The Lambda-structure Of The Representation Rings Of The Classical Weyl Groups

First, we introduce a class of operations, called {dollar}\phi{dollar}-operations, on the representation rings of the classical Weyl groups {dollar}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){dollar} and {dollar}{lcub}\cal W{rcub}(D\sb{lcub}k{rcub}){dollar}. These operations are shown to generate the exterior power operations in the representation rings {dollar}R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar} and {dollar}R({lcub}\cal W{rcub}(D\sb{lcub}k{rcub})).{dollar} Given integers l, h satisfying {dollar}l + h=k{dollar}, let {dollar}\beta{dollar} be a partition of l and {dollar}\alpha{dollar} be a partition of h. The main theorem shows that induced representations of the form {dollar}{dollar}Ind\sbsp{lcub}{lcub}\cal W{rcub}\sb{lcub}\beta,\alpha{rcub}{rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1,{dollar}{dollar}where {dollar}{lcub}\cal W{rcub}\sb{lcub}B,a{rcub}=\prod{lcub}\cal W{rcub}(B\sb{lcub}B{rcub})\times\prod{lcub}\cal W{rcub}(A\sb{lcub}a{rcub}),{dollar} can be expressed as an algebraic combination of {dollar}\phi{dollar}-operations acting on the two canonical induced representations {dollar}{dollar}\eqalign{lcub}X\sb{lcub}k{rcub}&= Ind\sbsp{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k-1{rcub})\times{lcub}\cal W{rcub}(B\sb1){rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1\cr\cr Y\sb{lcub}k{rcub}&= Ind\sbsp{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k-1{rcub}){rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1.\cr{rcub}{dollar}{dollar};Next, we show that the set {dollar}{dollar}\left\{lcub}1 \otimes Ind\sbsp{lcub}{lcub}\cal W{rcub}\sb{lcub}\beta,a{rcub}{rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1\right\{rcub}{dollar}{dollar}is a basis of {dollar}\doubq \otimes R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar}. Since the {dollar}\phi{dollar}-operations generate the {dollar}\lambda{dollar}-operations, one can deduce that {dollar}\doubq\otimes R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar} is generated as a {dollar}\lambda{dollar}-ring over {dollar}\doubq{dollar} by the elements {dollar}1 \otimes X\sb{lcub}k{rcub}{dollar} and {dollar}1 \otimes Y\sb{lcub}k{rcub}{dollar}. By applying a result of Lusztig which characterizes the irreducible representations of the Weyl groups {dollar}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){dollar} and {dollar}{lcub}\cal W{rcub}(D\sb{lcub}k{rcub}){dollar} it follows, as a corollary, that {dollar}\doubq\otimes R({lcub}\cal W{rcub}(D\sb{lcub}k{rcub})){dollar} is generated by two elements as a {dollar}\lambda{dollar}-ring over {dollar}\doubq{dollar}

Star - Planet - Debris Disk Alignment in the HD 82943 system: Is planetary system coplanarity actually the norm?

Recent results suggest that the two planets in the HD 82943 system are inclined to the sky plane by 20 +/- 4deg. Here, we show that the debris disk in this system is inclined by 27 +/- 4deg, thus adding strength to the derived planet inclinations and suggesting that the planets and debris disk are consistent with being aligned at a level similar to the Solar System. Further, the stellar equator is inferred to be inclined by 28 +/- 4deg, suggesting that the entire star - planet - disk system is aligned, the first time such alignment has been tested for radial velocity discovered planets on ~AU wide orbits. We show that the planet-disk alignment is primordial, and not the result of planetary secular perturbations to the disk inclination. In addition, we note three other systems with planets at >10AU discovered by direct imaging that already have good evidence of alignment, and suggest that empirical evidence of system-wide star - planet - disk alignment is therefore emerging, with the exception of systems that host hot Jupiters. While this alignment needs to be tested in a larger number of systems, and is perhaps unsurprising, it is a reminder that the system should be considered as a whole when considering the orientation of planetary orbits.Comment: Accepted to MNRA

Huisgen-based conjugation of water-soluble porphyrins to deprotected sugars: Towards mild strategies for the labelling of glycans

Fully deprotected alkynyl-functionalised mono- and oligosaccharides undergo CuAAC-based conjugation with water-soluble porphyrin azides in aqueous environments. The mild reaction conditions are fully compatible with the presence of labile glycosidic bonds. This approach provides an ideal strategy to conjugate tetrapyrroles to complex carbohydrates

