A Probablistic Origin for a New Class of Bivariate Polynomials

We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresponding to a bivariate Markov chain with a transition kernel formed by a convolution of simple binomial and trinomial distributions. The solution of the relevant eigenfunction problem, giving the spectral resolution of the kernel, leads to what we believe to be a new class of orthogonal polynomials in two discrete variables. Possibilities for the extension of this approach are discussed.Comment: This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

VLTI/MIDI 10 micron interferometry of the forming massive star W33A

We report on resolved interferometric observations with VLTI/MIDI of the massive young stellar object (MYSO) W33A. The MIDI observations deliver spectrally dispersed visibilities with values between 0.03 and 0.06, for a baseline of 45m over the wavelength range 8-13 micron. The visibilities indicate that W33A has a FWHM size of approximately 120AU (0.030'') at 8 micron which increases to 240AU at 13 micron, scales previously unexplored among MYSOs. This observed trend is consistent with the temperature falling off with distance. 1D dust radiative transfer models are simultaneously fit to the visibility spectrum, the strong silicate feature and the shape of the mid infrared spectral energy distribution (SED). For any powerlaw density distribution, we find that the sizes (as implied by the visibilities) and the stellar luminosity are incompatible. A reduction to a third of W33A's previously adopted luminosity is required to match the visibilities; such a reduction is consistent with new high resolution 70 micron data from Spitzer's MIPSGAL survey. We obtain best fits for models with shallow dust density distributions of r^(-0.5) and r^(-1.0) and for increased optical depth in the silicate feature produced by decreasing the ISM ratio of graphite to silicates and using optical grain properties by Ossenkopf et al. (1992).Comment: 4 pages, 4 figures. Accepted for ApJ letter

IR Dust Bubbles: Probing the Detailed Structure and Young Massive Stellar Populations of Galactic HII Regions

We present an analysis of wind-blown, parsec-sized, mid-infrared bubbles and associated star-formation using GLIMPSE/IRAC, MIPSGAL/MIPS and MAGPIS/VLA surveys. Three bubbles from the Churchwell et al. (2006) catalog were selected. The relative distribution of the ionized gas (based on 20 cm emission), PAH emission (based on 8 um, 5.8 um and lack of 4.5 um emission) and hot dust (24 um emission) are compared. At the center of each bubble there is a region containing ionized gas and hot dust, surrounded by PAHs. We identify the likely source(s) of the stellar wind and ionizing flux producing each bubble based upon SED fitting to numerical hot stellar photosphere models. Candidate YSOs are also identified using SED fitting, including several sites of possible triggered star formation.Comment: 37 pages, 17 figure

Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids

We present some new theoretical and computational results for the stationary points of bulk systems. First we demonstrate how the potential energy surface can be partitioned into catchment basins associated with every stationary point using a combination of Newton-Raphson and eigenvector-following techniques. Numerical results are presented for a 256-atom supercell representation of a binary Lennard-Jones system. We then derive analytical formulae for the number of stationary points as a function of both system size and the Hessian index, using a framework based upon weakly interacting subsystems. This analysis reveals a simple relation between the total number of stationary points, the number of local minima, and the number of transition states connected on average to each minimum. Finally we calculate two measures of localisation for the displacements corresponding to Hessian eigenvectors in samples of stationary points obtained from the Newton-Raphson-based geometry optimisation scheme. Systematic differences are found between the properties of eigenvectors corresponding to positive and negative Hessian eigenvalues, and localised character is most pronounced for stationary points with low values of the Hessian index.Comment: 16 pages, 2 figure

A Branching Time Model of CSP

I present a branching time model of CSP that is finer than all other models of CSP proposed thus far. It is obtained by taking a semantic equivalence from the linear time - branching time spectrum, namely divergence-preserving coupled similarity, and showing that it is a congruence for the operators of CSP. This equivalence belongs to the bisimulation family of semantic equivalences, in the sense that on transition systems without internal actions it coincides with strong bisimilarity. Nevertheless, enough of the equational laws of CSP remain to obtain a complete axiomatisation for closed, recursion-free terms.Comment: Dedicated to Bill Roscoe, on the occasion of his 60th birthda

Velocity dependence of friction and Kramers relaxation rates

We study the influence of the velocity dependence of friction on the escape of a Brownian particle from the deep potential well ($E_{b} \gg k_{B}T$, $E_{b}$ is the barrier height, $k_{B}$ is the Boltzmann constant, $T$ is the bath temperature). The bath-induced relaxation is treated within the Rayleigh model (a heavy particle of mass $M$ in the bath of light particles of mass $m\ll M$) up to the terms of the order of $O(\lambda^{4})$, $\lambda^{2}=m/M\ll1$. The term $\sim 1$ is equivalent to the Fokker-Planck dissipative operator, and the term $\sim \lambda^{2}$ is responsible for the velocity dependence of friction. As expected, the correction to the Kramers escape rate in the overdamped limit is proportional to $\lambda^{2}$ and is small. The corresponding correction in the underdamped limit is proportional to $\lambda^{2}E_{b}/(k_{B}T)$ and is not necessarily small. We thus suggest that the effects due to the velocity-dependent friction may be of considerable importance in determining the rate of escape of an under- and moderately damped Brownian particle from a deep potential well, while they are of minor importance for an overdamped particle

Vermiforichnus (Polychaeta) Borings in Paraspirifer Bownockeri (Brachiopoda: Devonian)

Author Institution: Department of Geology, Bowling Green UniversityShells of Paraspirifer bownockeri (Stewart) from the Silica Formation, Middle Devonian of northwestern Ohio, commonly contain numerous borings of a polychaete worm forming the endolithic trace fossil Vermiforichnus clarki Cameron (1969a) which can be exposed by acidizing the specimens. The borings are most abundant on the brachial valve, and their surface openings tend to be concentrated along major growth lines thence extending dominantly in the general direction of the beaks of the valves. Infestations of the polychaete occurred at 2 different time intervals as indicated by the spacing of the borings on 2 major growth lines with renewed shell growth between them. Growth of the host was severely reduced immediately following the infestation and in some areas damage to the mantle caused deformation in the shell of the host