Proof of the Thin Sandwich Conjecture

We prove that the Thin Sandwich Conjecture in general relativity is valid, provided that the data $(g_{ab},\dot g_{ab})$ satisfy certain geometric conditions. These conditions define an open set in the class of possible data, but are not generically satisfied. The implications for the ``superspace'' picture of the Einstein evolution equations are discussed.Comment: 8 page

Weak Lensing with SDSS Commissioning Data: The Galaxy-Mass Correlation Function To 1/h Mpc

(abridged) We present measurements of galaxy-galaxy lensing from early commissioning imaging data from the Sloan Digital Sky Survey (SDSS). We measure a mean tangential shear around a stacked sample of foreground galaxies in three bandpasses out to angular radii of 600'', detecting the shear signal at very high statistical significance. The shear profile is well described by a power-law. A variety of rigorous tests demonstrate the reality of the gravitational lensing signal and confirm the uncertainty estimates. We interpret our results by modeling the mass distributions of the foreground galaxies as approximately isothermal spheres characterized by a velocity dispersion and a truncation radius. The velocity dispersion is constrained to be 150-190 km/s at 95% confidence (145-195 km/s including systematic uncertainties), consistent with previous determinations but with smaller error bars. Our detection of shear at large angular radii sets a 95% confidence lower limit $s>140^{\prime\prime}$, corresponding to a physical radius of $260h^{-1}$ kpc, implying that galaxy halos extend to very large radii. However, it is likely that this is being biased high by diffuse matter in the halos of groups and clusters. We also present a preliminary determination of the galaxy-mass correlation function finding a correlation length similar to the galaxy autocorrelation function and consistency with a low matter density universe with modest bias. The full SDSS will cover an area 44 times larger and provide spectroscopic redshifts for the foreground galaxies, making it possible to greatly improve the precision of these constraints, measure additional parameters such as halo shape, and measure the properties of dark matter halos separately for many different classes of galaxies.Comment: 28 pages, 11 figures, submitted to A

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Search for top squark pair production using dilepton final states in pp collision data collected at root s=13TeV

A search is presented for supersymmetric partners of the top quark (top squarks) in final states with two oppositely charged leptons (electrons or muons), jets identified as originating from bquarks, and missing transverse momentum. The search uses data from proton-proton collisions at root s = 13 TeV collected with the CMS detector, corresponding to an integrated luminosity of 137 fb(-1). Hypothetical signal events are efficiently separated from the dominant top quark pair production background with requirements on the significance of the missing transverse momentum and on transverse mass variables. No significant deviation is observed from the expected background. Exclusion limits are set in the context of simplified supersymmetric models with pair-produced lightest top squarks. For top squarks decaying exclusively to a top quark and a lightest neutralino, lower limits are placed at 95% confidence level on the masses of the top squark and the neutralino up to 925 and 450 GeV, respectively. If the decay proceeds via an intermediate chargino, the corresponding lower limits on the mass of the lightest top squark are set up to 850 GeV for neutralino masses below 420 GeV. For top squarks undergoing a cascade decay through charginos and sleptons, the mass limits reach up to 1.4 TeV and 900 GeV respectively for the top squark and the lightest neutralino.Peer reviewe

Measurement of the Higgs boson production rate in association with top quarks in final states with electrons, muons, and hadronically decaying tau leptons at s√=13TeV

The rate for Higgs (H) bosons production in association with either one (tH) or two (tt¯H) top quarks is measured in final states containing multiple electrons, muons, or tau leptons decaying to hadrons and a neutrino, using proton–proton collisions recorded at a center-of-mass energy of 13TeV by the CMS experiment. The analyzed data correspond to an integrated luminosity of 137fb−1. The analysis is aimed at events that contain H→WW, H→ττ, or H→ZZ decays and each of the top quark(s) decays either to lepton+jets or all-jet channels. Sensitivity to signal is maximized by including ten signatures in the analysis, depending on the lepton multiplicity. The separation among tH, tt¯H, and the backgrounds is enhanced through machine-learning techniques and matrix-element methods. The measured production rates for the tt¯H and tH signals correspond to 0.92±0.19(stat)+0.17−0.13(syst) and 5.7±2.7(stat)±3.0(syst) of their respective standard model (SM) expectations. The corresponding observed (expected) significance amounts to 4.7 (5.2) standard deviations for tt¯H, and to 1.4 (0.3) for tH production. Assuming that the Higgs boson coupling to the tau lepton is equal in strength to its expectation in the SM, the coupling yt of the Higgs boson to the top quark divided by its SM expectation, κt=yt/ySMt, is constrained to be within −0.9<κt<−0.7 or 0.7<κt<1.1, at 95% confidence level. This result is the most sensitive measurement of the tt¯H production rate to date.SCOAP