Formulations of the 3+1 evolution equations in curvilinear coordinates

Following Brown, in this paper we give an overview of how to modify standard hyperbolic formulations of the 3+1 evolution equations of General Relativity in such a way that all auxiliary quantities are true tensors, thus allowing for these formulations to be used with curvilinear sets of coordinates such as spherical or cylindrical coordinates. After considering the general case for both the Nagy-Ortiz-Reula (NOR) and the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulations, we specialize to the case of spherical symmetry and also discuss the issue of regularity at the origin. Finally, we show some numerical examples of the modified BSSN formulation at work in spherical symmetry.Comment: 19 pages, 12 figure

Faint blue objects on the Hubble Deep Field North & South as possible nearby old halo white dwarfs

Using data derived from the deepest and finest angular resolution images of the universe yet acquired by astronomers at optical wavelengths using the Hubble Space Telescope (HST) in two postage-stamp sections of the sky (Williams et al. 1996a,b), plus simple geometrical and scaling arguments, we demonstrate that the faint blue population of point-source objects detected on those two fields (M\'endez et al. 1996) could actually be ancient halo white dwarfs at distances closer than about 2 kpc from the Sun. This finding has profound implications, as the mass density of the detected objects would account for about half of the missing dark matter in the Milky-Way (Bahcall and Soneira 1980), thus solving one of the most controversial issues of modern astrophysics (Trimble 1987, Ashman 1992). The existence of these faint blue objects points to a very large mass locked into ancient halo white dwarfs. Our estimate indicates that they could account for as much as half of the dark matter in our Galaxy, confirming the suggestions of the MACHO microlensing experiment (Alcock et al. 1997). Because of the importance of this discovery, deep follow-up observations with HST within the next two years would be needed to determine more accurately the kinematics (tangential motions) for these faint blue old white dwarfs.Comment: Accepted for publication on The Astrophysical Journal, Part 1. 8 pages (AAS Latex macros V4.0), 1 B&W postscript figure, 2 color postscript figure

Perspectives from community-based doulas and mothers: Neighborhood context and pregnancy

Objectives: Limited research explores the potential pathways by which neighborhoods influence pregnancy or how community members conceptualize and interpret how neighborhood contexts and living environments influence pregnancy and birth. Study Design: We applied participatory Concept Mapping and a series of focused discussions with community-based doulas and mothers. Methods: We collaborated with a community-based doula program to investigate how mothers and community doulas perceived the neighborhood to influence reproductive health. We conducted a series of focused discussions including ‘Brainstorming’ to uncover key themes related to how neighborhood context influenced pregnancy, ‘Sorting and Rating’ of key themes in association with pregnancy and birth outcomes, and further discussion to uncover potential relationships. Data from the ‘Sorting and Rating’ activities were entered into Concept Systems software to generate concept maps of the themes and ideas discussed. Results: The women identified 79 key themes/items related to the neighborhood context that they thought were important for pregnancy and birth. Participants ranked most of the neighborhood factors as moderate or high in importance in influencing pregnancy health and birth. These 79 items were further aggregated to develop 9 clusters related to various themes such as ‘Access/Potential Barriers to Adequate Care,’ ‘The Environment and Infrastructure,’ ‘Neighborhood History, Demographics and Dynamics,’ ‘Community, Relationships, and Autonomy.’ The group further discussed how neighborhood contexts have a particularly influence on individual behaviors such as physical activity; and how key infrastructure issues such as transportation may impede or facilitate access to resources important for health. Conclusion: This study provides additional insight into how neighborhoods may influence pregnancy and birth and how multiple neighborhood factors may act synergistically to influence health. Concept mapping and community perspectives reinforce the importance of participant and community input in developing future research and interventions

Dynamical properties of a dissipative discontinuous map: A scaling investigation

The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action \left as a function of the $n$-th iteration of the map as well as the parameters $K$ and $\gamma$, controlling nonlinearity and dissipation, respectively. We concentrate our efforts to study the case where the nonlinearity is large; i.e., $K\gg 1$. In this regime and for large initial action $I_0\gg K$, we prove that dissipation produces an exponential decay for the average action \left. Also, for $I_0\cong 0$, we describe the behavior of \left using a scaling function and analytically obtain critical exponents which are used to overlap different curves of \left onto an universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action $\omega$.Comment: 20 pages, 7 figure

Old Main-Sequence Turnoff Photometry in the Small Magellanic Cloud. I. Constraints on the Star Formation History in Different Fields

We present ground-based B and R-band color-magnitude diagrams (CMDs), reaching the oldest main-sequence turnoffs with good photometric accuracy for twelve fields in the Small Magellanic Cloud (SMC). Our fields, located between ~1 and ~4 degrees from the center of the galaxy, are situated in different parts of the SMC such as the "Wing'' area, and towards the West and South. In this paper we perform a first analysis of the stellar content in our SMC fields through comparison with theoretical isochrones and color functions (CFs). We find that the underlying spheroidally distributed population is composed of both intermediate-age and old stars and that its age composition does not show strong galacto-centric gradients. The three fields situated toward the east, in the Wing region, show very active current star formation. However, only in the eastern field closest to the center do we find an enhancement of recent star formation with respect to a constant SFR(t). The fields corresponding to the western side of the SMC present a much less populated young MS, and the CF analysis indicates that the SFR(t) greatly diminished around 2 Gyr ago in these parts. Field smc0057, the closest to the center of the galaxy and located in the southern part, shows recent star formation, while the rest of the southern fields present few bright MS stars. The structure of the red clump in all the CMDs is consistent with the large amount of intermediate-age stars inferred from the CMDs and color functions. None of the SMC fields presented here are dominated by old stellar populations, a fact that is in agreement with the lack of a conspicuous horizontal branch in all these SMC CMDs. This could indicate that a disk population is ruling over a possible old halo in all the observed fields.Comment: To appear in A