressions for
the front velocity and the wavelength of the propagating spiral waves.Comment: 4 pages of main text, 3 color figures + 2 pages of supplementary
material (EPAPS Document). Final version for Physical Review Letter
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