Connections on modules over quasi-homogeneous plane curves

Let k be an algebraically closed field of characteristic 0, and let $A = k[x,y]/(f)$ be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M, there exists a natural graded integrable connection, i.e. a graded A-linear homomorphism $\nabla: \operatorname{Der}_k(A) \to \operatorname{End}_k(M)$ that satisfy the derivation property and preserves the Lie product. In particular, a torsion free module N over the complete local ring $B = \hat A$ admits a natural integrable connection if A is a simple curve singularity, or if A is irreducible and N is a gradable module.Comment: AMS-LaTeX, 12 pages, minor changes. To appear in Comm. Algebr

The two-and three-point correlation functions of the polarized five-year WMAP sky maps

We present the two- and three-point real space correlation functions of the five-year WMAP sky maps, and compare the observed functions to simulated LCDM concordance model ensembles. In agreement with previously published results, we find that the temperature correlation functions are consistent with expectations. However, the pure polarization correlation functions are acceptable only for the 33GHz band map; the 41, 61, and 94 GHz band correlation functions all exhibit significant large-scale excess structures. Further, these excess structures very closely match the correlation functions of the two (synchrotron and dust) foreground templates used to correct the WMAP data for galactic contamination, with a cross-correlation statistically significant at the 2sigma-3sigma confidence level. The correlation is slightly stronger with respect to the thermal dust template than with the synchrotron template.Comment: 10 pages, 5 figures, published in ApJ. v2: New title, minor changes to appendix, and fixed some typos. v3: Matches version published in Ap

Genetic variation within and among asexual populations of Porphyra umbilicalis Kützing (Bangiales, Rhodophyta) in the Gulf of Maine, USA

The intertidal marine red alga Porphyra umbilicalis reproduces asexually in the Northwest Atlantic. We looked for population substructure among typical open-coastal and atypical estuarine habitats in seven asexual populations of P. umbilicalis from Maine to New Hampshire using eight expressed sequence tag-simple sequence repeats (EST-SSR) or microsatellite loci. Six genotypes were identified, four of which may represent recombinant genotypes from a recombination event that took place locally, or that took place prior to introduction to the Northwest Atlantic. Genotypic diversity was lowest in a population from Wiscasset, Maine, which inhabits an atypical habitat high in the intertidal zone of a bridge piling in an estuarine tidal rapid. Genotypic diversity was highest in the southernmost populations from New Hampshire; we identified two genotypes that were unique to the southernmost populations, and probably represent the most derived genotypes. We looked at genetic distances among populations in similar habitats, and found that populations were more closely related to their closest neighboring population than to a population in a similar habitat. We show that genotypic diversity within P. umbilicalis populations in the Gulf of Maine is relatively high and thus fits a model of high steady-state variation within asexual populations

A Director’s Gut and Craft

An exploration of the director's work with form and leadership

Frequentist comparison of CMB local extrema statistics in the five-year WMAP data with two anisotropic cosmological models

We present local extrema studies of two models that introduce a preferred direction into the observed cosmic microwave background (CMB) temperature field. In particular, we make a frequentist comparison of the one- and two-point statistics for the dipole modulation and ACW models with data from the five-year Wilkinson Microwave Anisotropy Probe (WMAP). This analysis is motivated by previously revealed anomalies in the WMAP data, and particularly the difference in the statistical nature of the temperature anisotropies when analysed in hemispherical partitions. The analysis of the one-point statistics indicates that the previously determined hemispherical variance difficulties can be apparently overcome by a dipole modulation field, but new inconsistencies arise if the mean and the l-dependence of the statistics are considered. The two-point correlation functions of the local extrema, the temperature pair product and the point-point spatial pair-count, demonstrate that the impact of such a modulation is to over-`asymmetrise' the temperature field on smaller scales than the wave-length of the dipole or quadrupole, and this is disfavored by the observed data.The results from the ACW model predictions, however, are consistent with the standard isotropic hypothesis. The two-point analysis confirms that the impact of this type of violation of isotropy on the temperature extrema statistics is relatively weak. From this work, we conclude that a model with more spatial structure than the dipole modulated or rotational-invariance breaking models are required to fully explain the observed large-scale anomalies in the WMAP data.Comment: 10 pages, 4 figures, 3 tables, accepted for publication in MNRA

The effects of the exhaust plume on the lightning triggering conditions for launch vehicles

Apollo 12 and Atlas Centaur 67 are two launch vehicles that have experienced triggered lightning strikes. Serious consequences resulted from the events; in the case of Atlas Centaur 67, the vehicle and the payload were lost. These events indicate that it is necessary to develop launch rules which would prevent such occurrences. In order to develop valid lightning related rules, it is necessary to understand the effects of the plume. Some have assumed that the plume can be treated as a perfect conductor, and have computed electric field enhancement factors on that basis. The authors have looked at the plume, and believe that these models are not correct, because they ignore the fluid motion of the conducting plates. The authors developed a model which includes this flow character. In this model, the external field is excluded from the plume as it would be for any good conductor, but, in addition, the charge must distribute so that the charge density is zero at some location in the exhaust. When this condition is included in the calculation of triggering enhancement factors, they can be two to three times larger than calculated by other methods which include a conductive plume but don't include the correct boundary conditions. Here, the authors review the relevant features of rocket exhausts for the triggered lightning problem, present an approach for including flowing conductive gases, and present preliminary calculations to demonstrate the effect that the plume has on enhancement factors

Development of intermolecular potential models for electrolyte solutions using an electrolyte SAFT-VR Mie equation of state

We present a theoretical framework and parameterisation of intermolecular potentials for aqueous electrolyte solutions using the statistical associating fluid theory based on the Mie interaction potential (SAFT-VR Mie), coupled with the primitive, non-restricted mean-spherical approximation (MSA) for electrolytes. In common with other SAFT approaches, water is modelled as a spherical molecule with four off-centre association sites to represent the hydrogen-bonding interactions; the repulsive and dispersive interactions between the molecular cores are represented with a potential of the Mie (generalised Lennard-Jones) form. The ionic species are modelled as fully dissociated, and each ion is treated as spherical: Coulombic ion–ion interactions are included at the centre of a Mie core; the ion–water interactions are also modelled with a Mie potential without an explicit treatment of ion–dipole interaction. A Born contribution to the Helmholtz free energy of the system is included to account for the process of charging the ions in the aqueous dielectric medium. The parameterisation of the ion potential models is simplified by representing the ion–ion dispersive interaction energies with a modified version of the London theory for the unlike attractions. By combining the Shannon estimates of the size of the ionic species with the Born cavity size reported by Rashin and Honig, the parameterisation of the model is reduced to the determination of a single ion–solvent attractive interaction parameter. The resulting SAFT-VRE Mie parameter sets allow one to accurately reproduce the densities, vapour pressures, and osmotic coefficients for a broad variety of aqueous electrolyte solutions; the activity coefficients of the ions, which are not used in the parameterisation of the models, are also found to be in good agreement with the experimental data. The models are shown to be reliable beyond the molality range considered during parameter estimation. The inclusion of the Born free-energy contribution, together with appropriate estimates for the size of the ionic cavity, allows for accurate predictions of the Gibbs free energy of solvation of the ionic species considered. The solubility limits are also predicted for a number of salts; in cases where reliable reference data are available the predictions are in good agreement with experiment