Invariant expectations and vanishing of bounded cohomology for exact groups

We study exactness of groups and establish a characterization of exact groups in terms of the existence of a continuous linear operator, called an invariant expectation, whose properties make it a weak counterpart of an invariant mean on a group. We apply this operator to show that exactness of a finitely generated group $G$ implies the vanishing of the bounded cohomology of $G$ with coefficients in a new class of modules, which are defined using the Hopf algebra structure of $\ell_1(G)$.Comment: Final version, to appear in the Journal of Topology and Analysi

Superlattice Patterns in Surface Waves

We report novel superlattice wave patterns at the interface of a fluid layer driven vertically. These patterns are described most naturally in terms of two interacting hexagonal sublattices. Two frequency forcing at very large aspect ratio is utilized in this work. A superlattice pattern ("superlattice-I") consisting of two hexagonal lattices oriented at a relative angle of 22^o is obtained with a 6:7 ratio of forcing frequencies. Several theoretical approaches that may be useful in understanding this pattern have been proposed. In another example, the waves are fully described by two superimposed hexagonal lattices with a wavelength ratio of sqrt(3), oriented at a relative angle of 30^o. The time dependence of this "superlattice-II" wave pattern is unusual. The instantaneous patterns reveal a time-periodic stripe modulation that breaks the 6-fold symmetry at any instant, but the stripes are absent in the time average. The instantaneous patterns are not simply amplitude modulations of the primary standing wave. A transition from the superlattice-II state to a 12-fold quasi-crystalline pattern is observed by changing the relative phase of the two forcing frequencies. Phase diagrams of the observed patterns (including superlattices, quasicrystalline patterns, ordinary hexagons, and squares) are obtained as a function of the amplitudes and relative phases of the driving accelerations.Comment: 15 pages, 14 figures (gif), to appear in Physica

The structural sensitivity of open shear flows calculated with a local stability analysis

The structural sensitivity shows where an instability of a fluid flow is most sensitive to changes in internal feedback mechanisms. It is formed from the overlap of the flow's direct and adjoint global modes. These global modes are usually calculated with 2D or 3D global stability analyses, which can be very computationally expensive. For weakly non-parallel flows the direct global mode can also be calculated with a local stability analysis, which is orders of magnitude cheaper. In this theoretical paper we show that, if the direct global mode has been calculated with a local analysis, then the adjoint global mode follows at little extra cost. We also show that the maximum of the structural sensitivity is the location at which the local k+ and k- branches have the same imaginary value. Finally, we use the local analysis to derive the structural sensitivity of two flows: a confined co-flow wake at Re = 400, for which it works very well, and the flow behind a cylinder at Re = 50, for which it works reasonably well. As expected, we find that the local analysis becomes less accurate when the flow becomes less parallel.This is the preprint version of the manuscript as submitted to the journal. The final version will be published by Elsevier

A Preliminary Discussion of the Kinematics of BHB and RR Lyrae Stars near the North Galactic Pole

The radial velocity dispersion of 67 RR Lyrae variable and blue horizontal branch (BHB) stars that are more than 4 kpc above the galactic plane at the North Galactic Pole is 110 km/sec and shows no trend with Z (the height above the galactic plane). Nine stars with Z < 4 kpc show a smaller velocity dispersion (40 +/-9 km/sec) as is to be expected if they mostly belong to a population with a flatter distribution. Both RR Lyrae stars and BHB stars show evidence of stream motion; the most significant is in fields RR2 and RR3 where 24 stars in the range 4.0 < Z < 11.0 kpc have a mean radial velocity of -59 +/- 16 km/sec. Three halo stars in field RR 2 appear to be part of a moving group with a common radial velocity of -90 km/sec. The streaming phenomenon therefore occurs over a range of spatial scales. The BHB and RR Lyrae stars in our sample both have a similar range of metallicity (-1.2 < [Fe/H] < -2.2). Proper motions of BHB stars in fields SA 57 (NGP) and the Anticenter field (RR 7) (both of which lie close to the meridional plane of the Galaxy) show that the stars that have Z 4 kpc have a Galactic V motion that is < -200 km/sec and which is characteristic of the halo. Thus the stars that have a flatter distribution are really halo stars and not members of the metal-weak thick-disk.Comment: Accepted for publication in the March 1996 AJ. 15 pages, AASTeX V4.0 latex format (including figures), 2 eps figures, 2 separate AASTeX V4.0 latex table

Poly-N-Acetylglucosamine Expression by Wild-Type Yersinia pestis Is Maximal at Mammalian, Not Flea, Temperatures

Numerous bacteria, including Yersinia pestis, express the poly-N-acetylglucosamine (PNAG) surface carbohydrate, a major component of biofilms often associated with a specific appearance of colonies on Congo red agar. Biofilm formation and PNAG synthesis by Y. pestis have been reported to be maximal at 21 to 28°C or “flea temperatures,” facilitating the regurgitation of Y. pestis into a mammalian host during feeding, but production is diminished at 37°C and thus presumed to be decreased during mammalian infection. Most studies of PNAG expression and biofilm formation by Y. pestis have used a low-virulence derivative of strain KIM, designated KIM6+, that lacks the pCD1 virulence plasmid, and an isogenic mutant without the pigmentation locus, which contains the hemin storage genes that encode PNAG biosynthetic proteins. Using confocal microscopy, fluorescence-activated cell sorter analysis and growth on Congo red agar, we confirmed prior findings regarding PNAG production with the KIM6+ strain. However, we found that fully virulent wild-type (WT) strains KIM and CO92 had maximal PNAG expression at 37°C, with lower PNAG production at 28°C both in broth medium and on Congo red agar plates. Notably, the typical dark colony morphology appearing on Congo red agar was maintained at 28°C, indicating that this phenotype is not associated with PNAG expression in WT Y. pestis. Extracts of WT sylvatic Y. pestis strains from the Russian Federation confirmed the maximal expression of PNAG at 37°C. PNAG production by WT Y. pestis is maximal at mammalian and not insect vector temperatures, suggesting that this factor may have a role during mammalian infection