Powers of the Vandermonde determinant, Schur Functions, and recursive formulas

Since every even power of the Vandermonde determinant is a symmetric polynomial, we want to understand its decomposition in terms of the basis of Schur functions. We investigate several combinatorial properties of the coefficients in the decomposition. In particular, we give recursive formulas for the coefficient of the Schur function s_{\m} in the decomposition of an even power of the Vandermonde determinant in $n + 1$ variables in terms of the coefficient of the Schur function s_{\l} in the decomposition of the same even power of the Vandermonde determinant in $n$ variables if the Young diagram of \m is obtained from the Young diagram of \l by adding a tetris type shape to the top or to the left. An extended abstract containing the statement of the results presented here appeared in the Proceedings of FPSAC11Comment: 23 pages; extended abstract appeared in the Proceedings of FPSAC1

Conical diffraction and the dispersion surface of hyperbolic metamaterials

Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal dielectric constants $\epsilon_1<0$, $0<\epsilon_2\neq\epsilon_3$. In this general case the two sheets of the index surface intersect forming conical singularities. We derive the ray description of conical refraction in these materials, and show that it is topologically and quantitatively distinct from conical refraction in a conventional biaxial material. We also develop a wave optics description, which allows us to obtain the diffraction patterns formed from arbitrary beams incident close to the optic axis. The resulting patterns lack circular symmetry, and hence are qualitatively different from those obtained in conventional, positive index materials.Comment: 10 pages, 7 figure

Investigation of Polymer–Plasticizer Blends as SH-SAW Sensor Coatings for Detection of Benzene in Water with High Sensitivity and Long-Term Stability

We report the first-ever direct detection of benzene in water at concentrations below 100 ppb (parts per billion) using acoustic wave (specifically, shear-horizontal surface acoustic wave, SH-SAW) sensors with plasticized polymer coatings. Two polymers and two plasticizers were studied as materials for sensor coatings. For each polymer–plasticizer combination, the influence of the mixing ratio of the blend on the sensitivity to benzene was measured and compared to commercially available polymers that were used for BTEX (benzene, toluene, ethylbenzene, and xylene) detection in previous work. After optimizing the coating parameters, the highest sensitivity and lowest detection limit for benzene were found for a 1.25 μm thick sensor coating of 17.5%-by-weight diisooctyl azelate-polystyrene on the tested acoustic wave device. The calculated detection limit was 45 ppb, with actual sensor responses to concentrations down to 65 ppb measured directly. Among the sensor coatings that showed good sensitivity to benzene, the best long-term stability was found for a 1.0 μm thick coating of 23% diisononyl cyclohexane-1,2-dicarboxylate-polystyrene, which was studied here because it is known to show no detectable leaching in water. The present work demonstrates that, by varying type of plasticizer, mixing ratio, and coating thickness, the mechanical and chemical properties of the coatings can be conveniently tailored to maximize analyte sorption and partial chemical selectivity for a given class of analytes as well as to minimize acoustic-wave attenuation in contact with an aqueous phase at the operating frequency of the sensor device

There are many ways to spin a photon : half-quantization of a total optical angular momentum

This work was supported by the Higher Education Authority of Ireland under PRTLI (Programme for Research in Third-Level Institutions) funding cycle 5 and by Science Foundation Ireland (09/SIRG/I1592, 12/RC/2278).The angular momentum of light plays an important role in many areas, from optical trapping to quantum information. In the usual three-dimensional setting, the angular momentum quantum numbers of the photon are integers, in units of the Planck constant ħ. We show that, in reduced dimensions, photons can have a half-integer total angular momentum. We identify a new form of total angular momentum, carried by beams of light, comprising an unequal mixture of spin and orbital contributions. We demonstrate the half-integer quantization of this total angular momentum using noise measurements. We conclude that for light, as is known for electrons, reduced dimensionality allows new forms of quantization.Publisher PDFPeer reviewe

Gas loading of graphene-quartz surface acoustic wave devices

Copyright © 2013 AIP PublishingGraphene was transferred to the propagation path of quartz surface acoustic wave devices and the attenuation due to gas loading of air and argon measured at 70 MHz and 210 MHz and compared to devices with no graphene. Under argon loading, there was no significant difference between the graphene and non-graphene device and the values of measured attenuation agree well with those calculated theoretically. Under air loading, at 210 MHz, there was a significant difference between the non-graphene and graphene devices, with the average value of attenuation obtained with the graphene devices being approximately twice that obtained from the bare quartz devices.Royal Societ

Deep-water macroalgae from the Canary Islands: new records and biogeographical relationships

Due to the geographical location and paleobiogeography of the Canary Islands, the seaweed flora contains macroalgae with different distributional patterns. In this contribution, the biogeographical relations of several new records of deep-water macroalgae recently collected around the Canarian archipelago are discussed. These are Bryopsidella neglecta (Berthotd) Rietema,Discosporangium mesarthrocarpum (Meneghini) Hauck, Hincksia onslowensis (Amsler et Kapraun)P.C. Silva, Syringoderma floridana Henry, Peyssonnelia harveyana J. Agardh, Cryptonemia seminervis(C. Agardh) J. Agardh, Botryodadia wynnei Ballantine, Gloiocladia blomquistii (Searles) R. E.Norris, PIahchrysis peltata (W. R. Taylor) P. Huv4 et H. Huv4, Leptofauchea brasiliensis Joly, and Sarcodiotheca divaricata W. R. Taylor. These new records, especially those in the Florideophyceae,support the strong affinity of the Canary Islands seaweed flora with the warm-temperate Mediterranean-Atlantic region. Some species are recorded for the first time from the east coast of the Atlantic Ocean, enhancing the biogeographic relations of the Canarian marine flora with that of the western Atlantic regions

Using Molecular-Assisted Alpha Taxonomy to Better Understand Red Algal Biodiversity in Bermuda

Molecular-assisted alpha taxonomy has recently become an effective practice in reassessing biodiversity and floristics for a variety of different organisms. This paper presents a series of examples that have been drawn from biodiversity work being carried out on the marine red algae of Bermuda. Molecular sequencing of DNA from Bermuda samples has already begun to greatly alter the makeup of the flora as it was known just decades ago, and will help set a new database for future comparison as climate change affects species composition in the islands

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Eco-engineered rock pools: a concrete solution to biodiversity loss and urban sprawl in the marine environment

journal_title: Environmental Research Letters article_type: lett article_title: Eco-engineered rock pools: a concrete solution to biodiversity loss and urban sprawl in the marine environment copyright_information: © 2016 IOP Publishing Ltd license_information: cc-by Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. date_received: 2016-05-12 date_accepted: 2016-08-10 date_epub: 2016-09-1

Structural and Functional Loss in Restored Wetland Ecosystems

In restored wetland ecosystems with apparently natural hydrology and biological structure, biogeochemical function may remain degraded, even a century after restoration efforts