London dispersion forces without density distortion: a path to first principles inclusion in density functional theory

We analyse a path to construct density functionals for the dispersion interaction energy from an expression in terms of the ground state densities and exchange-correlation holes of the isolated fragments. The expression is based on a constrained search formalism for a supramolecular wavefunction that is forced to leave the diagonal of the many-body density matrix of each fragment unchanged, and is exact for the interaction between one-electron densities. We discuss several aspects: the needed features a density functional approximation for the exchange-correlation holes of the monomers should have, the optimal choice of the one-electron basis needed (named "dispersals"), and the functional derivative with respect to monomer density variations.Comment: 12 pages, 4 figure

Designing Professional Learning Tasks for Mathematics Learning Trajectories

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers’ learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project

Fingerprints of giant planets in the photospheres of Herbig stars

Around 2% of all A stars have photospheres depleted in refractory elements. This is hypothesized to arise from a preferential accretion of gas rather than dust, but the specific processes and the origin of the material -- circum- or interstellar -- are not known. The same depletion is seen in 30% of young, disk-hosting Herbig Ae/Be stars. We investigate whether the chemical peculiarity originates in a circumstellar disk. Using a sample of systems for which both the stellar abundances and the protoplanetary disk structure are known, we find that stars hosting warm, flaring group I disks typically have Fe, Mg and Si depletions of 0.5 dex compared to the solar-like abundances of stars hosting cold, flat group II disks. The volatile, C and O, abundances in both sets are identical. Group I disks are generally transitional, having radial cavities depleted in millimetre-sized dust grains, while those of group II are usually not. Thus we propose that the depletion of heavy elements emerges as Jupiter-like planets block the accretion of part of the dust, while gas continues to flow towards the central star. We calculate gas to dust ratios for the accreted material and find values consistent with models of disk clearing by planets. Our results suggest that giant planets of ~0.1 to 10 M_Jup are hiding in at least 30% of Herbig Ae/Be disks.Comment: 5 pages, 3 figures, accepted for publication in A&A Letter

On Eta-Einstein Sasakian Geometry

We study eta-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem for Sasakian geometry to prove the existence of eta-Einstein structures on many different compact manifolds, including exotic spheres. We also relate these results to the existence of Einstein-Weyl structures.Comment: 31 pages, minor changes made, to appear in Commun. Math. Phy

Geometry and Mechanics of Thin Growing Bilayers

We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness $\gamma$ that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourth's the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude.Comment: 5 pages, 4 figure

X-ray Spectroscopy of the Contact Binary VW Cephei

Short-period binaries represent extreme cases in the generation of stellar coronae via a rotational dynamo. Such stars are important for probing the origin and nature of coronae in the regimes of rapid rotation and activity saturation. VW Cep (P=0.28 d) is a relatively bright, partially eclipsing, and very active object. Light curves made from Chandra/HETGS data show flaring and rotational modulation, but no eclipses. Velocity modulation of emission lines indicates that one component dominates the X-ray emission. The emission measure is highly structured, having three peaks. Helium-like triplet lines give electron densities of about 3.0E+10 - 18.0E+10 /cm^3. We conclude that the corona is predominantly on the polar regions of the primary star and compact.Comment: Accepted for publication in the Astropysical Journal, 23 June 2006; 22 pages, 15 figure