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 $d$-dimensional annulus or for the Tonelli Hamiltonian flows defined on a cotangent bundle $T^*M$. 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

Excitonic and Quasiparticle Life Time Effects on Silicon Electron Energy Loss Spectrum from First Principles

The quasiparticle decays due to electron-electron interaction in silicon are studied by means of first-principles all-electron GW approximation. The spectral function as well as the dominant relaxation mechanisms giving rise to the finite life time of quasiparticles are analyzed. It is then shown that these life times and quasiparticle energies can be used to compute the complex dielectric function including many-body effects without resorting to empirical broadening to mimic the decay of excited states. This method is applied for the computation of the electron energy loss spectrum of silicon. The location and line shape of the plasmon peak are discussed in detail.Comment: 4 pages, 3 figures, submitted to PR

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}

Is MS1054-03 an exceptional cluster? A new investigation of ROSAT/HRI X-ray data

We reanalyzed the ROSAT/HRI observation of MS1054-03, optimizing the channel HRI selection and including a new exposure of 68 ksec. From a wavelet analysis of the HRI image we identify the main cluster component and find evidence for substructure in the west, which might either be a group of galaxies falling onto the cluster or a foreground source. Our 1-D and 2-D analysis of the data show that the cluster can be fitted well by a classical betamodel centered only 20arcsec away from the central cD galaxy. The core radius and beta values derived from the spherical model(beta = 0.96_-0.22^+0.48) and the elliptical model (beta = 0.73+/-0.18) are consistent. We derived the gas mass and total mass of the cluster from the betamodel fit and the previously published ASCA temperature (12.3^{+3.1}_{-2.2} keV). The gas mass fraction at the virial radius is fgas = (14[-3,+2.5]+/-3)% for Omega_0=1, where the errors in brackets come from the uncertainty on the temperature and the remaining errors from the HRI imaging data. The gas mass fraction computed for the best fit ASCA temperature is significantly lower than found for nearby hot clusters, fgas=20.1pm 1.6%. This local value can be matched if the actual virial temperature of MS1054-032 were close to the lower ASCA limit (~10keV) with an even lower value of 8 keV giving the best agreement. Such a bias between the virial and measured temperature could be due to the presence of shock waves in the intracluster medium stemming from recent mergers. Another possibility, that reconciles a high temperature with the local gas mass fraction, is the existence of a non zero cosmological constant.Comment: 12 pages, 5 figures, accepted for publication in Ap

Incompatibility boundaries for properties of community partitions

We prove the incompatibility of certain desirable properties of community partition quality functions. Our results generalize the impossibility result of [Kleinberg 2003] by considering sets of weaker properties. In particular, we use an alternative notion to solve the central issue of the consistency property. (The latter means that modifying the graph in a way consistent with a partition should not have counterintuitive effects). Our results clearly show that community partition methods should not be expected to perfectly satisfy all ideally desired properties. We then proceed to show that this incompatibility no longer holds when slightly relaxed versions of the properties are considered, and we provide in fact examples of simple quality functions satisfying these relaxed properties. An experimental study of these quality functions shows a behavior comparable to established methods in some situations, but more debatable results in others. This suggests that defining a notion of good partition in communities probably requires imposing additional properties.Comment: 17 pages, 3 figure