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

Gravitational Wave Propagation in Isotropic Cosmologies

We study the propagation of gravitational waves carrying arbitrary information through isotropic cosmologies. The waves are modelled as small perturbations of the background Robertson-Walker geometry. The perfect fluid matter distribution of the isotropic background is, in general, modified by small anisotropic stresses. For pure gravity waves, in which the perturbed Weyl tensor is radiative (i.e. type N in the Petrov classification), we construct explicit examples for which the presence of the anisotropic stress is shown to be essential and the histories of the wave-fronts in the background Robertson-Walker geometry are shear-free null hypersurfaces. The examples derived in this case are analogous to the Bateman waves of electromagnetic theory.Comment: 27 pages, accepted for publication in Phys.Rev.

Estimating drizzle drop size and precipitation rate using two-colour lidar measurements

A method to estimate the size and liquid water content of drizzle drops using lidar measurements at two wavelengths is described. The method exploits the differential absorption of infrared light by liquid water at 905 nm and 1.5 μm, which leads to a different backscatter cross section for water drops larger than ≈50 μm. The ratio of backscatter measured from drizzle samples below cloud base at these two wavelengths (the colour ratio) provides a measure of the median volume drop diameter D0. This is a strong effect: for D0=200 μm, a colour ratio of ≈6 dB is predicted. Once D0 is known, the measured backscatter at 905 nm can be used to calculate the liquid water content (LWC) and other moments of the drizzle drop distribution. The method is applied to observations of drizzle falling from stratocumulus and stratus clouds. High resolution (32 s, 36 m) profiles of D0, LWC and precipitation rate R are derived. The main sources of error in the technique are the need to assume a value for the dispersion parameter μ in the drop size spectrum (leading to at most a 35% error in R) and the influence of aerosol returns on the retrieval (≈10% error in R for the cases considered here). Radar reflectivities are also computed from the lidar data, and compared to independent measurements from a colocated cloud radar, offering independent validation of the derived drop size distributions

Light-like Signals in General relativity and Cosmology

The modelling of light-like signals in General Relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon Penrose's hierarchical classification of the geometry induced on the null hypersurface history of the surface by its imbedding in the space-times to the future and to the past of it. The signals are not confined to propagate in a vacuum and thus their interaction with matter (a burst of radiation propagating through a cosmic fluid, for example) is also studied. Results are accompanied by illustrative examples using cosmological models, vacuum space-times, the de sitter univers and Minkowskian space-time.Comment: 21 pages, latex, no figure

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

Simultaneous measurement of forward-backward asymmetry and top polarization in dilepton final states from ttˉt\bar t production at the Tevatron

We present a simultaneous measurement of the forward-backward asymmetry and the top-quark polarization in $t\bar t$ production in dilepton final states using 9.7 fb$^{-1}$ of proton-antiproton collisions at $\sqrt{s}=1.96$ TeV with the D0 detector. To reconstruct the distributions of kinematic observables we employ a matrix element technique that calculates the likelihood of the possible $t\bar t$ kinematic configurations. After accounting for the presence of background events and for calibration effects, we obtain a forward-backward asymmetry of $A^{t\bar t} = (15.0 \pm 6.4 \text{ (stat)} \pm 4.9 \text{ (syst)})\%$ and a top-quark polarization times spin analyzing power in the beam basis of $\kappa P = (7.2 \pm 10.5 \text{ (stat)} \pm 4.2 \text{ (syst)})\%$, with a correlation of $-56\%$ between the measurements. If we constrain the forward-backward asymmetry to its expected standard model value, we obtain a measurement of the top polarization of $\kappa P = (11.3 \pm 9.1 \text{ (stat)} \pm 1.9 \text{ (syst)})\%.$ If we constrain the top polarization to its expected standard model value, we measure a forward-backward asymmetry of $A^{t\bar t} = (17.5 \pm 5.6 \text{ (stat)} \pm 3.1 \text{ (syst)})\%.$ A combination with the D0 $A^{t\bar t}$ measurement in the lepton+jets final state yields an asymmetry of $A^{t\bar t} = (11.8 \pm 2.5 \text{ (stat)} \pm 1.3 \text{ (syst)})\% .$ Within their respective uncertainties, all these results are consistent with the standard model expectations.Comment: 16 pages, 16 figures, published versio

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.

Geodesics in spacetimes with expanding impulsive gravitational waves

We study geodesic motion in expanding spherical impulsive gravitational waves propagating in a Minkowski background. Employing the continuous form of the metric we find and examine a large family of geometrically preferred geodesics. For the special class of axially symmetric spacetimes with the spherical impulse generated by a snapping cosmic string we give a detailed physical interpretation of the motion of test particles.Comment: 12 pages, Revtex, final versio