Twisted Jacobi manifolds, twisted Dirac-Jacobi structures and quasi-Jacobi bialgebroids

We study twisted Jacobi manifolds, a concept that we had introduced in a previous Note. Twisted Jacobi manifolds can be characterized using twisted Dirac-Jacobi, which are sub-bundles of Courant-Jacobi algebroids. We show that each twisted Jacobi manifold has an associated Lie algebroid with a 1-cocycle. We introduce the notion of quasi-Jacobi bialgebroid and we prove that each twisted Jacobi manifold has a quasi-Jacobi bialgebroid canonically associated. Moreover, the double of a quasi-Jacobi bialgebroid is a Courant-Jacobi algebroid. Several examples of twisted Jacobi manifolds and twisted Dirac-Jacobi structures are presented

Zero-temperature TAP equations for the Ghatak-Sherrington model

The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field $D$ for a large number of spins. This allows us to locate a first-order transition between the spin-glass and paramagnetic phases within a good accuracy. The total number of solutions is also determined as a function of $D$.Comment: 11 pages, 2 ps figures include

On quasi-Jacobi and Jacobi-quasi bialgebroids

We study quasi-Jacobi and Jacobi-quasi bialgebroids and their relationships with twisted Jacobi and quasi Jacobi manifolds. We show that we can construct quasi-Lie bialgebroids from quasi-Jacobi bialgebroids, and conversely, and also that the structures induced on their base manifolds are related via a quasi Poissonization

Effects of Random Biquadratic Couplings in a Spin-1 Spin-Glass Model

A spin-1 model, appropriated to study the competition between bilinear (J_{ij}S_{i}S_{j}) and biquadratic (K_{ij}S_{i}^{2}S_{j}^{2}) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins.Comment: 16 pages plus 2 ps figure

PAIRWISE VELOCITIES OF GALAXIES IN THE CFA AND SSRS2 REDSHIFT SURVEYS

(compressed version) We combine the CfA Redshift Survey (CfA2) and the Southern Sky Redshift Survey (SSRS2) to estimate the pairwise velocity dispersion of galaxies \sig12 on a scale of \sim 1 \hmpc. Both surveys are complete to an apparent magnitude limit $B(0)=15.5$. Our sample includes 12,812 galaxies distributed in a volume 1.8 \times 10^6 \hmpc3. We conclude: 1) The pairwise velocity dispersion of galaxies in the combined CfA2+SSRS2 redshift survey is \sig12=540 \kms \pm 180 \kms. Both the estimate and the variance of \sig12 significantly exceed the canonical values \sig12=340 \pm40 measured by Davis \& Peebles (1983) using CfA1. 2) We derive the uncertainty in \sig12 from the variation among subsamples with volumes on the order of $7 \times 10^5$ \hmpc3. This variation is nearly an order of magnitude larger than the formal error, 36 \kms, derived using least-squares fits to the CfA2+SSRS2 correlation function. This variation among samples is consistent with the conclusions of Mo \etal (1993) for a number of smaller surveys and with the analysis of CfA1 by Zurek \etal (1994). 3) When we remove Abell clusters with $R\ge1$ from our sample, the pairwise velocity dispersion of the remaining galaxies drops to 295 \pm 99 \kms. Thus the dominant source of variance in \sig12 is the shot noise contributed by dense virialized systems. 4) The distribution of pairwise velocities is consistent with an isotropic exponential with velocity dispersion independent of scale.Comment: 61 pages uuencoded, compressed postscript in 5 pieces. Also available in one piece at http://www.dao.nrc.ca/DAO/SCIENCE/science.htm

The Power Spectrum of Galaxies in the Nearby Universe

We compute the power spectrum of galaxy density fluctuations in a recently completed redshift survey of optically-selected galaxies in the southern hemisphere (SSRS2). The amplitude and shape of the SSRS2 power spectrum are consistent with results of the Center for Astrophysics redshift survey of the northern hemisphere (CfA2), including the abrupt change of slope on a scale of 30-50Mpc/h; these results are reproducible for independent volumes of space and variations are consistent with the errors estimated from mock surveys. Taken together, the SSRS2 and CfA2 form a complete sample of 14,383 galaxies which covers one-third of the sky. The power spectrum of this larger sample continues to rise on scales up to ~ 200Mpc/h, with weak evidence for flattening on the largest scales. The SSRS2+CfA2 power spectrum and the power spectrum constraints implied by COBE are well-matched by an Omega*h ~ 0.2, Omega+lambda_0=1 CDM model with minimal biasing of optically-selected galaxies.Comment: Accepted for publication in The Astrophysical Journal Letters, Sept. 23, 1994. 10 pages uuencoded compressed postscript, including two figures. JHU-9410200

Efficiency of low versus high airline pressure in stunning cattle with a pneumatically powered penetrating captive bolt gun

The efficiency of stunning cattle was assessed in 443 animals (304 pure Zebu and 139 crossbred cattle), being mainly mature bulls and cows. Cattle were stunned using a Jarvis pneumatically powered penetrating captive bolt gun operating with low (160–175 psi, N = 82) and high (190 psi, N = 363) airline pressure, which was within the manufactures specifications. Signs of brain function and the position of the shots on the heads were recorded after stunning. Velocity of the captive bolt and its physical parameters were calculated. Cattle shot with low pressures showed more rhythmic respiration (27 vs. 8%, P < 0.001), less tongue protrusion (4 vs. 12%, P = 0.03) and less masseter relaxation (22 vs. 48%, P < 0.001). There was an increased frequency of shots in the ideal position when cattle were shot with the low compared to high airline pressures (15.3 vs. 3.1%). Bolt velocity and its physical parameters were significantly (P < 0.01) higher when using high pressure. Airline pressures below 190 psi are inappropriate when shooting adult Zebu beef cattle with pneumatically powered penetrating captive bolt guns