The Biot-Savart operator and electrodynamics on subdomains of the three-sphere

We study steady-state magnetic fields in the geometric setting of positive curvature on subdomains of the three-dimensional sphere. By generalizing the Biot-Savart law to an integral operator BS acting on all vector fields, we show that electrodynamics in such a setting behaves rather similarly to Euclidean electrodynamics. For instance, for current J and magnetic field BS(J), we show that Maxwell's equations naturally hold. In all instances, the formulas we give are geometrically meaningful: they are preserved by orientation-preserving isometries of the three-sphere. This article describes several properties of BS: we show it is self-adjoint, bounded, and extends to a compact operator on a Hilbert space. For vector fields that act like currents, we prove the curl operator is a left inverse to BS; thus the Biot-Savart operator is important in the study of curl eigenvalues, with applications to energy-minimization problems in geometry and physics. We conclude with two examples, which indicate our bounds are typically within an order of magnitude of being sharp.Comment: 24 pages (was 28 pages) Revised to include a new introduction, a detailed example, and results about helicity; other changes for readabilit

UGC 3995: A Close Pair of Spiral Galaxies

UGC 3995 is a close pair of spiral galaxies whose eastern component hosts a Seyfert 2 nucleus. We present a detailed analysis of this system using long slit spectroscopy and narrow (\ha + \nii) as well as broad band (B, R) imaging and an archive WFPC2 image. The component galaxies reveal surprisingly small signs of interaction considering their spatial proximity and almost identical recession velocities, as the bright filament is probably an optical illusion due to the superposition of the bar of the Seyfert galaxy and of the spiral arms of the companion. The broad band morphology, a B--R color map, and a continuum-subtracted \ha + \nii image demonstrate that the western component UGC 3995B is in front of the Seyfert-hosting component UGC 3995A, partly obscuring its western side. The small radial velocity difference leaves the relative motion of the two galaxies largely unconstrained. The observed lack of major tidal deformations, along with some morphological peculiarities, suggests that the galaxies are proximate in space but may have recently approached each other on the plane of the sky. The geometry of the system and the radial velocity curve at P. A. = 106 suggest that the encounter may be retrograde or, alternatively, prograde before perigalacticon. The partial overlap of the two galaxies allows us to estimate the optical thickness of the disk of component B. We derive an extinction = 0.18 visual magnitudes in the infra-arms parts of the foreground galaxy disk, and >= 1-1.5 visual magnitudes in correspondence of the spiral arms.Comment: Accepted for publication in the Astronomical Journal (June 1999 issue

Standard monomial theory for wonderful varieties

A general setting for a standard monomial theory on a multiset is introduced and applied to the Cox ring of a wonderful variety. This gives a degeneration result of the Cox ring to a multicone over a partial flag variety. Further, we deduce that the Cox ring has rational singularities.Comment: v3: 20 pages, final version to appear on Algebras and Representation Theory. The final publication is available at Springer via http://dx.doi.org/10.1007/s10468-015-9586-z. v2: 20 pages, examples added in Section 3 and in Section

ALLSMOG: an APEX Low-redshift Legacy Survey for MOlecular Gas. I - molecular gas scaling relations, and the effect of the CO/H2 conversion factor

We present ALLSMOG, the APEX Low-redshift Legacy Survey for MOlecular Gas. ALLSMOG is a survey designed to observe the CO(2-1) emission line with the APEX telescope, in a sample of local galaxies (0.01 < z < 0.03), with stellar masses in the range 8.5 < log(M*/Msun) < 10. This paper is a data release and initial analysis of the first two semesters of observations, consisting of 42 galaxies observed in CO(2-1). By combining these new CO(2-1) emission line data with archival HI data and SDSS optical spectroscopy, we compile a sample of low-mass galaxies with well defined molecular gas masses, atomic gas masses, and gas-phase metallicities. We explore scaling relations of gas fraction and gas consumption timescale, and test the extent to which our findings are dependent on a varying CO/H2 conversion factor. We find an increase in the H2/HI mass ratio with stellar mass which closely matches semi-analytic predictions. We find a mean molecular gas fraction for ALLSMOG galaxies of MH2/M* = (0.09 - 0.13), which decreases with stellar mass. We measure a mean molecular gas consumption timescale for ALLSMOG galaxies of 0.4 - 0.7 Gyr. We also confirm the non-universality of the molecular gas consumption timescale, which varies (with stellar mass) from ~100 Myr to ~2 Gyr. Importantly, we find that the trends in the H2/HI mass ratio, gas fraction, and the non-universal molecular gas consumption timescale are all robust to a range of recent metallicity-dependent CO/H2 conversion factors.Comment: 25 pages, 15 figures. Accepted for publication in MNRA

