Geometric phases for corotating elliptical vortex patches

We describe a geometric phase that arises when two elliptical vortex patches corotate. Using the Hamiltonian moment model of Melander, Zabusky, and Styczek [J. Fluid Mech. 167, 95–115 (1986)] we consider two corotating uniform elliptical patches evolving according to the second order truncated equations of the model. The phase is computed in the adiabatic setting of a slowly varying Hamiltonian as in the work of Hannay [J. Phys. A 18, 221–230 (1985)] and Berry [Proc. R. Soc. London, Ser. A 392, 45–57 (1984)]. We also discuss the geometry of the symplectic phase space of the model in the context of nonadiabatic phases. The adiabatic phase appears in the orientation angle of each patch—it is similiar in form and is calculated using a multiscale perturbation procedure as in the point vortex configuration of Newton [Physica D 79, 416–423 (1994)] and Shashikanth and Newton [J. Nonlinear Sci. 8, 183–214 (1998)], however, an extra factor due to the internal stucture of the patch is present. The final result depends on the initial orientation of the patches unlike the phases in the works of Hannay and Berry [J. Phys. A 18, 221–230 (1985)]; [Proc. R. Soc. London, Ser. A 392, 45–57 (1984)]. We then show that the adiabatic phase can be interpreted as the holonomy of a connection on the trivial principal fiber bundle pi:T2×S1-->S1, where T2 is identified with the product of the momentum level sets of two Kirchhoff vortex patches and S1 is diffeomorphic to the momentum level set of two point vortex motion. This two point vortex motion is the motion that the patch centroids approach in the adiabatic limit

Remarkable symmetries in the Milky Way disk's magnetic field

Using a new, expanded compilation of extragalactic source Faraday rotation measures (RM) we investigate the broad underlying magnetic structure of the Galactic disk at latitudes $|b|$ $\lesssim 15^{\circ}$ over all longitudes $l$, where our total number of RM's in this low-latitude range of the Galactic sky is comparable to those in the combined Canadian Galactic Plane Survey(CGPS) at $|b| < 4^{\circ}$ and the Southern Galactic Plane (SGPS) $|b| < 1.5^{\circ}$ survey. We report newly revealed, remarkably coherent patterns of RM at $|b|$ $\lesssim 15^{\circ}$ from $l \sim 270^{\circ}$ to $\sim 90^\circ$ and RM($l$) features of unprecedented clarity that replicate in $l$ with opposite sign on opposite sides of the Galactic center. They confirm a highly patterned bisymmetric field structure toward the inner disc, an axisymmetic pattern toward the outer disc, and a very close coupling between the CGPS/SGPS RM's at $|b| \lesssim 3^{\circ}$ ("mid-plane") and our new RM's up to $|b| \sim 15^{\circ}$ ("near-plane"). Our analysis also shows the approximate $z$-height -- the vertical height of the coherent component of the disc field above the Galactic disc's mid-plane -- to be $\sim 1.5$kpc out to $\sim 6$ kpc from the Sun. This identifies the approximate height of the transition layer to the halo field structure. We find no RM sign change across the plane within $|b| \sim 15^{\circ}$ in any longitude range. The prevailing {\it disc} field pattern, and its striking degree of large scale ordering confirm that our side of the Milky Way has a very organized underlying magnetic structure, for which the inward spiral pitch angle is $5.5^{\circ}\, \pm 1^{\circ}$ at all $|b|$ up to $\sim 12^{\circ}$ in the inner semicircle of Galactic longitudes. It decreases to $\sim 0^{\circ}$ toward the anticentre.Comment: 7 pages, 5 figures, Version 3. Accepted 2011 for publication in Publications of the Astronomical Society of Australia(PASA

Viscous evolution of point vortex equilibria: The collinear state

When point vortex equilibria of the 2D Euler equations are used as initial conditions for the corre- sponding Navier-Stokes equations (viscous), typically an interesting dynamical process unfolds at short and intermediate time scales, before the long time single peaked, self-similar Oseen vortex state dom- inates. In this paper, we describe the viscous evolution of a collinear three vortex structure that cor- responds to an inviscid point vortex fixed equilibrium. Using a multi-Gaussian 'core-growth' type of model, we show that the system immediately begins to rotate unsteadily, a mechanism we attribute to a 'viscously induced' instability. We then examine in detail the qualitative and quantitative evolution of the system as it evolves toward the long-time asymptotic Lamb-Oseen state, showing the sequence of topological bifurcations that occur both in a fixed reference frame, and in an appropriately chosen rotating reference frame. The evolution of passive particles in this viscously evolving flow is shown and interpreted in relation to these evolving streamline patterns.Comment: 17 pages, 15 figure

