Point vortices on the sphere: a case with opposite vorticities

We study systems formed of 2N point vortices on a sphere with N vortices of strength +1 and N vortices of strength -1. In this case, the Hamiltonian is conserved by the symmetry which exchanges the positive vortices with the negative vortices. We prove the existence of some fixed and relative equilibria, and then study their stability with the ``Energy Momentum Method''. Most of the results obtained are nonlinear stability results. To end, some bifurcations are described.Comment: 35 pages, 9 figure

Un-reduction

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was originally concieved for an application to image dynamics, uses Lagrangian reduction by symmetry in reverse. A deeper understanding of un-reduction leads to new developments in image matching which serve to illustrate the mathematical power of the technique.Comment: 25 pages, revised versio

Surface differential rotation and photospheric magnetic field of the young solar-type star HD 171488 (V889 Her)

We present spectropolarimetric observations of the young, single early G-dwarf HD 171488. These observations were obtained over a five-night period in 2004 September at the 3.9-m Anglo-Australian Telescope using the SEMPOL spectropolarimeter visitor instrument. Using the technique of least-squares deconvolution to increase the signal-to-noise ratio of the data, we have applied Zeeman Doppler imaging to reconstruct brightness and magnetic surface topologies of the star. The brightness image shows a large polar spot with weaker low- to mid-latitude features, confirming an earlier Doppler imaging observation. The reconstruction of the surface magnetic field shows regions of radial field at all latitudes (except near the pole) and regions of azimuthal field predominantly at high latitudes (60°-70°), with the azimuthal field almost forming a ring around the polar regions. We have incorporated a solar-like differential rotation law into the imaging process to determine the surface differential rotation of cool spots on HD 171488. This gives an equatorial rotation rate of 1.313 ± 0.004 d and a surface shear of dΩ= 0.402 ± 0.044 rad-d−1. This means that the equator of HD 171488 laps the poles every ∼16 ± 2 d and that HD 171488 has a photospheric shear approximately seven times the solar value. This is the largest measurement of surface differential rotation yet obtained using the Doppler imaging method and is over twice the value of previously observed early G-dwarf

Magnetic cycles of the planet-hosting star tauBootis

We have obtained new spectropolarimetric observations of the planet-hosting star tauBootis, using the ESPaDOnS and NARVAL spectropolarimeters at the Canada-France-Hawaii Telescope and Telescope Bernard-Lyot. With this data set, we are able to confirm the presence of a magnetic field at the surface of tauBoo and map its large-scale structure over the whole star. The overall polarity of the magnetic field has reversed with respect to our previous observation (obtained a year before), strongly suggesting that tauBoo is undergoing magnetic cycles similar to those of the Sun. This is the first time that a global magnetic polarity switch is observed in a star other than the Sun; we speculate that the magnetic cycle period of tauBoo is much shorter than that of the Sun. Our new data also allow us to confirm the presence of differential rotation from the latitudinal shearing that the magnetic structure is undergoing. The differential rotation surface shear that tauBoo experiences is found to be 6 to 10 times larger than that of the Sun. We propose that the short magnetic cycle period is due to the strong level of differential rotation. With a rotation period of 3.0 and 3.9 d at the equator and pole respectively, tauBoo appears as the first planet-hosting star whose rotation (at intermediate latitudes) is synchronised with the orbital motion of its giant planet (period 3.3 d). Assuming that this synchronisation is not coincidental, it suggests that the tidal effects induced by the giant planet can be strong enough to force the thin convective enveloppe (though not the whole star) into corotation and thus to play a role in the activity cycle of tauBoo.Comment: MNRAS, in pres

On the integrability of stationary and restricted flows of the KdV hierarchy.

A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: in a case it connects an integrable Henon--Heiles system and the Garnier system. Moreover a new integrability scheme for Hamiltonian systems is proposed, holding in the standard phase space.Comment: 25 pages, AMS-LATEX 2.09, no figures, to be published in J. Phys. A: Math. Gen.

Does Pulsar B1757--24 Have a Fallback Disk?

Radio pulsars are thought to spin-down primarily due to torque from magnetic dipole radiation (MDR) emitted by the time-varying stellar magnetic field as the star rotates. This assumption yields a `characteristic age' for a pulsar which has generally been assumed to be comparable to the actual age. Recent observational limits on the proper motion of pulsar B1757-24, however, revealed that the actual age (>39 kyr) of this pulsar is much greater than its MDR characteristic age (16 kyr) - calling into question the assumption of pure MDR spin-down for this and other pulsars. To explore the possible cause of this discrepancy, we consider a scenario in which the pulsar acquired an accretion disk from supernova ejecta, and the subsequent spin-down occurred under the combined action of MDR and accretion torques. A simplified model of the accretion torque involving a constant mass inflow rate at the pulsar magnetosphere can explain the age and period derivative of the pulsar for reasonable values of the pulsar magnetic field and inflow rate. We discuss testable predictions of this model.Comment: Accepted by ApJ Letters. 15 pages with 1 figur

The influence of building materials on the residual action of BHC

A atividade residual dos vapores do inseticida BHC de vários materiais de construção em câmaras com controle de umidade, no laboratório, foram significativamente diferentes entre si. Ninfas do primeiro estágio de Dipetalogaster maximus, criados em laboratório, foram expostas a vapores de BHC liberados da superfície tratada dos materiais de construção trazidos de Mambaí, Goiás.Residual insecticide activity of BHC vapors from various building materials in controlled humidity chambers in the laboratory were significantly different. Laboratory-reared, first instar nymphs of Dipetalogaster maximus were exposed to vapors of BHC which were being released from the treated surfaces of building materials taken from Mambaí, Goiás

The first magnetic maps of a pre-main sequence binary star system - HD 155555

We present the first maps of the surface magnetic fields of a pre-main sequence binary system. Spectropolarimetric observations of the young, 18 Myr, HD 155555 (V824 Ara, G5IV + K0IV) system were obtained at the Anglo-Australian Telescope in 2004 and 2007. Both datasets are analysed using a new binary Zeeman Doppler imaging (ZDI) code. This allows us to simultaneously model the contribution of each component to the observed circularly polarised spectra. Stellar brightness maps are also produced for HD 155555 and compared to previous Doppler images. Our radial magnetic maps reveal a complex surface magnetic topology with mixed polarities at all latitudes. We find rings of azimuthal field on both stars, most of which are found to be non-axisymmetric with the stellar rotational axis. We also examine the field strength and the relative fraction of magnetic energy stored in the radial and azimuthal field components at both epochs. A marked weakening of the field strength of the secondary star is observed between the 2004 and 2007 epochs. This is accompanied by an apparent shift in the location of magnetic energy from the azimuthal to radial field. We suggest that this could be indicative of a magnetic activity cycle. We use the radial magnetic maps to extrapolate the coronal field (by assuming a potential field) for each star individually - at present ignoring any possible interaction. The secondary star is found to exhibit an extreme tilt (~75 deg) of its large scale magnetic field to that of its rotation axis for both epochs. The field complexity that is apparent in the surface maps persists out to a significant fraction of the binary separation. Any interaction between the fields of the two stars is therefore likely to be complex also. Modelling this would require a full binary field extrapolation.Comment: 17 pages, 12 figures, accepted for publication in MNRA