Toric Genera

Our primary aim is to develop a theory of equivariant genera for stably complex manifolds equipped with compatible actions of a torus T^k. In the case of omnioriented quasitoric manifolds, we present computations that depend only on their defining combinatorial data; these draw inspiration from analogous calculations in toric geometry, which seek to express arithmetic, elliptic, and associated genera of toric varieties in terms only of their fans. Our theory focuses on the universal toric genus \Phi, which was introduced independently by Krichever and Loeffler in 1974, albeit from radically different viewpoints. In fact \Phi is a version of tom Dieck's bundling transformation of 1970, defined on T^k-equivariant complex cobordism classes and taking values in the complex cobordism algebra of the classifying space. We proceed by combining the analytic, the formal group theoretic, and the homotopical approaches to genera, and refer to the index theoretic approach as a recurring source of insight and motivation. The resultant flexibility allows us to identify several distinct genera within our framework, and to introduce parametrised versions that apply to bundles equipped with a stably complex structure on the tangents along their fibres. In the presence of isolated fixed points, we obtain universal localisation formulae, whose applications include the identification of Krichever's generalised elliptic genus as universal amongst genera that are rigid on SU-manifolds. We follow the traditions of toric geometry by working with a variety of illustrative examples wherever possible. For background and prerequisites we attempt to reconcile the literature of east and west, which developed independently for several decades after the 1960s.Comment: 35 pages, LaTeX. In v2 references made to the index theoretical approach to genera; rigidity and multiplicativity results improved; acknowledgements adde

Restoring Native Oysters in Great Bay Estuary, NH (2011)

The eastern oyster (Crassostrea virginica) in New Hampshire’s Great Bay Estuary has declined in the past decades, with local populations at very low densities due primarily to disease, excessive siltation, and past over-harvest. The loss of filtering oysters results in diminished ecological benefits for water quality, nitrogen control, and other services that healthy oyster populations provide. In support of regional management objectives to restore millions of oysters to the estuary, the Nature Conservancy (TNC) and the University of New Hampshire (UNH) piloted and scaled-up methods to successfully rebuild oyster reefs. Based on pilot results in 2009, we developed a technique using a thin layer of recycled clamshell “planted” over silted channel bottom as a hard substrate foundation to recruit natural spawn, supplemented with hatchery-raised and volunteer-grown seed “spat”. In 2010, a full acre reef was constructed and seeded at the mouth of the Oyster River in Durham, producing a one-year standing stock of \u3e200K oysters. In 2011, restoration efforts were scaled up significantly, led by support from the Piscataqua Region Estuaries Partnership (PREP), with two acres of reef construction at the mouth of the Lamprey River (Newmarket NH). In June 2011, approximately 200 yd3 of seasoned surf clam shell was deployed at the site for total shell coverage of 80,000 ft2 (7,432 m2). Fall monitoring results showed that an estimated 58K oyster spat were recruited to the reef (19.5 spat/m2). Supplements from UNH remote setting operations added 428K spat to the reef areas, plus an additional 17K spat were raised by community volunteers. By fall 2011, the completed reefs achieved a standing stock of \u3e500K oysters. In addition, another half-acre restoration site was built nearby with farmer support. Collectively, our efforts demonstrate significant progress towards a regional goal of 20 acres of oyster reef restored by 2020, and position us for further expansion of restoration work going forward

The Formal Underpinnings of the Response Functions used in X-Ray Spectral Analysis

This work provides an in-depth mathematical description of the response functions that are used for spatial and spectral analysis of X-ray data. The use of such functions is well-known to anyone familiar with the analysis of X-ray data where they may be identified with the quantities contained in the Ancillary Response File (ARF), the Redistribution Matrix File (RMF), and the Exposure Map. Starting from first-principles, explicit mathematical expressions for these functions, for both imaging and dispersive modes, are arrived at in terms of the underlying instrumental characteristics of the telescope including the effects of pointing motion. The response functions are presented in the context of integral equations relating the expected detector count rate to the source spectrum incident upon the telescope. Their application to the analysis of several source distributions is considered. These include multiple, possibly overlapping, and spectrally distinct point sources, as well as extended sources. Assumptions and limitations behind the usage of these functions, as well as their practical computation are addressed.Comment: 22 pages, 3 figures (LaTeX

Restoring Oyster Reefs in Great Bay Estuary, NH 2012 Annual Program Report

The eastern oyster (Crassostrea virginica) in New Hampshire’s Great Bay Estuary has declined in the past decades, with local populations reduced due primarily to disease, excessive siltation, and past over-harvest. The loss of filtering oysters results in diminished ecological benefits for water quality, nitrogen control, and other services that healthy oyster populations provide. In support of management objectives to restore oyster populations, The Nature Conservancy (TNC) and the University of New Hampshire (UNH) have combined for a fourth consecutive year of scaled-up methods to rebuild reefs and oyster populations. Since 2009, we have “planted” dried shell, primarily surf-clam and oyster mix, on channel bottom as a hard substrate foundation to recruit spawn from nearby native populations. Constructed areas are amended with laboratory raised and volunteer-grown “spat-on-shell” from remotely set larvae to supplement recruitment. In 2012, despite limited funding, we successfully constructed and seeded two new acres of reef adjacent to native oysters in the mouth of Squamscott River, Newmarket. Results were somewhat below target for shell cover and live oyster density but natural recruitment was strong and encouraging for future reef development. Overall, we restored about a quarter of a million new oysters to the estuary. Community engagement, particularly through the volunteer Oyster Conservationist program, reached an all-time high with thirty-nine families participating in direct restoration activities and another twenty-three volunteers assisting in various project tasks

