A Compactness Theorem for Riemannian Manifolds with Boundary and Applications

In this paper we prove weak L^{1,p} (and thus C^{\alpha}) compactness for the class of uniformly mean-convex Riemannian n-manifolds with boundary satisfying bounds on curvature quantities, diameter, and (n-1)-volume of the boundary. We obtain two stability theorems from the compactness result. The first theorem applies to 3-manifolds (contained in the aforementioned class) that have Ricci curvature close to 0 and whose boundaries are Gromov-Hausdorff close to a fixed metric on S^2 with positive curvature. Such manifolds are C^{\alpha} close to the region enclosed by a Weyl embedding of the fixed metric into \R^3. The second theorem shows that a 3-manifold with Ricci curvature close to 0 (resp. -2, 2) and mean curvature close to 2 (resp. 2\sqrt 2, 0) is C^{\alpha} close to a metric ball in the space form of constant curvature 0 (resp -1, 1), provided that the boundary is a topological sphere.Comment: 17 pages; comments welcom

Cosmic Microwave and Infrared Backgrounds cross-correlation for ISW detection

We investigate the cross-correlation between the cosmic infrared and microwave backgrounds (CIB & CMB) anisotropies through the integrated Sachs-Wolfe effect. We first describe the CIB anisotropies using a linearly biased power spectrum, then derive the theoretical angular power spectrum of the CMB-CIB cross-correlation for different instruments and frequencies. We discuss the detectability of the ISW signal by performing a signal-to-noise (SNR) analysis with our predicted spectra. The significances obtained range from 6{\sigma} to 7{\sigma} in an ideal case, depending on the frequency ; in realistic cases which account for the presence of noise including astrophysical contaminants, the results span the range 2-5{\sigma}, depending strongly on the major contribution to the noise term.Comment: 4 pages, 1 table. Contribution to the proceedings of the International Conference on Gravitation and Cosmology, Goa, India, December, 201

21st century social work: reducing re-offending - key practice skills

This literature review was commissioned by the Scottish Executive’s Social Work Services Inspectorate in order to support the work of the 21st Century Social Work Review Group. Discussions in relation to the future arrangements for criminal justice social work raised issues about which disciplines might best encompass the requisite skills for reducing re-offending in the community. Rather than starting with what is known or understood about the skills of those professionals currently involved in such interventions, this study sought to start with the research evidence on effective work with offenders to reduce re-offending and then work its way back to the skills required to promote this outcome

Squeeze-Film Flow in the Presence of a Thin Porous Bed, with Application to the Human Knee Joint

Motivated by the desire for a better understanding of the lubrication of the human knee joint, the squeeze-film flow of a thin layer of Newtonian fluid (representing the synovial fluid) filling the gap between a flat impermeable surface (representing the femoral condyles) and a flat thin porous bed (representing the articular cartilage) coating a stationary flat impermeable surface (representing the tibial plateau) is considered. As the impermeable surface approaches the porous bed under a prescribed constant load all of the fluid is squeezed out of the gap in a finite contact time. In the context of the knee, the size of this contact time suggests that when a person stands still for a short period of time their knees may be fluid lubricated, but that when they stand still for a longer period of time contact between the cartilage-coated surfaces may occur. The fluid particle paths are calculated, and the penetration depths of fluid particles into the porous bed are determined. In the context of the knee, these penetration depths provide a measure of how far into the cartilage nutrients are carried by the synovial fluid, and suggest that when a person stands still nutrients initially in the fluid layer penetrate only a relatively small distance into the cartilage. However, the model also suggests that the cumulative effect of repeated loading and unloading of the knees during physical activity such as walking or running may be sufficient to carry nutrients deep into the cartilage

The use of music in the Elizabethan theatre: an enquiry into the dramatic value of the musical element in the drama of the Elizabethan period

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Disc wind models for FU Ori objects

We present disc wind models aimed at reproducing the main features of the strong Na I resonance line P-Cygni profiles in the rapidly-accreting pre-main sequence FU Ori objects. We conducted Monte Carlo radiative transfer simulations for a standard magnetocentrifugally driven wind (MHD) model and our own "Genwind" models, which allows for a more flexible wind parameterisation. We find that the fiducial MHD wind and similar Genwind models, which have flows emerging outward from the inner disc edge, and thus have polar cavities with no absorbing gas, cannot reproduce the deep, wide Na I absorption lines in FU Ori objects viewed at low inclination. We find that it is necessary to include an "inner wind" to fill this polar cavity to reproduce observations. In addition, our models assuming pure scattering source functions in the Sobolev approximation at intermediate viewing angles ($30^{\circ} \lesssim i \lesssim 60^{\circ}$) do not yield sufficiently deep line profiles. Assuming complete absorption yields better agreement with observations, but simple estimates strongly suggest that pure scattering should be a much better approximation. The discrepancy may indicate that the Sobolev approximation is not applicable, possibly due to turbulence or non-monotonic velocity fields; there is some observational evidence for the latter. Our results provide guidance for future attempts to constrain FU Ori wind properties using full MHD wind simulations, by pointing to the importance of the boundary conditions necessary to give rise to an inner wind, and by suggesting that the winds must be turbulent to produce sufficiently deep line profiles.Comment: 12 pages, 17 figures, accepted for publication in MNRA