Binary Decision Diagrams: from Tree Compaction to Sampling

Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of each unique subtree. This yields the celebrated and widely used structure called reduced ordered binary decision diagram (ROBDD). We propose to revisit the classical compaction process to give a new way of enumerating ROBDDs of a given size without considering fully expanded trees and the compaction step. Our method also provides an unranking procedure for the set of ROBDDs. As a by-product we get a random uniform and exhaustive sampler for ROBDDs for a given number of variables and size

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

M 33 X-7: ChASeM33 reveals the first eclipsing black hole X-ray binary

The first observations conducted as part of the Chandra ACIS survey of M 33 (ChASeM33) sampled the eclipsing X-ray binary M 33 X-7 over a large part of the 3.45 d orbital period and have resolved eclipse ingress and egress for the first time. The occurrence of the X-ray eclipse allows us to determine an improved ephemeris of mid-eclipse and binary period as HJD (2453639.119+-0.005) +- N x (3.453014+-0.000020) and constrain the eclipse half angle to (26.5+-1.1) degree. There are indications for a shortening of the orbital period. The X-ray spectrum is best described by a disk blackbody spectrum typical for black hole X-ray binaries in the Galaxy. We find a flat power density spectrum and no significant regular pulsations were found in the frequency range of 10^{-4} to 0.15 Hz. HST WFPC2 images resolve the optical counterpart, which can be identified as an O6III star with the help of extinction and colour corrections derived from the X-ray absorption. Based on the optical light curve, the mass of the compact object in the system most likely exceeds 9 M_sun. This mass, the shape of the X-ray spectrum and the short term X-ray time variability identify M 33 X-7 as the first eclipsing black hole high mass X-ray binary.Comment: 14 pages, 5 figures, ApJ accepte

Transport through a quantum dot with SU(4) Kondo entanglement

We investigate a mesoscopic setup composed of a small electron droplet (dot) coupled to a larger quantum dot (grain) also subject to Coulomb blockade as well as two macroscopic leads used as source and drain. An exotic Kondo ground state other than the standard SU(2) Fermi liquid unambiguously emerges: an SU(4) Kondo correlated liquid. The transport properties through the small dot are analyzed for this regime, through boundary conformal field theory, and allow a clear distinction with other regimes such as a two-channel spin state or a two-channel orbital state.Comment: 13 pages, 3 figure

Detection of antibody-dependent complement mediated inactivation of both autologous and heterologous virus in primary HIV-1 infection

Specific CD8 T-cell responses to human immunodeficiency virus type 1 (HIV-1) are induced in primary infection and make an important contribution to the control of early viral replication. The importance of neutralizing antibodies in containing primary viremia is questioned because they usually arise much later. Nevertheless antienvelope antibodies develop simultaneously with, or even before, peak viremia. We determined whether such antibodies might control viremia by complement-mediated inactivation (CMI). In each of seven patients studied, antibodies capable of CMI appeared at or shortly after the peak in viremia, concomitantly with detection of virus-specific T-cell responses. The CMI was effective on both autologous and heterologous HIV-1 isolates. Activation of the classical pathway and direct viral lysis were at least partly responsible. Since immunoglobulin G (IgG)-antibodies triggered the CMI, specific memory B cells could also be induced by vaccination. Thus, consideration should be given to vaccination strategies that induce IgG antibodies capable of CMI

Winter Conditions Influence Biological Responses of Migrating Hummingbirds

Conserving biological diversity given ongoing environmental changes requires the knowledge of how organisms respond biologically to these changes; however, we rarely have this information. This data deficiency can be addressed with coordinated monitoring programs that provide field data across temporal and spatial scales and with process-based models, which provide a method for predicting how species, in particular migrating species that face different conditions across their range, will respond to climate change. We evaluate whether environmental conditions in the wintering grounds of broad-tailed hummingbirds influence physiological and behavioral attributes of their migration. To quantify winter ground conditions, we used operative temperature as a proxy for physiological constraint, and precipitation and the normalized difference vegetation index (NDVI) as surrogates of resource availability. We measured four biological response variables: molt stage, timing of arrival at stopover sites, body mass, and fat. Consistent with our predictions, we found that birds migrating north were in earlier stages of molt and arrived at stopover sites later when NDVI was low. These results indicate that wintering conditions impact the timing and condition of birds as they migrate north. In addition, our results suggest that biologically informed environmental surrogates provide a valuable tool for predicting how climate variability across years influences the animal populations