Stability of strange stars (SS) derived from a realistic equation of state

A realistic equation of state (EOS) leads to realistic strange stars (ReSS) which are compact in the mass radius plot, close to the Schwarzchild limiting line (Dey et al 1998). Many of the observed stars fit in with this kind of compactness, irrespective of whether they are X-ray pulsars, bursters or soft $\gamma$ repeaters or even radio pulsars. We point out that a change in the radius of a star can be small or large, when its mass is increasing and this depends on the position of a particular star on the mass radius curve. We carry out a stability analysis against radial oscillations and compare with the EOS of other strange star (SS) models. We find that the ReSS is stable and an M-R region can be identified to that effect.Comment: 16 pages including 5 figures. Accepted for publication in MPL

Scaling-Up: A Fifth Year of Restoring Oyster Reefs in Great Bay Estuary, NH 2013 Annual Program Report

The eastern oyster (Crassostrea virginica) in New Hampshire’s Great Bay Estuary has declined in the past decades, with local populations reduced due primarily to disease, excessive siltation, and past over-harvest. The loss of filtering oysters results in diminished ecological benefits for water quality, nitrogen control, and other services that healthy oyster populations provide. In support of management objectives to restore oyster populations, The Nature Conservancy (TNC) and the University of New Hampshire (UNH) have combined for a fifth consecutive year of scaled-up methods to rebuild oyster reefs and populations. Since 2009, we have “planted” seasoned shell, primarily surf-clam and oyster mix, on channel bottom as a hard substrate foundation to recruit spawn from nearby native populations. Constructed areas are amended to supplement recruitment with laboratory-raised and volunteer-grown “spat-on-shell” from remotely set larvae. Following four consecutive years of experience and adaptation, 2013 was a year of unprecedented effort and conservation outcomes. We successfully constructed and seeded five new acres of reef adjacent to native oysters in the Piscataqua River in Dover (1.5 acres) and in the Lamprey River in Newmarket (3.5 acres). Notably, we employed a new shell deployment method to achieve large-scale reef construction. Restoration efforts were greatly enhanced by excellent remote set success and outstanding natural recruitment, resulting in over 2M oysters. In addition, community engagement through the volunteer Oyster Conservationist program reached another all-time high with fifty families producing our largest oyster stock ever for restoration. Over the past five years, our efforts have added over 13 acres and 3M oysters to the ecosystem, increasing native Great Bay Estuary oyster populations by about 10%

Coupling between magnetic ordering and structural instabilities in perovskite biferroics: A first-principles study

We use first-principles density functional theory-based calculations to investigate structural instabilities in the high symmetry cubic perovskite structure of rare-earth (R $=$ La, Y, Lu) and Bi-based biferroic chromites, focusing on $\Gamma$ and $R$ point phonons of states with para-, ferro-, and antiferromagnetic ordering. We find that (a) the structure with G-type antiferromagnetic ordering is most stable, (b) the most dominant structural instabilities in these oxides are the ones associated with rotations of oxygen octahedra, and (c) structural instabilities involving changes in Cr-O-Cr bond angle depend sensitively on the changes in magnetic ordering. The dependence of structural instabilities on magnetic ordering can be understood in terms of how super-exchange interactions depend on the Cr-O-Cr bond angles and Cr-O bond lengths. We demonstrate how adequate buckling of Cr-O-Cr chains can favour ferromagnetism. Born effective charges (BEC) calculated using the Berry phase expression are found to be anomalously large for the A-cations, indicating their chemical relevance to ferroelectric distortions.Comment: 8 pages, 13 figure

Sub-arcsecond high sensitivity measurements of the DG~Tau jet with e-MERLIN

We present very high spatial resolution deep radio continuum observations at 5 GHz (6 cm) made with e-MERLIN of the young stars DG Tau A and B. Assuming it is launched very close (~=1 au) from the star, our results suggest that the DG Tau A outflow initially starts as a poorly focused wind and undergoes significant collimation further along the jet (~=50 au). We derive jet parameters for DG Tau A and find an initial jet opening angle of 86 degrees within 2 au of the source, a mass-loss rate of 1.5x10^-8 solar masses/yr for the ionised component of the jet, and the total ejection/accretion ratio to range from 0.06-0.3. These results are in line with predictions from MHD jet-launching theories.Comment: Accepted MNRAS Letter