Approximations of Sobolev norms in Carnot groups

This paper deals with a notion of Sobolev space $W^{1,p}$ introduced by J.Bourgain, H.Brezis and P.Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by A.Ponce to obtain a Poincar\'e-type inequality. The main results that we present are a generalization of these two works to a non-Euclidean setting, namely that of Carnot groups. We show that the seminorm expressd in terms of the intrinsic distance is equivalent to the $L^p$ norm of the intrinsic gradient, and provide a Poincar\'e-type inequality on Carnot groups by means of a constructive approach which relies on one-dimensional estimates. Self-improving properties are also studied for some cases of interest

3D MHD Simulations of Planet Migration in Turbulent Stratified Disks

We performed 3D MHD simulations of planet migration in stratified disks using the Godunov code PLUTO, where the disk is turbulent due to the magnetorotational instability. We study the migration for planets with different planet-star mass ratios $q=M_{p}/M_{s}$. In agreement with previous studies, for the low-mass planet cases ($q=5\times10^{-6}$ and $10^{-5}$), migration is dominated by random fluctuations in the torque. For a Jupiter-mass planet $(q=M_{p}/M_{s}=10^{-3}$ for $M_{s}=1M_{\odot})$, we find a reduction of the magnetic stress inside the orbit of the planet and around the gap region. After an initial stage where the torque on the planet is positive, it reverses and we recover migration rates similar to those found in disks where the turbulent viscosity is modelled by an $\alpha$ viscosity. For the intermediate-mass planets ($q=5\times10^{-5}, 10^{-4}$ and $2\times10^{-4}$) we find a new and so far unexpected behavior. In some cases they experience sustained and systematic outwards migration for the entire duration of the simulation. For this case, the horseshoe region is resolved and torques coming from the corotation region can remain unsaturated due to the stresses in the disk. These stresses are generated directly by the magnetic field. The magnitude of the horseshoe drag can overcome the negative Lindblad contribution when the local surface density profile is flat or increasing outwards, which we see in certain locations in our simulations due to the presence of a zonal flow. The intermediate-mass planet is migrating radially outwards in locations where there is a positive gradient of a pressure bump (zonal flow).Comment: Accepted for publication in Ap

Collective Sideband Cooling in an Optical Ring Cavity

We propose a cavity based laser cooling and trapping scheme, providing tight confinement and cooling to very low temperatures, without degradation at high particle densities. A bidirectionally pumped ring cavity builds up a resonantly enhanced optical standing wave which acts to confine polarizable particles in deep potential wells. The particle localization yields a coupling of the degenerate travelling wave modes via coherent photon redistribution. This induces a splitting of the cavity resonances with a high frequency component, that is tuned to the anti-Stokes Raman sideband of the particles oscillating in the potential wells, yielding cooling due to excess anti-Stokes scattering. Tight confinement in the optical lattice together with the prediction, that more than 50% of the trapped particles can be cooled into the motional ground state, promise high phase space densities.Comment: 4 pages, 1 figur

Dusty OB stars in the Small Magellanic Cloud - II: Extragalactic Disks or Examples of the Pleiades Phenomenon?

We use mid-infrared Spitzer spectroscopy and far-infrared Herschel photometry for a sample of twenty main sequence O9--B2 stars in the Small Magellanic Cloud (SMC) with strong 24 micron excesses to investigate the origin of the mid-IR emission. Either debris disks around the stars or illuminated patches of dense interstellar medium (ISM) can cause such mid-IR emission. In a companion paper, Paper I, we use optical spectroscopy to show that it is unlikely for any of these sources to be classical Be stars or Herbig Ae/Be stars. We focus our analysis on debris disks and cirrus hot spots. We find three out of twenty stars to be significantly extended in the mid-IR, establishing them as cirrus hot spots. We then fit the IR spectral energy distributions to determine dust temperatures and masses. We find the dust masses in the SMC stars to be larger than for any known debris disks, although this evidence against the debris disk hypothesis is circumstantial. Finally, we created a local comparison sample of bright mid-IR OB stars in the Milky Way (MW) by cross-matching the WISE and Hipparcos catalogs. All such local stars in the appropriate luminosity range that can be unambiguously classified are young stars with optical emission lines or are spatially resolved by WISE with sizes too large to be plausible debris disk candidates. We conclude that the very strong mid-IR flux excesses are most likely explained as cirrus hot spots, although we cannot rigorously rule out that a small fraction of the sample is made up of debris disks or transition disks. We present suggestive evidence that bow-shock heating around runaway stars may be a contributing mechanism to the interstellar emission. These sources, interpreted as cirrus hot spots, offer a new localised probe of diffuse interstellar dust in a low metallicity environment. (Abridged)Comment: Accepted for publication in ApJ, 23 pages, 11 figures, 8 table

