The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks

We consider a non-autonomous dynamical system formed by coupling two piecewise-smooth systems in \RR^2 through a non-autonomous periodic perturbation. We study the dynamics around one of the heteroclinic orbits of one of the piecewise-smooth systems. In the unperturbed case, the system possesses two $C^0$ normally hyperbolic invariant manifolds of dimension two with a couple of three dimensional heteroclinic manifolds between them. These heteroclinic manifolds are foliated by heteroclinic connections between $C^0$ tori located at the same energy levels. By means of the {\em impact map} we prove the persistence of these objects under perturbation. In addition, we provide sufficient conditions of the existence of transversal heteroclinic intersections through the existence of simple zeros of Melnikov-like functions. The heteroclinic manifolds allow us to define the {\em scattering map}, which links asymptotic dynamics in the invariant manifolds through heteroclinic connections. First order properties of this map provide sufficient conditions for the asymptotic dynamics to be located in different energy levels in the perturbed invariant manifolds. Hence we have an essential tool for the construction of a heteroclinic skeleton which, when followed, can lead to the existence of Arnol'd diffusion: trajectories that, on large time scales, destabilize the system by further accumulating energy. We validate all the theoretical results with detailed numerical computations of a mechanical system with impacts, formed by the linkage of two rocking blocks with a spring

Shear-Free Gravitational Waves in an Anisotropic Universe

We study gravitational waves propagating through an anisotropic Bianchi I dust-filled universe (containing the Einstein-de-Sitter universe as a special case). The waves are modeled as small perturbations of this background cosmological model and we choose a family of null hypersurfaces in this space-time to act as the histories of the wavefronts of the radiation. We find that the perturbations we generate can describe pure gravitational radiation if and only if the null hypersurfaces are shear-free. We calculate the gauge-invariant small perturbations explicitly in this case. How these differ from the corresponding perturbations when the background space-time is isotropic is clearly exhibited.Comment: 32 pages, accepted for publication in Physical Review

Inclusive production of the X(4140)X(4140) state in pp‾p \overline p collisions at D0

We present a study of the inclusive production of the $X(4140)$ with the decay to the $J/\psi \phi$ final state in hadronic collisions. Based on $10.4~\rm{fb^{-1}}$ of $p \overline p$ collision data collected by the D0 experiment at the Fermilab Tevatron collider, we report the first evidence for the prompt production of $X(4140)$ and find the fraction of $X(4140)$ events originating from $b$ hadrons to be $f_b=0.39\pm 0.07 {\rm \thinspace (stat)} \pm 0.10 {\rm \thinspace (syst)}$. The ratio of the non-prompt $X(4140)$ production rate to the $B_s^0$ yield in the same channel is $R=0.19 \pm 0.05 {\rm \thinspace (stat)} \pm 0.07 {\rm \thinspace (syst)}$. The values of the mass $M=4152.5 \pm 1.7 (\rm {stat}) ^{+6.2}_{-5.4} {\rm \thinspace (syst)}$~MeV and width $\Gamma=16.3 \pm 5.6 {\rm \thinspace (stat)} \pm 11.4 {\rm \thinspace (syst)}$~MeV are consistent with previous measurements. 8 pages, 2 figuesComment: Submitted to PRL. * pages, 2 figure

Precise measurement of the top quark mass in dilepton decays using optimized neutrino weighting

We measure the top quark mass in dilepton final states of top-antitop events in proton-antiproton collisions at sqrt(s) = 1.96 TeV, using data corresponding to an integrated luminosity of 9.7 fb^-1 at the Fermilab Tevatron Collider. The analysis features a comprehensive optimization of the neutrino weighting method to minimize the statistical uncertainties. We also improve the calibration of jet energies using the calibration determined in top-antitop to lepton+jets events, which reduces the otherwise limiting systematic uncertainty from the jet energy scale. The measured top quark mass is mt = 173.32 +/- 1.36(stat) +/- 0.85(syst) GeV.Comment: 10 pages, 2 figures, 2 tables, subm. to Phys. Lett.

Scales of the Extra Dimensions and their Gravitational Wave Backgrounds

Circumstances are described in which symmetry breaking during the formation of our three-dimensional brane within a higher-dimensional space in the early universe excites mesoscopic classical radion or brane-displacement degrees of freedom and produces a detectable stochastic background of gravitational radiation. The spectrum of the background is related to the unification energy scale and the the sizes and numbers of large extra dimensions. It is shown that properties of the background observable by gravitational-wave observatories at frequencies $f\approx 10^{-4}$ Hz to $10^3$ Hz contain information about unification on energy scales from 1 to $10^{10}$ TeV, gravity propagating through extra-dimension sizes from 1 mm to $10^{-18}$mm, and the dynamical history and stabilization of from one to seven extra dimensions.Comment: 6 pages, Latex, 1 figure, submitted to Phys. Re