Two isoperimetric inequalities for the Sobolev constant

In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.Comment: 11 page

Structure and Vibrations of the Vicinal Copper (211) Surface

We report a first principles theoretical study of the surface relaxation and lattice dynamics of the Cu(211) surface using the plane wave pseudopotential method. We find large atomic relaxations for the first several atomic layers near the step edges on this surface, and a substantial step-induced renormalization of the surface harmonic force constants. We use the results to study the harmonic fluctuations around the equilibrium structure and find three new step-derived features in the zone center vibrational spectrum. Comparison of these results with previous theoretical work and weith experimental studies using inelastic He scattering are reported.Comment: 6 Pages RevTex, 7 Figures in Postscrip

Prototype scintillator cell for an In-based solar neutrino detector

We describe the work carried out at MPIK to design, model, build and characterize a prototype cell filled with a novel indium-loaded scintillator of interest for real-time low energy solar neutrino spectroscopy. First, light propagation in optical modules was studied with experiments and Monte Carlo simulations. Subsequently a 5 cm x 5 cm x 100 cm prototype detector was set up and the optical performances of several samples were measured. We first tested a benchmark PXE-based scintillator, which performed an attenuation length of ~ 4.2 m and a photo-electron yield of ~ 730 pe/MeV. Then we measured three In-loaded samples. At an In-loading of 44 g/l, an energy resolution of ~ 11.6 % and a spatial resolution of ~ 7 cm were attained for 477 keV recoil electrons. The long-range attenuation length in the cell was ~1.3 m and the estimated photo-electron yield ~ 200 pe/MeV. Light attenuation and relative light output of all tested samples could be reproduced reasonably well by MC. All optical properties of this system have remained stable over a period of > 1 y.Comment: 57 pages, 19 figures, 10 tables elsevier template for manuscript submission submitted to NIMA 10 February 200

Electronic structure of superconducting graphite intercalate compounds: The role of the interlayer state

Although not an intrinsic superconductor, it has been long--known that, when intercalated with certain dopants, graphite is capable of exhibiting superconductivity. Of the family of graphite--based materials which are known to superconduct, perhaps the most well--studied are the alkali metal--graphite intercalation compounds (GIC) and, of these, the most easily fabricated is the C${}_8$K system which exhibits a transition temperature $\bm{T_c\simeq 0.14}$K. By increasing the alkali metal concentration (through high pressure fabrication techniques), the transition temperature has been shown to increase to as much as $\bm 5$K in C${}_2$Na. Lately, in an important recent development, Weller \emph{et al.} have shown that, at ambient conditions, the intercalated compounds \cyb and \cca exhibit superconductivity with transition temperatures $\bm{T_c\simeq 6.5}$K and $\bm{11.5}$K respectively, in excess of that presently reported for other graphite--based compounds. We explore the architecture of the states near the Fermi level and identify characteristics of the electronic band structure generic to GICs. As expected, we find that charge transfer from the intercalant atoms to the graphene sheets results in the occupation of the $\bm\pi$--bands. Yet, remarkably, in all those -- and only those -- compounds that superconduct, we find that an interlayer state, which is well separated from the carbon sheets, also becomes occupied. We show that the energy of the interlayer band is controlled by a combination of its occupancy and the separation between the carbon layers.Comment: 4 Figures. Please see accompanying experimental manuscript "Superconductivity in the Intercalated Graphite Compounds C6Yb and C6Ca" by Weller et a

Characterization of serous retinal detachments in uveitis patients with optical coherence tomography

To determine the prevalence of serous retinal detachments (SRD) using optical coherence tomography (OCT) in a large database of patients with uveitis from a tertiary referral setting, to describe clinical features of patients with SRD, and to ascertain retinal architectural features found in association with SRD. Main outcome measures Prevalence of SRD in uveitis patients imaged with OCT, correlation of visual acuity with SRD, anatomic subtypes of uveitis identified, and association of SRD with various subtypes of macular edema (focal and diffuse) and retinal architectural abnormalities. Design Retrospective, single-setting cross-sectional study of all OCTs in a digital imaging base ordered on patients from a tertiary referral uveitis clinic between July 2006 and March 2008. Results SRD were identified in 17 of 111 uveitis patients (15 %) reviewed; bilateral SRD were found in 5 of 17 patients (29 %). Intermediate uveitis was the most common disease association (47 %), but other conditions identified included Vogt-Koyanagi-Harada syndrome, multifocal choroiditis/panuveitis, and sarcoidosis. Retinal architectural features identified in association with SRD included focal macular edema (59 %), diffuse macular edema (50 %), any intraretinal edema (77 %), both diffuse and focal macular edema (32 %), and retinal pigment epithelial alteration (27 %). Moderate or severe visual impairment, defined as visual acuity 20/50 or poorer was seen in 71 % of patients with SRD. Poorer visual acuity was correlated with increased central subfield thickness in patients with SRD (r2=0.41, p<0.001). Conclusion SRD were present in 15 % of the uveitis patients reviewed. Moderate to severe vision impairment was present in the majority of eyes (71 %) with SRD. Diffuse macular edema and focal cystoid macular edema were the OCT features most commonly associated with SRD. Intermediate and panuveitis were the most common anatomic sites of inflammation. A variety of pathogenic mechanisms, both inflammatory and non-inflammatory, may be involved in SRD in uveitis patients; identification of the precise mechanism is important for appropriate therapy.This work is supported in part by an Unrestricted Grant from Research to Prevent Blindness (Casey Eye Institute, Emory Eye Center), the Stan and Madelle Rosenfeld Family Trust (JTR), the William and Mary Bauman Foundation (JTR), the William C. Kuzell Foundation (JTR), and the Ronald G. Michels Fellowship Foundation (SY)