A Spitzer IRS Study of Debris Disks Around Planet-Host Stars

Since giant planets scatter planetesimals within a few tidal radii of their orbits, the locations of existing planetesimal belts indicate regions where giant planet formation failed in bygone protostellar disks. Infrared observations of circumstellar dust produced by colliding planetesimals are therefore powerful probes of the formation histories of known planets. Here we present new Spitzer IRS spectrophotometry of 111 Solar-type stars, including 105 planet hosts. Our observations reveal 11 debris disks, including two previously undetected debris disks orbiting HD 108874 and HD 130322. Combining our 32 micron spectrophotometry with previously published MIPS photometry, we find that the majority of debris disks around planet hosts have temperatures in the range 60 < T < 100 K. Assuming a dust temperature T = 70 K, which is representative of the nine debris disks detected by both IRS and MIPS, we find that debris rings surrounding Sunlike stars orbit between 15 and 240 AU, depending on the mean particle size. Our observations imply that the planets detected by radial-velocity searches formed within 240 AU of their parent stars. If any of the debris disks studied here have mostly large, blackbody emitting grains, their companion giant planets must have formed in a narrow region between the ice line and 15 AU.Comment: Accepted for publication in the Astronomical Journal. 14 pages, including five figures and two table

Predicting the frequencies of diverse exo-planetary systems

Extrasolar planetary systems range from hot Jupiters out to icy comet belts more distant than Pluto. We explain this diversity in a model where the mass of solids in the primordial circumstellar disk dictates the outcome. The star retains measures of the initial heavy-element (metal) abundance that can be used to map solid masses onto outcomes, and the frequencies of all classes are correctly predicted. The differing dependences on metallicity for forming massive planets and low-mass cometary bodies are also explained. By extrapolation, around two-thirds of stars have enough solids to form Earth-like planets, and a high rate is supported by the first detections of low-mass exo-planets.Comment: 5 pages, 2 figures; accepted by MNRA

Multiscale Design of Materials

Current methods of materials development, relying mostly on experimental tests, are slow and expensive. It often takes over a decade and costs many millions of dollars to develop and certify new materials for critical applications. With evolving constraints being placed on the use of materials arising from concerns with energy and materials resource sustainability, new approaches for materials development is essential. Moreover, it is increasingly important for materials development to be integrated into overall product design and development, allowing for optimal use of materials as well as enhancing our ability to recycle and reuse. In this paper, we discuss a new program in which we link methodologies developed over the past few decades in computational materials science to a modern computational design platform (VE-Suite) to enable the multiscale design of materials. Development of such multiscale design platforms is essential for the successful implementation of integrated computational materials engineering (ICME), an emerging discipline within materials development. We will present the basic framework of our program and discuss progress to date

The circumbinary disk of HD 98800B: Evidence for disk warping

The quadruple young stellar system HD 98800 consists of two spectroscopic binary pairs with a circumbinary disk around the B component. Recent work by Boden and collaborators using infrared interferometry and radial velocity data resulted in a determination of the physical orbit for HD 98800B. We use the resulting inclination of the binary and the measured extinction toward the B component stars to constrain the distribution of circumbinary material. Although a standard optically and geometrically thick disk model can reproduce the spectral energy distribution, it cannot account for the observed extinction if the binary and the disk are coplanar. We next constructed a dynamical model to investigate the influence of the A component, which is not in the Ba‐Bb orbital plane, on the B disk. We find that these interactions have a substantial impact on the inclination of the B circumbinary disk with respect to the Ba‐Bb orbital plane. The resulting warp would be sufficient to place material into the line of sight and the noncoplanar disk orientation may also cause the upper layers of the disk to intersect the line of sight if the disk is geometrically thick. These simulations also support that the dynamics of the Ba‐Bb orbit clear the inner region to a radius of~3 AU. We then discuss whether the somewhat unusual properties of the HD 98800B disk are consistent with material remnant from the star formation process or with more recent creation by collisions from larger bodies

Origin of the Mediterranean outflow

Toe origin of the Mediterranean outflow is one of oceanography\u27s oldest problems. In this work, the flow of western Mediterranean deep water up and over the sill at Gibraltar is investigated from hydrographic observations and current measurements. The deep water is found to flow westward along the Moroccan continental slope in the western Mediterranean or Alboran Sea and to rise as it approaches the Strait of Gibraltar...