The construction of a reliable potential for GeO2, from first-principles, is described. The obtained potential, which includes dipole polarization effects, is able to reproduce all the studied properties (structural, dynamical and vibrational) to a high degree of precision with a single set of parameters. In particular, the infrared spectrum was obtained with the expression proposed for the dielectric function of polarizable ionic solutions by Weis et al. [J.M. Caillol, D. Levesque and J.J. Weis, J. Chem. Phys. 91, 5544 (1989)]. The agreement with the experimental spectrum is very good, with three main bands that are associated to tetrahedral modes of the GeO2 network. Finally, we give a comparison with a simpler pair-additive potential.

D. Marrocchelli M. Salanne P. A. Madden C. Simon P. Turq

Let $\alpha$ be an algebraic number of degree $d\ge 3$ and let $K$ be the algebraic number field $\Q(\alpha)$. When $\varepsilon$ is a unit of $K$ such that $\Q(\alpha\varepsilon)=K$, we consider the irreducible polynomial $f_\varepsilon(X) \in \Z[X]$ such that $f_\varepsilon(\alpha\varepsilon)=0$. Let $F_\varepsilon(X,Y)$ be the irrreducible binary form of degree $d$ associated to $f_{\varepsilon}(X) $ under the condition $F_{\varepsilon}(X,1)=f_{\varepsilon}(X)$. For each positive integer $m$, we want to exhibit an effective upper bound for the solutions $(x,y,\varepsilon)$ of the diophantine inequation $|F_\varepsilon(x,y)|\le m$. We achieve this goal by restricting ourselves to a subset of units $\varepsilon$ which we prove to be sufficiently large as soon as the degree of $K$ is $\geq 4$.

Claude Levesque Michel Waldschmidt

We investigate the possibility of generating initial conditions for cosmological N-body simulations by simulating a system whose correlations at thermal equilibrium approximate well those of cosmological density perturbations. The system is an appropriately modified version of the standard ``one component plasma'' (OCP). We show first how a well-known semi-analytic method can be used to determine the potential required to produce the desired correlations, and then verify our results for some cosmological type spectra with simulations of the full molecular dynamics. The advantage of the method, compared to the standard one, is that it gives by construction an accurate representation of both the real and reciprocal space correlation properties of the theoretical model. Furthermore the distributions are also statistically homogeneous and isotropic. We discuss briefly the modifications needed to implement the method to produce configurations appropriate for large N-body simulations in cosmology, and also the generation of initial velocities in this context.

M. Joyce D. Levesque B. Marcos

Red supergiants (RSGs) are an evolved stage in the life of intermediate massive stars (<25Mo). For many years their location in the H-R diagram was at variance with the evolutionary models. Using the MARCS stellar atmosphere models, we have determined new effective temperatures and bolometric luminosities for RSGs in the Milky Way, LMC, and SMC, and our work has resulted in much better agreement with the evolutionary models. We have also found evidence of significant visual extinction due to circumstellar dust. Although in the Milky Way the RSGs contribute only a small fraction (<1%) of the dust to the interstellar medium (ISM), in starburst galaxies or galaxies at large look-back times, we expect that RSGs may be the main dust source. We are in the process of extending this work now to RSGs of higher and lower metallicities using the galaxies M31 and WLM.

Philip Massey Bertrand Plez Emily M. Levesque K. A. G. Olsen David R. Silva Geoffery C. Clayton

We have obtained H-band interferometric observations of three galactic red supergiant stars using the MIRC instrument on the CHARA array. The targets include AZ Cyg, a field RSG and two members of the Per OB1 association, RS Per and T Per. We find evidence of departures from circular symmetry in all cases, which can be modelled with the presence of hotspots. This is the first detection of these features in the $H$-band. The measured mean diameters and the spectral energy distributions were combined to determine effective temperatures. The results give further support to the recently derived hotter temperature scale of red supergiant stars by Levesque et al. (2005), which has been evoked to reconcile the empirically determined physical parameters and stellar evolutionary theories. We see a possible correlation between spottedness and mid-IR emission of the circumstellar dust, suggesting a connection between mass-loss and the mechanism that generates the spots.

