Non-degenerate solutions of universal Whitham hierarchy

The notion of non-degenerate solutions for the dispersionless Toda hierarchy is generalized to the universal Whitham hierarchy of genus zero with $M+1$ marked points. These solutions are characterized by a Riemann-Hilbert problem (generalized string equations) with respect to two-dimensional canonical transformations, and may be thought of as a kind of general solutions of the hierarchy. The Riemann-Hilbert problem contains $M$ arbitrary functions $H_a(z_0,z_a)$, $a = 1,...,M$, which play the role of generating functions of two-dimensional canonical transformations. The solution of the Riemann-Hilbert problem is described by period maps on the space of $(M+1)$-tuples $(z_\alpha(p) : \alpha = 0,1,...,M)$ of conformal maps from $M$ disks of the Riemann sphere and their complements to the Riemann sphere. The period maps are defined by an infinite number of contour integrals that generalize the notion of harmonic moments. The $F$-function (free energy) of these solutions is also shown to have a contour integral representation.Comment: latex2e, using amsmath, amssym and amsthm packages, 32 pages, no figur

Understanding the tsunami with a simple model

In this paper, we use the approximation of shallow water waves (Margaritondo G 2005 Eur. J. Phys. 26 401) to understand the behaviour of a tsunami in a variable depth. We deduce the shallow water wave equation and the continuity equation that must be satisfied when a wave encounters a discontinuity in the sea depth. A short explanation about how the tsunami hit the west coast of India is given based on the refraction phenomenon. Our procedure also includes a simple numerical calculation suitable for undergraduate students in physics and engineering

Can optical spectroscopy directly elucidate the ground state of C20?

The optical response of the lowest energy members of the C20 family is calculated using time-dependent density functional theory within a real-space, real-time scheme. Significant differences are found among the spectra of the different isomers, and thus we propose optical spectroscopy as a tool for experimental investigation of the structure of these important clusters.Comment: 11 pages, 2 figures. To be published in J. Chem. Phy

The multicomponent 2D Toda hierarchy: Discrete flows and string equations

The multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated to an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov--Shabat equations are characterized. Reductions of block Toeplitz and Hankel bi-infinite matrix types are proposed and studied. Orlov--Schulman operators, string equations and additional symmetries (discrete and continuous) are considered. The continuous-discrete Lax equations are shown to be equivalent to a factorization problem as well as to a set of string equations. A congruence method to derive site independent equations is presented and used to derive equations in the discrete multicomponent KP sector (and also for its modification) of the theory as well as dispersive Whitham equations.Comment: 27 pages. In the revised paper we improved the presentatio

Cooler and bigger than thought? Planetary host stellar parameters from the InfraRed Flux Method

Effective temperatures and radii for 92 planet-hosting stars as determined from the InfraRed Flux Method (IRFM) are presented and compared with those given by other authors using different approaches. The IRFM temperatures we have derived are systematically lower than those determined from the spectroscopic condition of excitation equilibrium, the mean difference being as large as 110 K. They are, however, consistent with previous IRFM studies and with the colors derived from Kurucz and MARCS model atmospheres. Comparison with direct measurements of stellar diameters for 7 dwarf stars, which approximately cover the range of temperatures of the planet-hosting stars, suggest that the IRFM radii and temperatures are reliable in an absolute scale. A better understanding of the fundamental properties of the stars with planets will be achieved once this discrepancy between the IRFM and the spectroscopic temperature scales is resolved.Comment: 15 pages, 4 figures. Accepted for publication in Ap

Beryllium in the Ultra-Lithium-Deficient,Metal-Poor Halo Dwarf, G186-26

The vast majority of low-metal halo dwarfs show a similar amount of Li; this has been attributed to the Li that was produced in the Big Bang. However, there are nine known halo stars with T $>$ 5900 K and [Fe/H] $<$ $-$1.0 that are ultra-Li-deficient. We have looked for Be in the very low metallicity star, G 186-26 at [Fe/H] = $-$2.71, which is one of the ultra-Li-deficient stars. This star is also ultra-Be deficient. Relative to Be in the Li-normal stars at [Fe/H] = $-$2.7, G 182-26 is down in Be by more than 0.8 dex. Of two potential causes for the Li-deficiency -- mass-transfer in a pre-blue straggler or extra rotationally-induced mixing in a star that was initially a very rapid rotator -- the absence of Be favors the blue-straggler hypothesis, but the rotation model cannot be ruled-out completely.Comment: Accepted for Ap.J. Letters 10 pages, 4 figure

Robust grid adaptation for efficient uncertainty quantification

In the recent past, adjoint methods have been successfully applied in error estimation of integral outputs (functionals) of the numerical solution of partial differential equations. The adjoint solution can also be used as a grid adaptation indicator, with the objective of optimally targeting and reducing the numerical error in the functional of interest below a prespecified threshold. In situations where we seek to quantify the effect of aleatory uncertainties on statistical moments of the output functional, it becomes necessary to evaluate the functional accurately at multiple sample points in probability space. If the numerical accuracy of these sample evaluations is not uniform, variations in the numerical error can affect the evaluation of the statistical moments. Although it is possible to independently adapt the meshes to obtain more accurate solutions at each sample point in stochastic space, such a procedure can be both cumbersome and computationally expensive. To improve the efficiency of this process, a new robust grid adaptation technique is proposed that is aimed at minimizing the numerical error over a range of variations of the uncertain parameters of interest about a nominal state. Using this approach, it is possible to generate computational grids that are insensitive to small variations of the uncertain parameters that can both locally and globally change the solution and, as a result, the error distribution. This is in contrast with classical adjoint techniques, which seek to adapt the grid with the aim of minimizing numerical errors for a specific flow condition (and geometry). It is demonstrated that flow computations on these robust grids result in low numerical errors under the expected range of variations of the uncertain input parameters. The effectiveness of this strategy is demonstrated in problems involving the Poisson equation and the Euler equations at transonic and supersonic/hypersonic speeds

Using Hubble Space Telescope Imaging of Nuclear Dust Morphology to Rule Out Bars Fueling Seyfert Nuclei

If AGN are powered by the accretion of matter onto massive black holes, how does the gas in the host galaxy lose the required angular momentum to approach the black hole? Gas easily transfers angular momentum to stars in strong bars, making them likely candidates. Although ground-based searches for bars in active galaxies using both optical and near infrared surface brightness have not found any excess of bars relative to quiescent galaxies, the searches have not been able to rule out small-scale nuclear bars. To look for these nuclear bars we use HST WFPC2-NICMOS color maps to search for the straight dust lane signature of strong bars. Of the twelve Seyfert galaxies in our sample, only three have dust lanes consistent with a strong nuclear bar. Therefore, strong nuclear bars cannot be the primary fueling mechanism for Seyfert nuclei. We do find that a majority of the galaxies show an spiral morphology in their dust lanes. These spiral arms may be a possible fueling mechanism.Comment: To be published in the Astronomical Journal, June 1999. 25 pages and 14 figures. Full resolution figures are available at ftp://www.ciw.edu/pub/mregan/fullfigs.tar.g