Confirming Fundamental Parameters of the Exoplanet Host Star epsilon Eridani Using the Navy Optical Interferometer

We measured the angular diameter of the exoplanet host star epsilon Eridani using the Navy Optical Interferometer. We determined its physical radius, effective temperature, and mass by combining our measurement with the star's parallax, photometry from the literature, and the Yonsei-Yale isochrones (Yi et al. 2001), respectively. We used the resulting stellar mass of 0.82 +/- 0.05 M_Sun plus the mass function from Benedict et al. (2006) to calculate the planet's mass, which is 1.53 +/- 0.22 M_Jupiter. Using our new effective temperature, we also estimated the extent of the habitable zone for the system.Comment: Accepted for publication in The Astrophysical Journa

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold

Automatic estimation of flux distributions of astrophysical source populations

In astrophysics a common goal is to infer the flux distribution of populations of scientifically interesting objects such as pulsars or supernovae. In practice, inference for the flux distribution is often conducted using the cumulative distribution of the number of sources detected at a given sensitivity. The resulting "$\log(N>S)$-$\log (S)$" relationship can be used to compare and evaluate theoretical models for source populations and their evolution. Under restrictive assumptions the relationship should be linear. In practice, however, when simple theoretical models fail, it is common for astrophysicists to use prespecified piecewise linear models. This paper proposes a methodology for estimating both the number and locations of "breakpoints" in astrophysical source populations that extends beyond existing work in this field. An important component of the proposed methodology is a new interwoven EM algorithm that computes parameter estimates. It is shown that in simple settings such estimates are asymptotically consistent despite the complex nature of the parameter space. Through simulation studies it is demonstrated that the proposed methodology is capable of accurately detecting structural breaks in a variety of parameter configurations. This paper concludes with an application of our methodology to the Chandra Deep Field North (CDFN) data set.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS750 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A moving grid finite element method applied to a model biological pattern generator

Many problems in biology involve growth. In numerical simulations it can therefore be very convenient to employ a moving computational grid on a continuously deforming domain. In this paper we present a novel application of the moving grid finite element method to compute solutions of reaction–diffusion systems in two-dimensional continuously deforming Euclidean domains. A numerical software package has been developed as a result of this research that is capable of solving generalised Turing models for morphogenesis

A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries

A moving mesh finite element algorithm is proposed for the adaptive solution of nonlinear diffusion equations with moving boundaries in one and two dimensions. The moving mesh equations are based upon conserving a local proportion, within each patch of finite elements, of the total “mass” that is present in the projected initial data. The accuracy of the algorithm is carefully assessed through quantitative comparison with known similarity solutions, and its robustness is tested on more general problems. Applications are shown to a variety of problems involving time-dependent partial differential equations with moving boundaries. Problems which conserve mass, such as the porous medium equation and a fourth order nonlinear diffusion problem, can be treated by a simplified form of the method, while problems which do not conserve mass require the full theory

Evidence of Titan's Climate History from Evaporite Distribution

Water-ice-poor, 5-$\mu$m-bright material on Saturn's moon Titan has previously been geomorphologically identified as evaporitic. Here we present a global distribution of the occurrences of the 5-$\mu$m-bright spectral unit, identified with Cassini's Visual Infrared Mapping Spectrometer (VIMS) and examined with RADAR when possible. We explore the possibility that each of these occurrences are evaporite deposits. The 5-$\mu$m-bright material covers 1\% of Titan's surface and is not limited to the poles (the only regions with extensive, long-lived surface liquid). We find the greatest areal concentration to be in the equatorial basins Tui Regio and Hotei Regio. Our interpretations, based on the correlation between 5-$\mu$m-bright material and lakebeds, imply that there was enough liquid present at some time to create the observed 5-$\mu$m-bright material. We address the climate implications surrounding a lack of evaporitic material at the south polar basins: if the south pole basins were filled at some point in the past, then where is the evaporite