11,133 research outputs found
Rigidity in topology C^0 of the Poisson bracket for Tonelli Hamiltonians
We prove the following rigidity result for the Tonelli Hamiltonians. Let T *
M be the cotangent bundle of a closed manifold M endowed with its usual
symplectic form. Let (F\_n) be a sequence of Tonelli Hamiltonians that C^0
converges on the compact subsets to a Tonelli Hamiltonian F. Let (G\_n) be a
sequence of Hamiltonians that that C^0 converges on the compact subsets to a
Hamiltonian G. We assume that the sequence of the Poisson brackets ({F\_n ,
G\_n }) C^0-converges on the compact subsets to a C^1 function H. Then H = {F,
G}
Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation
Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact
and connected manifold and let u be a semi-concave function defined on M. If E
(u) is the set of all the super-differentials of u and (\phi t) the Hamiltonian
flow of H, we prove that for t > 0 small enough, \phi-t (E (u)) is an exact
Lagrangian Lipschitz graph. This provides a geometric
interpretation/explanation of a regularization tool that was introduced by
P.~Bernard to prove the existence of C 1,1 subsolutions
Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting
We consider locally minimizing measures for the conservative twist maps of
the -dimensional annulus or for the Tonelli Hamiltonian flows defined on a
cotangent bundle . For weakly hyperbolic such measures (i.e. measures
with no zero Lyapunov exponents), we prove that the mean distance/angle between
the stable and the unstable Oseledet's bundles gives an upper bound of the sum
of the positive Lyapunov exponents and a lower bound of the smallest positive
Lyapunov exponent. Some more precise results are proved too
Increase of the Number of Detectable Gravitational Waves Signals due to Gravitational Lensing
This article deals with the gravitational lensing (GL) of gravitational waves
(GW). We compute the increase in the number of detected GW events due to GL.
First, we check that geometrical optics is valid for the GW frequency range on
which Earth-based detectors are sensitive, and that this is also partially true
for what concerns the future space-based interferometer LISA. To infer this
result, both the diffraction parameter and a cut-off frequency are computed.
Then, the variation in the number of GW signals is estimated in the general
case, and applied to some lens models: point mass lens and singular isothermal
sphere (SIS profile). An estimation of the magnification factor has also been
done for the softened isothermal sphere and for the King profile. The results
appear to be strongly model-dependent, but in all cases the increase in the
number of detected GW signals is negligible. The use of time delays among
images is also investigated.Comment: Accepted for publication in General Relativity and Gravitatio
Three results on the regularity of the curves that are invariant by an exact symplectic twist map
BEC-BCS crossover in an optical lattice
We present the microscopic theory for the BEC-BCS crossover of an atomic
Fermi gas in an optical lattice, showing that the Feshbach resonance underlying
the crossover in principle induces strong multiband effects. Nevertheless, the
BEC-BCS crossover itself can be described by a single-band model since it
occurs at magnetic fields that are relatively far away from the Feshbach
resonance. A criterion is proposed for the latter, which is obeyed by most
known Feshbach resonances in ultracold atomic gases.Comment: 4 pages, 3 figure
Report on the first round of the Mock LISA Data Challenges
The Mock LISA Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data analysis tools and capabilities, and demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data output. The first round of MLDCs has just been completed: nine challenges consisting of data sets containing simulated gravitational-wave signals produced either by galactic binaries or massive black hole binaries embedded in simulated LISA instrumental noise were released in June 2006 with deadline for submission of results at the beginning of December 2006. Ten groups have participated in this first round of challenges. All of the challenges had at least one entry which successfully characterized the signal to better than 95% when assessed via a correlation with phasing ambiguities accounted for. Here, we describe the challenges, summarize the results and provide a first critical assessment of the entries
Clone size distributions in networks of genetic similarity
We build networks of genetic similarity in which the nodes are organisms
sampled from biological populations. The procedure is illustrated by
constructing networks from genetic data of a marine clonal plant. An important
feature in the networks is the presence of clone subgraphs, i.e. sets of
organisms with identical genotype forming clones. As a first step to understand
the dynamics that has shaped these networks, we point up a relationship between
a particular degree distribution and the clone size distribution in the
populations. We construct a dynamical model for the population dynamics,
focussing on the dynamics of the clones, and solve it for the required
distributions. Scale free and exponentially decaying forms are obtained
depending on parameter values, the first type being obtained when clonal growth
is the dominant process. Average distributions are dominated by the power law
behavior presented by the fastest replicating populations.Comment: 17 pages, 4 figures. One figure improved and other minor changes. To
appear in Physica
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