Ab initio calculations for bromine adlayers on the Ag(100) and Au(100) surfaces: the c(2x2) structure

Ab initio total-energy density-functional methods with supercell models have been employed to calculate the c(2x2) structure of the Br-adsorbed Ag(100) and Au(100) surfaces. The atomic geometries of the surfaces and the preferred bonding sites of the bromine have been determined. The bonding character of bromine with the substrates has also been studied by analyzing the electronic density of states and the charge transfer. The calculations show that while the four-fold hollow-site configuration is more stable than the two-fold bridge-site topology on the Ag(100) surface, bromine prefers the bridge site on the Au(100) surface. The one-fold on-top configuration is the least stable configuration on both surfaces. It is also observed that the second layer of the Ag substrate undergoes a small buckling as a consequence of the adsorption of Br. Our results provide a theoretical explanation for the experimental observations that the adsorption of bromine on the Ag(100) and Au(100) surfaces results in different bonding configurations.Comment: 10 pages, 4 figure, 5 tables, Phys. Rev. B, in pres

Modelling the orbital modulation of ultraviolet resonance lines in high-mass X-ray binaries

The stellar-wind structure in high-mass X-ray binaries (HMXBs) is investigated through modelling of their ultraviolet (UV) resonance lines. For the OB supergiants in two systems, Vela X-1 and 4U1700-37, high-resolution UV spectra are available; for Cyg X-1, SMC X-1, and LMC X-4 low-resolution spectra are used. In order to account for the non-monotonic velocity structure of the stellar wind, a modified version of the Sobolev Exact Integration (SEI) method by Lamers et al. (1987) is applied. The orbital modulation of the UV resonance lines provides information on the size of the Stroemgren zone surrounding the X-ray source. The amplitude of the observed orbital modulation (known as the Hatchett-McCray effect), however, also depends on the density- and velocity structure of the ambient wind. Model profiles are presented that illustrate the effect on the appearance of the HM effect by varying stellar-wind parameters. The q parameter of Hatchett & McCray (1977), as well as other parameters describing the supergiant's wind structure, are derived for the 5 systems. The X-ray luminosity needed to create the observed size of the Stroemgren zone is consistent with the observed X-ray flux. The derived wind parameters are compared to those determined in single OB supergiants of similar spectral type. Our models naturally explain the observed absence of the HM effect in 4U1700-37. The orbital modulation in Vela X-1 indicates that besides the Stroemgren zone other structures are present in the stellar wind (such as a photo-ionization wake). The ratio of the wind velocity and the escape velocity is found to be lower in OB supergiants in HMXBs than in single OB supergiants of the same effective temperature.Comment: 29 pages, good quality figures 11, 12, 13, A2 & B1 available upon request from JvL. Accepted for publication in Astronomy & Astrophysic

Higher-Order Nuclear-Polarizability Corrections in Atomic Hydrogen

Nuclear-polarizability corrections that go beyond unretarded-dipole approximation are calculated analytically for hydrogenic (atomic) S-states. These retardation corrections are evaluated numerically for deuterium and contribute -0.68 kHz, for a total polarization correction of 18.58(7) kHz. Our results are in agreement with one previous numerical calculation, and the retardation corrections completely account for the difference between two previous calculations. The uncertainty in the deuterium polarizability correction is substantially reduced. At the level of 0.01 kHz for deuterium, only three primary nuclear observables contribute: the electric polarizability, $\alpha_E$, the paramagnetic susceptibility, $\beta_M$, and the third Zemach moment, $_{(2)}$. Cartesian multipole decomposition of the virtual Compton amplitude and its concomitant gauge sum rules are used in the analysis.Comment: 26 pages, latex, 1 figure -- Submitted to Phys. Rev. C -- epsfig.sty require

Self-diffusion of adatoms, dimers, and vacancies on Cu(100)

We use ab initio static relaxation methods and semi-empirical molecular-dynamics simulations to investigate the energetics and dynamics of the diffusion of adatoms, dimers, and vacancies on Cu(100). It is found that the dynamical energy barriers for diffusion are well approximated by the static, 0 K barriers and that prefactors do not depend sensitively on the species undergoing diffusion. The ab initio barriers are observed to be significantly lower when calculated within the generalized-gradient approximation (GGA) rather than in the local-density approximation (LDA). Our calculations predict that surface diffusion should proceed primarily via the diffusion of vacancies. Adatoms are found to migrate most easily via a jump mechanism. This is the case, also, of dimers, even though the corresponding barrier is slightly larger than it is for adatoms. We observe, further, that dimers diffuse more readily than they can dissociate. Our results are discussed in the context of recent submonolayer growth experiments of Cu(100).Comment: Submitted to the Physical Review B; 15 pages including postscript figures; see also http://www.centrcn.umontreal.ca/~lewi