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

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.

Astrophysical Effects of Scalar Dark Matter Miniclusters

We model the formation, evolution and astrophysical effects of dark compact Scalar Miniclusters (``ScaMs''). These objects arise when a scalar field, with an axion-like or Higgs-like potential, undergoes a second order phase transition below the QCD scale. Such a scalar field may couple too weakly to the standard model to be detectable directly through particle interactions, but may still be detectable by gravitational effects, such as lensing and baryon accretion by large, gravitationally bound miniclusters. The masses of these objects are shown to be constrained by the Ly$\alpha$ power spectrum to be less than $\sim 10^4 M_\odot$, but they may be as light as classical axion miniclusters, of the order of $10^{-12} M_\odot$. We simulate the formation and nonlinear gravitational collapse of these objects around matter-radiation equality using an N-body code, estimate their gravitational lensing properties, and assess the feasibility of studying them using current and future lensing experiments. Future MACHO-type variability surveys of many background sources can reveal either high-amplification, strong lensing events, or measure density profiles directly via weak-lensing variability, depending on ScaM parameters and survey depth. However, ScaMs, due to their low internal densities, are unlikely to be responsible for apparent MACHO events already detected in the Galactic halo. A simple estimate is made of parameters that would give rise to early structure formation; in principle, early stellar collapse could be triggered by ScaMs as early as recombination, and significantly affect cosmic reionization.Comment: 13 pages, 12 figures. Replaced to reflect published versio

A comparison among four different retrieval methods for ice-cloud properties using data from CloudSat, CALIPSO, and MODIS

The A-Train constellation of satellites provides a new capability to measure vertical cloud profiles that leads to more detailed information on ice-cloud microphysical properties than has been possible up to now. A variational radar–lidar ice-cloud retrieval algorithm (VarCloud) takes advantage of the complementary nature of the CloudSat radar and Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar to provide a seamless retrieval of ice water content, effective radius, and extinction coefficient from the thinnest cirrus (seen only by the lidar) to the thickest ice cloud (penetrated only by the radar). In this paper, several versions of the VarCloud retrieval are compared with the CloudSat standard ice-only retrieval of ice water content, two empirical formulas that derive ice water content from radar reflectivity and temperature, and retrievals of vertically integrated properties from the Moderate Resolution Imaging Spectroradiometer (MODIS) radiometer. The retrieved variables typically agree to within a factor of 2, on average, and most of the differences can be explained by the different microphysical assumptions. For example, the ice water content comparison illustrates the sensitivity of the retrievals to assumed ice particle shape. If ice particles are modeled as oblate spheroids rather than spheres for radar scattering then the retrieved ice water content is reduced by on average 50% in clouds with a reflectivity factor larger than 0 dBZ. VarCloud retrieves optical depths that are on average a factor-of-2 lower than those from MODIS, which can be explained by the different assumptions on particle mass and area; if VarCloud mimics the MODIS assumptions then better agreement is found in effective radius and optical depth is overestimated. MODIS predicts the mean vertically integrated ice water content to be around a factor-of-3 lower than that from VarCloud for the same retrievals, however, because the MODIS algorithm assumes that its retrieved effective radius (which is mostly representative of cloud top) is constant throughout the depth of the cloud. These comparisons highlight the need to refine microphysical assumptions in all retrieval algorithms and also for future studies to compare not only the mean values but also the full probability density function

Probing the Reionization History of the Universe using the Cosmic Microwave Background Polarization

The recent discovery of a Gunn--Peterson (GP) trough in the spectrum of the redshift 6.28 SDSS quasar has raised the tantalizing possibility that we have detected the reionization of the universe. However, a neutral fraction (of hydrogen) as small as 0.1% is sufficient to cause the GP trough, hence its detection alone cannot rule out reionization at a much earlier epoch. The Cosmic Microwave Background (CMB) polarization anisotropy offers an alternative way to explore the dark age of the universe. We show that for most models constrained by the current CMB data and by the discovery of a GP trough (showing that reionization occurred at z > 6.3), MAP can detect the reionization signature in the polarization power spectrum. The expected 1-sigma error on the measurement of the electron optical depth is around 0.03 with a weak dependence on the value of that optical depth. Such a constraint on the optical depth will allow MAP to achieve a 1-sigma error on the amplitude of the primordial power spectrum of 6%. MAP with two years (Planck with one year) of observation can distinguish a model with 50% (6%) partial ionization between redshifts of 6.3 and 20 from a model in which hydrogen was completely neutral at redshifts greater than 6.3. Planck will be able to distinguish between different reionization histories even when they imply the same optical depth to electron scattering for the CMB photons.Comment: ApJ version. Added Figure 2 and reference

Bifurcations of piecewise smooth flows:perspectives, methodologies and open problems

In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking. The clearest results to date concern equilibria undergoing bifurcations at switching boundaries, and limit cycles undergoing grazing and sliding bifurcations. After discussing fundamental concepts, such as topological equivalence of two piecewise smooth systems, discontinuity-induced bifurcations are defined for equilibria and limit cycles. Conditions for equilibria to exist in n-dimensions are given, followed by the conditions under which they generically undergo codimension-one bifurcations. The extent of knowledge of their unfoldings is also summarized. Codimension-one bifurcations of limit cycles and boundary-intersection crossing are described together with techniques for their classification. Codimension-two bifurcations are discussed with suggestions for further study

Holographic Geometry and Noise in Matrix Theory

Using Matrix Theory as a concrete example of a fundamental holographic theory, we show that the emergent macroscopic spacetime displays a new macroscopic quantum structure, holographic geometry, and a new observable phenomenon, holographic noise, with phenomenology similar to that previously derived on the basis of a quasi-monochromatic wave theory. Traces of matrix operators on a light sheet with a compact dimension of size $R$ are interpreted as transverse position operators for macroscopic bodies. An effective quantum wave equation for spacetime is derived from the Matrix Hamiltonian. Its solutions display eigenmodes that connect longitudinal separation and transverse position operators on macroscopic scales. Measurements of transverse relative positions of macroscopically separated bodies, such as signals in Michelson interferometers, are shown to display holographic nonlocality, indeterminacy and noise, whose properties can be predicted with no parameters except $R$. Similar results are derived using a detailed scattering calculation of the matrix wavefunction. Current experimental technology will allow a definitive and precise test or validation of this interpretation of holographic fundamental theories. In the latter case, they will yield a direct measurement of $R$ independent of the gravitational definition of the Planck length, and a direct measurement of the total number of degrees of freedom.Comment: 19 pages, 2 figures; v2: factors of Planck mass written explicitly, typos correcte

Indeterminacy of Holographic Quantum Geometry

An effective theory based on wave optics is used to describe indeterminacy of position in holographic spacetime with a UV cutoff at the Planck scale. Wavefunctions describing spacetime positions are modeled as complex disturbances of quasi-monochromatic radiation. It is shown that the product of standard deviations of two position wavefunctions in the plane of a holographic light sheet is equal to the product of their normal separation and the Planck length. For macroscopically separated positions the transverse uncertainty is much larger than the Planck length, and is predicted to be observable as a "holographic noise" in relative position with a distinctive shear spatial character, and an absolutely normalized frequency spectrum with no parameters once the fundamental wavelength is fixed from the theory of gravitational thermodynamics. The spectrum of holographic noise is estimated for the GEO600 interferometric gravitational-wave detector, and is shown to approximately account for currently unexplained noise between about 300 and 1400Hz. In a holographic world, this result directly and precisely measures the fundamental minimum interval of time.Comment: 4 pages, LaTeX. Considerably shortened from earlier version. Conclusions are unchanged. Submitted to PR