Nonequilibrium dynamics of a simple stochastic model

We investigate the low-temperature dynamics of a simple stochastic model, introduced recently in the context of the physics of glasses. The slowest characteristic time at equilibrium diverges exponentially at low temperature. On smaller time scales, the nonequilibrium dynamics of the system exhibits an aging regime. We present an analytical study of the scaling behaviour of the mean energy, of its local correlation and response functions, and of the associated fluctuation-dissipation ratio throughout the regime of low temperature and long times. This analysis includes the aging regime, the convergence to equilibrium, and the crossover behaviour between them.Comment: 36 pages, plain tex, 7 figures, to be published by Journal of Physics

Eosinophil and T Cell Markers Predict Functional Decline in COPD Patients

BACKGROUND. The major marker utilized to monitor COPD patients is forced expiratory volume in one second (FEV1). However, asingle measurement of FEV1 cannot reliably predict subsequent decline. Recent studies indicate that T lymphocytes and eosinophils are important determinants of disease stability in COPD. We therefore measured cytokine levels in the lung lavage fluid and plasma of COPD patients in order to determine if the levels of T cell or eosinophil related cytokines were predictive of the future course of the disease. METHODS. Baseline lung lavage and plasma samples were collected from COPD subjects with moderately severe airway obstruction and emphysematous changes on chest CT. The study participants were former smokers who had not had a disease exacerbation within the past six months or used steroids within the past two months. Those subjects who demonstrated stable disease over the following six months (ΔFEV1 % predicted = 4.7 ± 7.2; N = 34) were retrospectively compared with study participants who experienced a rapid decline in lung function (ΔFEV1 % predicted = -16.0 ± 6.0; N = 16) during the same time period and with normal controls (N = 11). Plasma and lung lavage cytokines were measured from clinical samples using the Luminex multiplex kit which enabled the simultaneous measurement of several T cell and eosinophil related cytokines. RESULTS AND DISCUSSION. Stable COPD participants had significantly higher plasma IL-2 levels compared to participants with rapidly progressive COPD (p = 0.04). In contrast, plasma eotaxin-1 levels were significantly lower in stable COPD subjects compared to normal controls (p < 0.03). In addition, lung lavage eotaxin-1 levels were significantly higher in rapidly progressive COPD participants compared to both normal controls (p < 0.02) and stable COPD participants (p < 0.05). CONCLUSION. These findings indicate that IL-2 and eotaxin-1 levels may be important markers of disease stability in advanced emphysema patients. Prospective studies will need to confirm whether measuring IL-2 or eotaxin-1 can identify patients at risk for rapid disease progression.National Heart, Lung, and Blood Institute (NO1-HR-96140, NO1-HR-96141-001, NO1-HR-96144, NO1-HR-96143; NO1-HR-96145; NO1-HR-96142, R01HL086936-03); The Flight Attendant Medical Research Institute; the Jo-Ann F. LeBuhn Center for Chest Diseas

Relation Between the Thickness of Stellar Disks and the Relative Mass of Dark Halo in Galaxies

We consider a thickness of stellar disks of late-type galaxies by analyzing the R and K_s band photometric profiles for two independent samples of edge-on galaxies. The main goal is to verify a hypotesis that a thickness of old stellar disks is related to the relative masses of the spherical and disk components of galaxies. We confirm that the radial-to-vertical scale length ratio for galactic disks increases (the disks become thinner) with the increasing of total mass-to-light ratio of the galaxies, which characterize the contribution of dark halo to the total mass, and with the decreasing of central deprojected disk brightness (surface density). Our results are in good agreement with numerical models of collisionless disks evolved from subcritical velocity dispersion state to a marginally stable equilibrium state. This suggests that in most galaxies the vertical stellar velocity dispersion, which determine the equilibrium disk thickness, is close to the minimum value, that ensures disk stability. The thinnest edge-on disks appear to be low brightness galaxies (after deprojection) in which a dark halo mass far exceeds a mass of the stellar disk.Comment: 13 pages. To be Published in Astronomy Letters, v.28(2002