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

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

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

Stellar Populations and Mass-Loss in M15: A Spitzer Detection of Dust in the Intra-Cluster Medium

We present Spitzer Space Telescope IRAC and MIPS observations of the galactic globular cluster M15 (NGC 7078), one of the most metal-poor clusters with a [Fe/H] = -2.4. Our Spitzer images reveal a population of dusty red giants near the cluster center, a previously detected planetary nebula (PN) designated K648, and a possible detection of the intra-cluster medium (ICM) arising from mass loss episodes from the evolved stellar population. Our analysis suggests 9 (+/-2) x 10^-4 solar masses of dust is present in the core of M15, and this material has accumulated over a period of approximately 10^6 years, a timescale ten times shorter than the last galactic plane crossing event. We also present Spitzer IRS follow up observations of K648, including the detection of the [NeII] 12.81 micron line, and discuss abundances derived from infrared fine structure lines.Comment: Accepted for publication in AJ. 20 pages, 10 figures, 6 tables. Full resolution versions of figures 1, 5, 7, and 8 are available in a PDF version of this manuscript at http://ir.astro.umn.edu/~mboyer/ms_060906.pd

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

Editorial: crime patterns in time and space: the dynamics of crime opportunities in urban areas

The routine activity approach and associated crime pattern theory emphasise how crime emerges from spatio-temporal routines. In order to understand this crime should be studied in both space and time. However, the bulk of research into crime patterns and related activities has investigated the spatial distributions of crime, neglecting the temporal dimension. Specifically, disaggregation of crime by place and by time, for example hour of day, day of week, month of year, season, or school day versus none school day, is extremely relevant to theory. Modern data make such spatio-temporal disaggregation increasingly feasible, as exemplified in this special issue. First, much larger data files allow disaggregation of crime data into temporal and spatial slices. Second, new forms of data are generated by modern technologies, allowing innovative and new forms of analyses. Crime pattern analyses and routine activity inquiries are now able to explore avenues not previously available. The unique collection of nine papers in this thematic issue specifically examine spatio-temporal patterns of crime to; demonstrate the value of this approach for advancing knowledge in the field; consider how this informs our theoretical understanding of the manifestations of crime in time and space; to consider the prevention implications of this; and to raise awareness of the need for further spatio-temporal research into crime event

Development of Evidence-Based Chinese Medicine Clinical Service Recommendations for Cancer Palliative Care Using Delphi Approach Based on the Evidence to Decision Framework.

Objectives: Existing evidence supports the use of certain Chinese medicine (CM) interventions for symptom management among palliative cancer patients. However, evidence-based service recommendations tailored to the local context are needed for CM planning and implementation. In response, we aimed to establish consensus on CM clinical service recommendations for cancer palliative care among Hong Kong experts. Methods: Seven CM interventions showing statistically significant favorable results in existing systematic reviews (SRs) and overviews of SRs were subjected to a GRADE-ADOLOPMENT-based 2-round Delphi survey. Twelve Hong Kong experts in cancer palliative care, including conventionally trained physicians, CM practitioners, and nurses (n = 4 from each category), were invited to participate. Use of the Evidence to Decision framework within the GRADE-ADOLOPMENT approach enabled experts to consider aspects of problem priority, benefits, harms, equity, acceptability, and feasibility when making CM recommendations in cancer palliative care. Results: Three evidence-based CM interventions reached positive consensus as service recommendations, namely: (1) acupuncture for reducing fatigue among palliative cancer patients; (2) acupressure for reducing fatigue among palliative cancer patients; and (3) moxibustion for reducing nausea and vomiting among patients receiving chemotherapy. Median rating of recommendation ranged from 2.5 to 3.0 (interquartile range = 0.00-1.00) on a 4-point Likert-type scale, and the percentage agreement ranged from 83.4% to 91.7%. Conclusions: The GRADE-ADOLOPMENT approach facilitates a consensus-based process of reaching 3 evidence-based CM recommendations for cancer palliative care. Future studies may develop tailored strategies to implement these recommendations in the Hong Kong health system

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

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