Diffractive Phenomena and Shadowing in Deep-Inelastic Scattering

Shadowing effects in deep-inelastic lepton-nucleus scattering probe the mass spectrum of diffractive leptoproduction from individual nucleons. We explore this relationship using current experimental information on both processes. In recent data from the NMC and E665 collaboration, taken at small x << 0.1 and Q^2 < 1 GeV^2, shadowing is dominated by the diffractive excitation and coherent interaction of low mass vector mesons. If shadowing is explored at small x > 1 GeV^2 as discussed at HERA, the situation is different. Here dominant contributions come from the coherent interaction of diffractively produced heavy mass states. Furthermore we observe that the energy dependence of shadowing is directly related to the mass dependence of the diffractive production cross section for free nucleon targets.Comment: 12 pages Latex, 8 figure

Ab initio Calculations of Multilayer Relaxations of Stepped Cu Surfaces

We present trends in the multilayer relaxations of several vicinals of Cu(100) and Cu(111) of varying terrace widths and geometry. The electronic structure calculations are based on density functional theory in the local density approximation with norm-conserving, non-local pseudopotentials in the mixed basis representation. While relaxations continue for several layers, the major effect concentrates near the step and corner atoms. On all surfaces the step atoms contract inwards, in agreement with experimental findings. Additionally, the corner atoms move outwards and the atoms in the adjacent chain undergo large inward relaxation. Correspondingly, the largest contraction (4%) is in the bond length between the step atom and its bulk nearest neighbor (BNN), while that between the corner atom and BNN is somewhat enlarged. The surface atoms also display changes in registry of upto 1.5%. Our results are in general in good agreement with LEED data including the controversial case of Cu(511). Subtle differences are found with results obtained from semi-empirical potentials.Comment: 21 pages and 3 figure

Large dust particles in disks around T Tauri stars

We present 7-mm continuum observations of 14 low-mass pre-main-sequence stars in the Taurus-Auriga star-forming region obtained with the Very Large Array with ~1.5" resolution and ~0.3 mJy rms sensitivity. For 10 objects, the circumstellar emission has been spatially resolved. The large outer disk radii derived suggest that the emission at this wavelength is mostly optically thin. The millimetre spectral energy distributions are characterised by spectral indices alpha = 2.3 to 3.2. After accounting for contribution from free-free emission and corrections for optical depth, we determine dust opacity indices beta in the range 0.5 to 1.6, which suggest that millimetre-sized dust aggregates are present in the circumstellar disks. Four of the sources with beta > 1 may be consistent with submicron-sized dust as found in the interstellar medium. Our findings indicate that dust grain growth to millimetre-sized particles is completed within less than 1 Myr for the majority of circumstellar disks.Comment: 11 pages, 4 figure

Grain growth and dust settling in a brown dwarf disk: Gemini/T-ReCS observations of CFHT-BD-Tau 4

We present accurate mid-infrared observations of the disk around the young, bona-fide brown dwarf CFHT-BD-Tau 4. We report GEMINI/T-ReCS measurements in the 7.9, 10.4 and 12.3 micron filters, from which we infer the presence of a prominent, broad silicate emission feature. The shape of the silicate feature is dominated by emission from 2 micron amorphous olivine grains. Such grains, being an order of magnitude larger than those in the interstellar medium, are a first proof of dust processing and grain growth in disks around brown dwarfs. The object's spectral energy distribution is below the prediction of the classical flared disk model but higher than that of the two-layer flat disk. A good match can be achieved by using an intermediate disk model with strongly reduced but non-zero flaring. Grain growth and dust settling processes provide a natural explanation for this disk geometry and we argue that such intermediate flaring might explain the observations of several other brown dwarf disks as well.Comment: Accepted for publication in Astronomy & Astrophysics Letters, 4.5 pages with 1 figur

Diffraction of complex molecules by structures made of light

We demonstrate that structures made of light can be used to coherently control the motion of complex molecules. In particular, we show diffraction of the fullerenes C60 and C70 at a thin grating based on a standing light wave. We prove experimentally that the principles of this effect, well known from atom optics, can be successfully extended to massive and large molecules which are internally in a thermodynamic mixed state and which do not exhibit narrow optical resonances. Our results will be important for the observation of quantum interference with even larger and more complex objects.Comment: 4 pages, 3 figure