The canonical Luminous Blue Variable AG Car and its neighbor Hen 3-519 are much closer than previously assumed

The strong mass loss of Luminous Blue Variables (LBVs) is thought to play a critical role in massive-star evolution, but their place in the evolutionary sequence remains debated. A key to understanding their peculiar instability is their high observed luminosities, which often depends on uncertain distances. Here we report direct distances and space motions of four canonical Milky Way LBVs---AG~Car, HR~Car, HD~168607, and (candidate) Hen~3-519---from the Gaia first data release. Whereas the distances of HR~Car and HD~168607 are consistent with previous literature estimates within the considerable uncertainties, Hen~3-519 and AG~Car, both at $\sim$2~kpc, are much closer than the 6--8~kpc distances previously assumed. As a result, Hen~3-519 moves far from the locus of LBVs on the HR Diagram, making it a much less luminous object. For AG~Car, considered a defining example of a classical LBV, its lower luminosity would also move it off the S~Dor instability strip. Lower luminosities allow both AG~Car and Hen~3-519 to have passed through a previous red supergiant phase, lower the mass estimates for their shell nebulae, and imply that binary evolution is needed to account for their peculiarities. These results may also impact our understanding of LBVs as potential supernova progenitors and their isolated environments. Improved distances will be provided in the Gaia second data release, which will include additional LBVs. AG~Car and Hen~3-519 hint that this new information may alter our traditional view of LBVs.Comment: 15 pages, 2 figures, 1 table. Accepted by Astronomical Journa

Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions

We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the semi-analytical method, relative to the number of eigenvalues, is investigated and the effect of varying the interface conditions on the solution behaviour is explored. Numerical experiments demonstrate that solutions can be computed using the new semi-analytical method that are more accurate and more efficient than the unified transform method of Sheils [Appl. Math. Model., 46:450-464, 2017]. Furthermore, unlike classical analytical solutions and the unified transform method, only the new semi-analytical method is able to correctly treat problems with both time-varying external boundary conditions and a large number of layers. The paper is concluded by replicating solutions to several important industrial, environmental and biological applications previously reported in the literature, demonstrating the wide applicability of the work.Comment: 24 pages, 8 figures, accepted version of paper published in Applied Mathematics and Computatio

Zone Leveling Crystal Growth of Thermoelectric PbTe Alloys with Sb_(2)Te_3 Widmanstätten Precipitates

Unidirectional solidification of PbTe-rich alloys in the pseudobinary PbTe-Sb_(2)Te_3 system using the zone leveling technique enables the production of large regions of homogeneous solid solutions for the formation of precipitate nanocomposites as compared with Bridgman solidification. (PbTe)_(0.940)(Sb_(2)Te_3)_(0.060) and (PbTe)_(0.952)(Sb_(2)Te_3)_(0.048) alloys were successfully grown using (PbTe)_(0.4)(Sb_(2)Te_3)_(0.6) and (PbTe)_(0.461)(Sb_(2)Te_3)_(0.539) as seed alloys, respectively, with 1 mm h^(–1) withdrawal velocity. In the unidirectionally solidified regions of both alloys, Widmanstatten precipitates are formed due to the decrease in solubility of Sb_(2)Te_3 in PbTe. To determine the compositions of the seed alloys for the zone leveling experiments, the solute distribution in solidification in the PbTe-richer part of the pseudobinary PbTe-Sb_(2)Te_3 system has been examined from the concentration profiles in the samples unidirectionally solidified by the Bridgman method

Quantum fluids in nanopores

We describe calculations of the properties of quantum fluids inside nanotubes of various sizes. Very small radius ($R$) pores confine the gases to a line, so that a one-dimensional (1D) approximation is applicable; the low temperature behavior of 1D $^4$He is discussed. Somewhat larger pores permit the particles to move off axis, resulting eventually in a transition to a cylindrical shell phase--a thin film near the tube wall; we explored this behavior for H$_2$. At even larger $R\sim 1$ nm, both the shell phase and an axial phase are present. Results showing strong binding of cylindrical liquids $^4$He and $^3$He are discussed.Comment: 8 pages, 4 figures, uses ws-ijmpb, graphicx, xspace; minor revisions from version published in Proc. 13th Intl. Conference on Recent Progress in Many-Body Theories (QMBT13), Buenos Aires, 200

Data-Driven Generalized Integer Aperture Bootstrapping for Real-Time High Integrity Applications

A new method is developed for integer ambiguity resolution in carrier-phase differential GPS (CDGPS) positioning. The method is novel in that it is (1) data-driven, (2) generalized to include partial ambiguity resolution, and (3) amenable to a full characterization of the prior and posterior distributions of the three-dimensional baseline vector that results from CDGPS. The technique is termed generalized integer aperture bootstrapping (GIAB). GIAB improves the availability of integer ambiguity resolution for high-integrity, safety-critical systems. Current high-integrity CDGPS algorithms, such as EPIC and GERAFS, evaluate the prior risk of position domain biases due to incorrect integer ambiguity resolution without further validation of the chosen solution. This model-driven approach introduces conservatism which tends to reduce solution availability. Common data-driven ambiguity validation methods, such as the ratio test, control the risk of incorrect ambiguity resolution by shrinking an integer aperture (IA), or acceptance region. The incorrect fixing risk of current IA methods is determined by functional approximations that are inappropriate for use in safety-of-life applications. Moreover, generalized IA (GIA) methods incorrectly assume that the baseline resulting from partial ambiguity resolution is zero mean. Each of these limitations is addressed by GIAB, and the claimed improvements are validated by Monte Carlo simulation. The performance of GIAB is then optimized by tuning the integer aperture size to maximize the prior probability of full ambiguity resolution. GIAB is shown to provide higher availability than EPIC for the same integrity requirements.Aerospace Engineering and Engineering Mechanic