8,760 research outputs found

    Blocking light in compact Riemannian manifolds

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    We study compact Riemannian manifolds for which the light between any pair of points is blocked by finitely many point shades. Compact flat Riemannian manifolds are known to have this finite blocking property. We conjecture that amongst compact Riemannian manifolds this finite blocking property characterizes the flat metrics. Using entropy considerations, we verify this conjecture amongst metrics with nonpositive sectional curvatures. Using the same approach, K. Burns and E. Gutkin have independently obtained this result. Additionally, we show that compact quotients of Euclidean buildings have the finite blocking property. On the positive curvature side, we conjecture that compact Riemannian manifolds with the same blocking properties as compact rank one symmetric spaces are necessarily isometric to a compact rank one symmetric space. We include some results providing evidence for this conjecture.Comment: 19 page

    Observational constraints for Lithium depletion before the RGB

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    Precise Li abundances are determined for 54 giant stars mostly evolving across the Hertzsprung gap. We combine these data with rotational velocity and with information related to the deepening of the convective zone of the stars to analyse their link to Li dilution in the referred spectral region. A sudden decline in Li abundance paralleling the one already established in rotation is quite clear. Following similar results for other stellar luminosity classes and spectral regions, there is no linear relation between Li abundance and rotation, in spite of the fact that most of the fast rotators present high Li content. The effects of convection in driving the Li dilution is also quite clear. Stars with high Li content are mostly those with an undeveloped convective zone, whereas stars with a developed convective zone present clear sign of Li dilution.Comment: 5 pages, 4 figures. accepted for publicatio

    The spatial and velocity distributions of hypervelocity stars

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    Hypervelocity stars (HVSs) found in the Galactic halo are probably the dynamical products of interactions between (binary) stars and the massive black hole(s) (MBH) in the Galactic center (GC). It has been shown that the detected HVSs are spatially consistent with being located on two thin disks (Lu et al.), one of which has the same orientation as the clockwise-rotating stellar disk in the GC. Here we perform a large number of three-body experiments of the interactions between the MBH and binary stars bound to it, and find that the probability of ejecting HVSs is substantially enhanced by multiple encounters between the MBH and binary stars at distances substantially larger than the initial tidal breakup radii. Assuming that the HVS progenitors are originated from the two disks, the inclination distribution of the HVSs relative to the disk planes can be reproduced by either the mechanism of tidal breakup of binary stars or the mechanism of ejecting HVSs by a hypothetical binary black hole (BBH) in the GC. However, an isotropical origination of HVS progenitors is inconsistent with the observed inclination distribution. Assuming that the HVSs were ejected out by the tidal breakup mechanism, its velocity distribution can be reproduced if their progenitors diffuse onto low angular momentum orbits slowly and most of the progenitors were broken up at relatively large distances due to multiple encounters. Assuming that the HVSs were ejected out by a BBH within the allowed parameter space in the GC, our simulations produce relatively flatter velocity spectra compared to the observed ones; however, the BBH mechanism cannot be statistically ruled out, yet. Future surveys of HVSs and better statistics of their spatial and velocity distributions should enable to distinguish the ejection mechanisms of HVSs and shed new light on the dynamical environment of the MBH.(abridged)Comment: 19 pages, 16 figure

    Socioeconomic and demographic factors modify the association between informal caregiving and health in the Sandwich Generation

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    BACKGROUND: Nearly 50 million Americans provide informal care to an older relative or friend. Many are members of the “sandwich generation”, providing care for elderly parents and children simultaneously. Although evidence suggests that the negative health consequences of caregiving are more severe for sandwiched caregivers, little is known about how these associations vary by sociodemographic factors. METHODS: We abstracted data from the Behavioral Risk Factor Surveillance System to determine how the association between caregiving and health varies by sociodemographic factors, using ordinal logistic regression with interaction terms and stratification by number of children, income, and race/ethnicity. RESULTS: The association between informal caregiving and health varied by membership in the “sandwich generation,” income, and race/ethnicity. This association was significant among subjects with one (OR = 1.13, 95% CI [1.04, 1.24]) and two or more children (OR = 1.17, 95% CI = 1.09, 1.26]), but not in those without children (OR = 1.01, 95% CI [0.97, 1.05]). Associations were strongest in those earning 50,00050,000-75,000 annually, but these income-dependent associations varied by race/ethnicity. In Whites with two or more children, the strongest associations between caregiving and health occurred in lower income individuals. These trends were not observed for Whites without children. CONCLUSIONS: Our findings suggest that the added burden of caregiving for both children and elderly relatives may be impacted by income and race/ethnicity. These differences should be considered when developing culturally appropriate interventions to improve caregiver health and maintain this vital component of the US health care system

