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

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

Three fermions with six single particle states can be entangled in two inequivalent ways

Using a generalization of Cayley's hyperdeterminant as a new measure of tripartite fermionic entanglement we obtain the SLOCC classification of three-fermion systems with six single particle states. A special subclass of such three-fermion systems is shown to have the same properties as the well-known three-qubit ones. Our results can be presented in a unified way using Freudenthal triple systems based on cubic Jordan algebras. For systems with an arbitrary number of fermions and single particle states we propose the Pl\"ucker relations as a sufficient and necessary condition of separability.Comment: 23 pages LATE

Non-equilibrium Thermodynamics: Structural Relaxation, Fictive temperature and Tool-Narayanaswamy phenomenology in Glasses

Starting from the second law of thermodynamics applied to an isolated system consisting of the system surrounded by an extremely large medium, we formulate a general non-equilibrium thermodynamic description of the system when it is out of equilibrium. We then apply it to study the structural relaxation in glasses and establish the phenomenology behind the concept of the fictive temperature and of the empirical Tool-Narayanaswamy equation on firmer theoretical foundation.Comment: 20 pages, 1 figur

Outburst of GX304-1 Monitored with INTEGRAL: Positive Correlation Between the Cyclotron Line Energy and Flux

Context. X-ray spectra of many accreting pulsars exhibit significant variations as a function of flux and thus of mass accretion rate. In some of these pulsars, the centroid energy of the cyclotron line(s), which characterizes the magnetic field strength at the site of the X-ray emission, has been found to vary systematically with flux. Aims. GX304-1 is a recently established cyclotron line source with a line energy around 50 keV. Since 2009, the pulsar shows regular outbursts with the peak flux exceeding one Crab. We analyze the INTEGRAL observations of the source during its outburst in January-February 2012. Methods. The observations covered almost the entire outburst, allowing us to measure the source's broad-band X-my spectrum at different flux levels. We report on the variations in the spectral parameters with luminosity and focus on the variations in the cyclotron line. Results. The centroid energy of the line is found to be positively correlated with the luminosity. We interpret this result as a manifestation of the local sub-Eddington (sub-critical) accretion regime operating in the source

Search for Magnetic Monopoles Trapped in Matter

There have been many searches for magnetic monopoles in flight, but few for monopoles in matter. We have searched for magnetic monopoles in meteorites, schists, ferromanganese nodules, iron ores and other materials. The detector was a superconducting induction coil connected to a SQUID (Superconducting Quantum Interference Device) with a room temperature bore 15 cm in diameter. We tested a total of more than 331 kg of material including 112 kg of meteorites. We found no monopole and conclude the overall monopole/nucleon ratio in the samples is $<1.2 \times 10^{-29}$ with a 90\% confidence level.Comment: 6 pages, rev tex, no figure

Amino acid availability acts as a metabolic rheostat to determine the magnitude of ILC2 responses

Group 2 innate lymphoid cells (ILC2) are functionally poised, tissue-resident lymphocytes that respond rapidly to damage and infection at mucosal barrier sites. ILC2 reside within complex microenvironments where they are subject to cues from both the diet and invading pathogens—including helminths. Emerging evidence suggests ILC2 are acutely sensitive not only to canonical activating signals but also perturbations in nutrient availability. In the context of helminth infection, we identify amino acid availability as a nutritional cue in regulating ILC2 responses. ILC2 are found to be uniquely preprimed to import amino acids via the large neutral amino acid transporters Slc7a5 and Slc7a8. Cell-intrinsic deletion of these transporters individually impaired ILC2 expansion, while concurrent loss of both transporters markedly impaired the proliferative and cytokine-producing capacity of ILC2. Mechanistically, amino acid uptake determined the magnitude of ILC2 responses in part via tuning of mTOR. These findings implicate essential amino acids as a metabolic requisite for optimal ILC2 responses within mucosal barrier tissues

Probing stellar winds and accretion physics in high-mass X-ray binaries and ultra-luminous X-ray sources with LOFT

This is a White Paper in support of the mission concept of the Large Observatory for X-ray Timing (LOFT), proposed as a medium-sized ESA mission. We discuss the potential of LOFT for the study of high-mass X-ray binaries and ultra-luminous X-ray sources. For a summary, we refer to the paper.Comment: White Paper in Support of the Mission Concept of the Large Observatory for X-ray Timing. (v2 few typos corrected

Gas Emission Spectrum in the Irr Galaxy IC 10

Spectroscopic long-slit observations of the dwarf Irr galaxy IC 10 were conducted at the 6-m Special Astrophysical Observatory telescope with the SCORPIO focal reducer. The ionized-gas emission spectra in the regions of intense current star formation were obtained for a large number of regions in IC 10. The relative abundances of oxygen, N+, and S+ in about twenty HII regions and in the synchrotron superbubble were estimated. We found that the galaxy-averaged oxygen abundance is 12 + log(O/H) = 8.17 +- 0.35 and the metallicity is Z = 0.18 +- 0.14 Z_sun. Our abundances estimated from the strong emission lines are found to be more reliable than those obtained by comparing diagnostic diagrams with photoionization models.Comment: Abridged; accepted in Astronomy Letter

Performance of the Space Telescope Imaging Spectrograph after SM4

On May 17, 2009, during the fourth EVA of SM4, astronauts Michael Good and Mike Massimino replaced the failed LVPS-2 circuit board on the Space Telescope Imaging Spectrograph (STIS), restoring this HST instrument to operation after a nearly 6 year hiatus. STIS after this 2009 repair operates in much the same way as it did during the 2001-2004 period of operations with the Side-2 electronics. Internal and external alignments of the instrument are similar to what they had been in 2004, and most changes in performance are modest. The STIS CCD detector continued to experience radiation damage during the hiatus in operations, leading to decreased charge transfer efficiency (CTE) and an increased number of hot pixels. The sensitivities for most modes are surprisingly close to what was expected from simple extrapolation of the 2003-2004 trends, although the echelle modes show somewhat more complex behavior. The biggest surprise was that the dark count rate for the NUV MAMA detector after SM4 has been much larger than had been expected; it is currently about 2.5 times bigger than it was in 2004 and is only slowly decreasing. We discuss how these changes will affect science with STIS now and in the future