Global existence, singular solutions, and ill-posedness for the Muskat problem

The Muskat, or Muskat--Leibenzon, problem describes the evolution of the interface between two immiscible fluids in a porous medium or Hele-Shaw cell under applied pressure gradients or fluid injection/extraction. In contrast to the Hele-Shaw problem (the one-phase version of the Muskat problem), there are few nontrivial exact solutions or analytic results for the Muskat problem. For the stable, forward Muskat problem, in which the higher viscosity fluid expands into the lower viscosity fluid, we show global in time existence for initial data that is a small perturbation of a flat interface. The initial data in this result may contain weak (e.g., curvature) singularities. For the unstable, backward problem, in which the higher viscosity fluid contracts, we construct singular solutions that start off with smooth initial data, but develop a point of infinite curvature at finite time

Swift/UVOT Photometry of the Planetary Nebula WeBo 1: Unmasking A Faint Hot Companion Star

We present an analysis of over 150 ks of data on the planetary nebula WeBo 1 (PN G135.6+01.0) obtained with the Swift Ultraviolet Optical Telescope (UVOT). The central object of this nebula has previously been described as a late-type K giant barium star with a possible hot companion, most likely a young pre-white dwarf. UVOT photometry shows that while the optical photometry is consistent with a large cool object, the near-ultraviolet (UV) photometry shows far more UV flux than could be produced by any late-type object. Using model stellar atmospheres and a comparison to UVOT photometry for the pre-white dwarf PG 1159-035, we find that the companion has a temperature of at least 40,000 K and a radius of, at most, 0.056 R_sun. While the temperature and radius are consistent with a hot compact stellar remnant, they are lower and larger, respectively, than expected for a typical young pre-white dwarf. This likely indicates a deficiency in the assumed UV extinction curve. We find that higher temperatures more consistent with expectations for a pre-white dwarf can be derived if the foreground dust has a strong "blue bump" at 2175 AA and a lower R_V. Our results demonstrate the ability of Swift to both uncover and characterize hot hidden companion stars and to constrain the UV extinction properties of foreground dust based solely on UVOT photometry.Comment: 26 pages, 9 figure, accepted to Astronomical Journa

The uBVI Photometric System. II. Standard Stars

Paper I of this series described the design of a CCD-based photometric system that is optimized for ground-based measurements of the size of the Balmer discontinuity in stellar spectra. This "uBVI" system combines the Thuan-Gunn u filter with the standard Johnson-Kron-Cousins BVI filters, and it can be used to discover luminous yellow supergiants in extragalactic systems and post-asymptotic-giant-branch stars in globular clusters and galactic halos. In the present paper we use uBVI observations obtained on 54 nights with 0.9-m telescopes at Kitt Peak and Cerro Tololo to construct a catalog of standardized u magnitudes for standard stars taken from the 1992 catalog of Landolt. We describe the selection of our 14 Landolt fields, and give details of the photometric reductions, including red-leak and extinction corrections, transformation of all of the observations onto a common magnitude system, and establishment of the photometric zero point. We present a catalog of u magnitudes of 103 stars suitable for use as standards. We show that data obtained with other telescopes can be transformed to our standard system with better than 1% accuracy.Comment: 24 pages, 4 figures, 4 tables; accepted by A

The Interplay of Web Aggregation and Regulation

The development of web technology has led to the emergence of web aggregation, a service that collects existing web data and turns them into more useful information. We review the development of both comparison and relationship aggregation and discuss their impacts on various stakeholders. The aggregator’s capability of transparently extracting web data has raised challenging issues in database and privacy protection. Consequently, new regulations are introduced or being proposed. We analyze the interactions between aggregation and related policies and provide our insights about the implications of new policies on the development of web aggregation.Singapore-MIT Alliance (SMA

Research Initiative to Understand & Model State Stability: Exploiting System Dynamics

In its Preface, The 9/11 Commission Report states: We learned that the institutions charted with protecting ... national security did not understand how grave this threat can be, and did not adjust their policies, plans, and practices to deter or defeat it (2004: xvi). Given current realities and uncertainties "better preparedness" can be achieved by identifying, controlling and managing the elusive linkages and situational factors that impact state stability and fuel state decay and destruction - and hence create new threats to the nation's security. We propose to focus on the use of system dynamics modeling techniques to help understand, measure and model the complex dynamics shaping state stability, initially for two regions. We will specifically consider the impacts of unanticipated disruptions, such as a tsunami and its aftermath, on the dynamics of the two regions. For each region, we will deliver a detailed country model, including 3-5 futures predictions in the 6-12 month range along with an analysis of conditions and casual links between predicted futures plus corresponding mitigated options

Context Mediation Demonstration of Counter-Terrorism Intelligence (CTI) Integration

Examination of intelligence failures prior to the 9/11/01 attacks made clear it that lack of effective information exchange among government agencies hindered the capability of identifying potential threats and preventing terrorist actions. A 2002 National Research Council study noted that “Although there are many private and public databases that contain information potentially relevant to counterterrorism programs, they lack the necessary context definitions (i.e., metadata) and access tools to enable interoperation with other databases and the extraction of meaningful and timely information.”[14] This report clearly recognized the importance of problems that the semantic data integration research community has been studying

Context Mediation Demonstration of Counter-Terrorism Intelligence Integration

In this report, we demonstrate the applicability and value of the context mediation approach in facilitating the effective and correct use of counter-terrorism intelligence information coming from diverse heterogeneous sources