    Tidal breakup of binary stars at the Galactic Center. II. Hydrodynamic simulations

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    In Paper I, we followed the evolution of binary stars as they orbited near the supermassive black hole (SMBH) at the Galactic center, noting the cases in which the two stars would come close enough together to collide. In this paper we replace the point-mass stars by fluid realizations, and use a smoothed-particle hydrodynamics (SPH) code to follow the close interactions. We model the binary components as main-sequence stars with initial masses of 1, 3 and 6 Solar masses, and with chemical composition profiles taken from stellar evolution codes. Outcomes of the close interactions include mergers, collisions that leave both stars intact, and ejection of one star at high velocity accompanied by capture of the other star into a tight orbit around the SMBH. For the first time, we follow the evolution of the collision products for many (100\gtrsim 100) orbits around the SMBH. Stars that are initially too small to be tidally disrupted by the SMBH can be puffed up by close encounters or collisions, with the result that tidal stripping occurs in subsequent periapse passages. In these cases, mass loss occurs episodically, sometimes for hundreds of orbits before the star is completely disrupted. Repeated tidal flares, of either increasing or decreasing intensity, are a predicted consequence. In collisions involving a low-mass and a high-mass star, the merger product acquires a high core hydrogen abundance from the smaller star, effectively resetting the nuclear evolution "clock" to a younger age. Elements like Li, Be and B that can exist only in the outermost envelope of a star are severely depleted due to envelope ejection during collisions and due to tidal forces from the SMBH. In the absence of collisions, tidal spin-up of stars is only important in a narrow range of periapse distances, rt/2rperrtr_t/2\lesssim r_per \lesssim r_t with rtr_t the tidal disruption radius.Comment: ApJ accepted, 22 pages, 19 figures. Version with high-resolution figures, and additional animations, available at this url: http://astrophysics.rit.edu/fantonini/tbbs2

    Engineering Valence Band Dispersion for High Mobility p-Type Semiconductors

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    The paucity of high performance transparent p-type semiconductors has been a stumbling block for the electronics industry for decades, effectively hindering the route to efficient transparent devices based on p–n junctions. Cu-based oxides and subsequently Cu-based oxychalcogenides have been heavily studied as affordable, earth-abundant p-type transparent semiconductors, where the mixing of the Cu 3d states with the chalcogenide 2p states at the top of the valence band encourages increased valence band dispersion. In this article, we extend this mixing concept further, by utilizing quantum chemistry techniques to investigate ternary copper phosphides as potential high mobility p-type materials. We use hybrid density functional theory to examine a family of phosphides, namely, MCuP (M = Mg, Ca, Sr, Ba) which all possess extremely disperse valence band maxima, comparable to the dispersion of excellent industry standard n-type transparent conducting oxides. As a proof of concept, we synthesized and characterized powders of CaCuP, showing that they display high levels of p-type conductivity, without any external acceptor dopant. Lastly, we discuss the role of Cu-coordination in promoting valence band dispersion and provide design principles for producing degenerate p-type materials

    Perturbations of Intermediate-mass Black Holes on Stellar Orbits in the Galactic Center

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    We study the short- and long-term effects of an intermediate mass black hole (IMBH) on the orbits of stars bound to the supermassive black hole (SMBH) at the center of the Milky Way. A regularized N-body code including post-Newtonian terms is used to carry out direct integrations of 19 stars in the S-star cluster for 10 Myr. The mass of the IMBH is assigned one of four values from 400 Msun to 4000 Msun, and its initial semi-major axis with respect to the SMBH is varied from 0.3-30 mpc, bracketing the radii at which inspiral of the IMBH is expected to stall. We consider two values for the eccentricity of the IMBH/SMBH binary, e=(0,0.7), and 12 values for the orientation of the binary's plane. Changes at the level of 1% in the orbital elements of the S-stars could occur in just a few years if the IMBH is sufficiently massive. On time scales of 1 Myr or longer, the IMBH efficiently randomizes the eccentricities and orbital inclinations of the S-stars. Kozai oscillations are observed when the IMBH lies well outside the orbits of the stars. Perturbations from the IMBH can eject stars from the cluster, producing hypervelocity stars, and can also scatter stars into the SMBH; stars with high initial eccentricities are most likely to be affected in both cases. The distribution of S-star orbital elements is significantly altered from its currently-observed form by IMBHs with masses greater than 1000 Msun if the IMBH/SMBH semi-major axis lies in the range 3-10 mpc. We use these results to further constrain the allowed parameters of an IMBH/SMBH binary at the Galactic center.Comment: 11 pages, 13 figures, revised versio
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