The algebra of supertraces for 2+1 super de Sitter gravity

The algebra of the observables for 2+1 super de Sitter gravity, for one genus of the spatial surface is calculated. The algebra turns out to be an infinite Lie algebra subject to non-linear constraints. The constraints are solved explicitly in terms of five independent complex supertraces. These variables are the true degrees of freedom of the system and their quantized algebra generates a new structure which is referred to as a 'central extension' of the quantum algebra SU(2)q

High Precision Ringdown Modeling: Multimode Fits and BMS Frames

Quasi-normal mode (QNM) modeling is an invaluable tool for studying strong gravity, characterizing remnant black holes, and testing general relativity. To date, most studies have focused on the dominant $(2, 2)$ mode, and have fit to standard strain waveforms from numerical relativity. But, as gravitational wave observatories become more sensitive, they can resolve higher-order modes. Multimode fits will be critically important, and in turn require a more thorough treatment of the asymptotic frame at $\mathscr{I}^+$. The first main result of this work is a method for systematically fitting a QNM model containing many modes to a numerical waveform produced using Cauchy-characteristic extraction, which is known to exhibit memory effects. We choose the modes to model based on their power contribution to the residual between numerical and model waveforms. We show that the all-angles mismatch improves by a factor of $\sim 10^5$ when using multimode fitting as opposed to only fitting $(2, \pm2, n)$ modes. Our second main result addresses a critical point that has been overlooked in the literature: the importance of matching the Bondi-van der Burg-Metzner-Sachs (BMS) frame of the simulated gravitational wave to that of the QNM model. We show that by mapping the numerical relativity waveforms to the super rest frame, there is an improvement of $\sim 10^5$ in the all-angles strain mismatch, compared to using the strain whose BMS frame is not fixed. We illustrate the effectiveness of these modeling enhancements by applying them to families of waveforms produced by numerical relativity, and comparing our results to previous studies

Weyl's law and quantum ergodicity for maps with divided phase space

For a general class of unitary quantum maps, whose underlying classical phase space is divided into several invariant domains of positive measure, we establish analogues of Weyl's law for the distribution of eigenphases. If the map has one ergodic component, and is periodic on the remaining domains, we prove the Schnirelman-Zelditch-Colin de Verdiere Theorem on the equidistribution of eigenfunctions with respect to the ergodic component of the classical map (quantum ergodicity). We apply our main theorems to quantised linked twist maps on the torus. In the Appendix, S. Zelditch connects these studies to some earlier results on `pimpled spheres' in the setting of Riemannian manifolds. The common feature is a divided phase space with a periodic component.Comment: Colour figures. Black & white figures available at http://www2.maths.bris.ac.uk/~majm. Appendix by Steve Zelditc

Homotopy Invariants and Time Evolution in (2+1)-Dimensional Gravity

We establish the relation between the ISO(2,1) homotopy invariants and the polygon representation of (2+1)-dimensional gravity. The polygon closure conditions, together with the SO(2,1) cycle conditions, are equivalent to the ISO(2,1) cycle conditions for the representa- tions of the fundamental group in ISO(2,1). Also, the symplectic structure on the space of invariants is closely related to that of the polygon representation. We choose one of the polygon variables as internal time and compute the Hamiltonian, then perform the Hamilton-Jacobi transformation explicitly. We make contact with other authors' results for g = 1 and g = 2 (N = 0).Comment: 34 pages, Mexico preprint ICN-UNAM-93-1

Nitrogen uptake and internal recycling in Zostera marina exposed to oyster farming: eelgrass potential as a natural biofilter

Oyster farming in estuaries and coastal lagoons frequently overlaps with the distribution of seagrass meadows, yet there are few studies on how this aquaculture practice affects seagrass physiology. We compared in situ nitrogen uptake and the productivity of Zostera marina shoots growing near off-bottom longlines and at a site not affected by oyster farming in San Quintin Bay, a coastal lagoon in Baja California, Mexico. We used benthic chambers to measure leaf NH4 (+) uptake capacities by pulse labeling with (NH4)-N-15 (+) and plant photosynthesis and respiration. The internal N-15 resorption/recycling was measured in shoots 2 weeks after incubations. The natural isotopic composition of eelgrass tissues and vegetative descriptors were also examined. Plants growing at the oyster farming site showed a higher leaf NH4 (+) uptake rate (33.1 mmol NH4 (+) m(-2) day(-1)) relative to those not exposed to oyster cultures (25.6 mmol NH4 (+) m(-2) day(-1)). We calculated that an eelgrass meadow of 15-16 ha (which represents only about 3-4 % of the subtidal eelgrass meadow cover in the western arm of the lagoon) can potentially incorporate the total amount of NH4 (+) excreted by oysters (similar to 5.2 x 10(6) mmol NH4 (+) day(-1)). This highlights the potential of eelgrass to act as a natural biofilter for the NH4 (+) produced by oyster farming. Shoots exposed to oysters were more efficient in re-utilizing the internal N-15 into the growth of new leaf tissues or to translocate it to belowground tissues. Photosynthetic rates were greater in shoots exposed to oysters, which is consistent with higher NH4 (+) uptake and less negative delta C-13 values. Vegetative production (shoot size, leaf growth) was also higher in these shoots. Aboveground/belowground biomass ratio was lower in eelgrass beds not directly influenced by oyster farms, likely related to the higher investment in belowground biomass to incorporate sedimentary nutrients

First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data

Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signalto- noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, narrow-band analysis methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of 11 pulsars using data from Advanced LIGO’s first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched; in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far