L. L. Kiss J. D. Monnier T. R. Bedding P. Tuthill M. Zhao M. J. Ireland T. A. ten Brummelaar

We present spectroscopy of the host of GRB 051022 with GMOS nod and shuffle on Gemini South and NIRSPEC on Keck II. We determine a metallicity for the host of log(O/H)+12 = 8.77 using the R23 method (Kobulnicky & Kewley 2004 scale) making this the highest metallicity long burst host yet observed. The galaxy itself is unusually luminous for a LGRB host with a rest frame B band absolute magnitude -21.5 and has the spectrum of a rapidly star-forming galaxy. Our work raises the question of whether other dark burst hosts will show high metallicities.

J. F. Graham A. S. Fruchter L. J. Kewley E. M. Levesque A. J. Levan N. R. Tanvir D. E. Reichart M. Nysewander

Let $\alpha$ be an algebraic number of degree $d\ge 3$ having at most one real conjugate and let $K$ be the algebraic number field ${\mathbf Q}(\alpha)$. For any unit $\epsilon$ of $K$ such that ${\mathbf Q}(\alpha\epsilon)=K$, we consider the irreducible polynomial $f_\epsilon(X)\in{\mathbf Z}[X]$ such that $f_\epsilon(\alpha\epsilon)=0$. Let $F_\epsilon(X,Y)\ = Y^df_\epsilon(X/Y)\in{\mathbf Z}[X,Y]$ be the associated binary form. For each positive integer $m$, we exhibit an effectively computable bound for the solutions $(x,y,\epsilon)$ of the diophantine equation $|F_\epsilon(x,y)|\leq m$.

Claude Levesque Michel Waldschmidt

E. Thomas was one of the first to solve an infinite family of Thue equations, when he considered the forms $F_n(X, Y )= X^3 -(n-1)X^2Y -(n+2)XY^2 -Y^3$ and the family of equations $F_n(X, Y )=\pm 1$, $n\in {\mathbf N}$. This family is associated to the family of the simplest cubic fields ${\mathbf Q}(\lambda)$ of D. Shanks, $\lambda$ being a root of $F_n(X,1)$. We introduce in this family a second parameter by replacing the roots of the minimal polynomial $F_n(X, 1) $ of $\lambda$ by the $a$-th powers of the roots and we effectively solve the family of Thue equations that we obtain and which depends now on the two parameters $n$ and $a$.

Claude Levesque Michel Waldschmidt

For the problem of molecular solvation, formulated as a liquid submitted to the external potential field created by a molecular solute of arbitrary shape dissolved in that solvent, we draw a connection between the Gaussian field theory derived by David Chandler [Phys. Rev. E, 1993, 48, 2898] and classical density functional theory. We show that Chandler's results concerning the solvation of a hard core of arbitrary shape can be recovered by either minimising a linearised HNC functional using an auxiliary Lagrange multiplier field to impose a vanishing density inside the core, or by minimising this functional directly outside the core --- indeed a simpler procedure. Those equivalent approaches are compared to two other variants of DFT, either in the HNC, or partially linearised HNC approximation, for the solvation of a Lennard-Jones solute of increasing size in a Lennard-Jones solvent. Compared to Monte-Carlo simulations, all those theories give acceptable results for the inhomogeneous solvent structure, but are completely out-of-range for the solvation free-energies. This can be fixed in DFT by adding a hard-sphere bridge correction to the HNC functional.

V. Sergiievskyi M. Levesque B. Rotenberg D. Borgis

Dorn-Wallenstein, Levesque, & Ruan recently presented the identification of a z=0.215 active galaxy located behind M31 and claimed the detection of multiple periodic variations in the object's light curve with as many as nine different periods. They interpreted these results as evidence for the presence of a binary supermassive black hole with an orbital separation of just a few hundred AU, and estimated the gravitational-wave signal implied by such a system. We demonstrate that the claimed periodicities are based on a misinterpretation of the null hypothesis test simulations and an error in the method used to calculate the false alarm probabilities. There is no evidence for periodicity in the data.

A. J. Barth D. Stern