Twisting commutative algebraic groups

If $V$ is a commutative algebraic group over a field $k$, $O$ is a commutative ring that acts on $V$, and $I$ is a finitely generated free $O$-module with a right action of the absolute Galois group of $k$, then there is a commutative algebraic group $I \otimes_O V$ over $k$, which is a twist of a power of $V$. These group varieties have applications to cryptography (in the cases of abelian varieties and algebraic tori over finite fields) and to the arithmetic of abelian varieties over number fields. For purposes of such applications we devote this article to making explicit this tensor product construction and its basic properties.Comment: To appear in Journal of Algebra. Minor changes from original versio

Numerical Studies of Weakly Stochastic Magnetic Reconnection

We study the effects of turbulence on magnetic reconnection using three-dimensional numerical simulations. This is the first attempt to test a model of fast magnetic reconnection proposed by Lazarian & Vishniac (1999), which assumes the presence of weak, small-scale magnetic field structure near the current sheet. This affects the rate of reconnection by reducing the transverse scale for reconnection flows and by allowing many independent flux reconnection events to occur simultaneously. We performed a number of simulations to test the dependencies of the reconnection speed, defined as the ratio of the inflow velocity to the Alfven speed, on the turbulence power, the injection scale and resistivity. Our results show that turbulence significantly affects the topology of magnetic field near the diffusion region and increases the thickness of the outflow region. We confirm the predictions of the Lazarian & Vishniac model. In particular, we report the growth of the reconnection speed proportional to ~ V^2, where V is the amplitude of velocity at the injection scale. It depends on the injection scale l as ~ (l/L)^(2/3), where L is the size of the system, which is somewhat faster but still roughly consistent with the theoretical expectations. We also show that for 3D reconnection the Ohmic resistivity is important in the local reconnection events only, and the global reconnection rate in the presence of turbulence does not depend on it.Comment: 8 pages, 8 figure

The gravitational path integral and trace of the diffeomorphisms

I give a resolution of the conformal mode divergence in the Euclidean gravitational path-integral by isolating the trace of the diffeomorphisms and its contribution to the Faddeev-Popov measure.Comment: 20 pgs

Large-scale radio continuum properties of 19 Virgo cluster galaxies The influence of tidal interactions, ram pressure stripping, and accreting gas envelopes

Deep scaled array VLA 20 and 6cm observations including polarization of 19 Virgo spirals are presented. This sample contains 6 galaxies with a global minimum of 20cm polarized emission at the receding side of the galactic disk and quadrupolar type large-scale magnetic fields. In the new sample no additional case of a ram-pressure stripped spiral galaxy with an asymmetric ridge of polarized radio continuum emission was found. In the absence of a close companion, a truncated HI disk, together with a ridge of polarized radio continuum emission at the outer edge of the HI disk, is a signpost of ram pressure stripping. 6 out of the 19 observed galaxies display asymmetric 6cm polarized emission distributions. Three galaxies belong to tidally interacting pairs, two galaxies host huge accreting HI envelopes, and one galaxy had a recent minor merger. Tidal interactions and accreting gas envelopes can lead to compression and shear motions which enhance the polarized radio continuum emission. In addition, galaxies with low average star formation rate per unit area have a low average degree of polarization. Shear or compression motions can enhance the degree of polarization. The average degree of polarization of tidally interacting galaxies is generally lower than expected for a given rotation velocity and star formation activity. This low average degree of polarization is at least partly due to the absence of polarized emission from the thin disk. Ram pressure stripping can decrease whereas tidal interactions most frequently decreases the average degree of polarization of Virgo spiral galaxies. We found that moderate active ram pressure stripping has no influence on the spectral index, but enhances the global radio continuum emission with respect to the FIR emission, while an accreting gas envelope can but not necessarily enhances the radio continuum emission with respect to the FIR emission.Comment: 37 pages, 26 figures, accepted for publication in A&

Using a well-being approach to develop a framework for an integrated socio-economic evaluation of professional fishing

© 2017 John Wiley & Sons Ltd The principles of Ecologically Sustainable Development and Ecosystem Based Fisheries Management require that fisheries be managed for social as well as environmental and economic objectives. Comprehensive assessments of the success of fisheries in achieving all three objectives are, however, rare. There are three main barriers to achieving integrated assessments of fisheries. Firstly, disciplinary divides can be considered “too hard” to bridge with inherent conflicts between the predominately empirical and deductive traditions of economics and biophysical sciences and the inductive and interpretative approach of much of the social sciences. Secondly, understanding of the social pillar of sustainability is less well developed. And finally, in-depth analysis of the social aspects of sustainability often involves qualitative analysis and there are practical difficulties in integrating this with largely quantitative economic and ecological assessments. This article explores the social well-being approach as a framework for an integrated evaluation of the social and economic benefits that communities in New South Wales, Australia, receive from professional fish harvesting. Using a review of existing literature and qualitative interviews with more than 160 people associated with the fishing industry the project was able to identify seven key domains of community well-being to which the industry contributes. Identification of these domains provided a framework through which industry contributions could be further explored, through quantitative surveys and economic analysis. This framework enabled successful integration of social and economic, and both qualitative and quantitative information in a manner that enabled a comprehensive assessment of the value of the fishery

Characteristic Energy of the Coulomb Interactions and the Pileup of States

Tunneling data on $\mathrm{La_{1.28}Sr_{1.72}Mn_2O_7}$ crystals confirm Coulomb interaction effects through the $\sqrt{\mathrm{E}}$ dependence of the density of states. Importantly, the data and analysis at high energy, E, show a pileup of states: most of the states removed from near the Fermi level are found between ~40 and 130 meV, from which we infer the possibility of universal behavior. The agreement of our tunneling data with recent photoemission results further confirms our analysis.Comment: 4 pages, 4 figures, submitted to PR

Quantum Diffeomorphisms and Conformal Symmetry

We analyze the constraints of general coordinate invariance for quantum theories possessing conformal symmetry in four dimensions. The character of these constraints simplifies enormously on the Einstein universe $R \times S^3$. The $SO(4,2)$ global conformal symmetry algebra of this space determines uniquely a finite shift in the Hamiltonian constraint from its classical value. In other words, the global Wheeler-De Witt equation is {\it modified} at the quantum level in a well-defined way in this case. We argue that the higher moments of $T^{00}$ should not be imposed on the physical states {\it a priori} either, but only the weaker condition $\langle \dot T^{00} \rangle = 0$. We present an explicit example of the quantization and diffeomorphism constraints on $R \times S^3$ for a free conformal scalar field.Comment: PlainTeX File, 37 page