Reduction of Jacobi manifolds via Dirac structures theory

We first recall some basic definitions and facts about Jacobi manifolds, generalized Lie bialgebroids, generalized Courant algebroids and Dirac structures. We establish an one-one correspondence between reducible Dirac structures of the generalized Lie bialgebroid of a Jacobi manifold $(M,\Lambda,E)$ for which 1 is an admissible function and Jacobi quotient manifolds of $M$. We study Jacobi reductions from the point of view of Dirac structures theory and we present some examples and applications.Comment: 18 page

Differential Geometry of the Vortex Filament Equation

Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting flows is shown to be hereditary. The system is shown to have a description with a Hamiltonian pair. Master symmetries are found and are applied to deriving an expression of the constants of motion in involution. The expression agrees with the inspection of Langer and Perline.Comment: 20 pages, LaTeX, no figure

Vortex Filament in Three-manifold and the Duistermaat-Heckman Formula

Symplectic geometry of the vortex filament in a curved three-manifold is investigated. There appears an infinite sequence of constants of motion in involution in the case of constant curvature. The Duistermaat-Heckman formula is examined perturbatively for the classical partition function in our model and verified up to the 3-loop order.Comment: Revised to include Figure2 (a PostScript file). 15 pages, LaTex2e, 2 figure

Bulgac-Kusnezov-Nos\'e-Hoover thermostats

In this paper we formulate Bulgac-Kusnezov constant temperature dynamics in phase space by means of non-Hamiltonian brackets. Two generalized versions of the dynamics are similarly defined: one where the Bulgac-Kusnezov demons are globally controlled by means of a single additional Nos\'e variable, and another where each demon is coupled to an independent Nos\'e-Hoover thermostat. Numerically stable and efficient measure-preserving time-reversible algorithms are derived in a systematic way for each case. The chaotic properties of the different phase space flows are numerically illustrated through the paradigmatic example of the one-dimensional harmonic oscillator. It is found that, while the simple Bulgac-Kusnezov thermostat is apparently not ergodic, both of the Nos\'e-Hoover controlled dynamics sample the canonical distribution correctly

Classical field theory on Lie algebroids: Variational aspects

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-Poincare and Lagrange Poincare cases), Sigma models or Chern-Simons theories.Comment: Talk deliverd at the 9th International Conference on Differential Geometry and its Applications, Prague, September 2004. References adde

Surface magnetism of cool stars

Magnetic fields are essential ingredients of many physical processes in the interiors and envelopes of cool stars. Yet their direct detection and characterisation is notoriously difficult, requiring high-quality observations and advanced analysis techniques. Significant progress has been recently achieved by several types of direct magnetic field studies on the surfaces of cool active stars. In particular, complementary techniques of the field topology mapping with polarisation data and total magnetic flux measurements from intensity spectra have been systematically applied to different classes of active stars leading to interesting and occasionally controversial results. In this paper we summarise the current status of direct magnetic field studies of cool stars, and investigations of surface inhomogeneities caused by the field, based on the material presented at the Cool Stars 19 splinter session.Comment: Summary of the splinter session "Surface Magnetism of Cool Stars" at the Cool Stars 19 conference; to be published in Astronomische Nachrichte

Constraining the Lyα escape fraction with far-infrared observations of Lyα emitters

We study the far-infrared properties of 498 Lyα emitters (LAEs) at z = 2.8, 3.1, and 4.5 in the Extended Chandra Deep Field-South, using 250, 350, and 500μm data from the Herschel Multi-tiered Extragalactic Survey and 870μm data from the LABOCA ECDFS Submillimeter Survey. None of the 126, 280, or 92 LAEs at z = 2.8, 3.1, and 4.5, respectively, are individually detected in the far-infrared data. We use stacking to probe the average emission to deeper flux limits, reaching 1σ depths of ∼0.1 to 0.4 mJy. The LAEs are also undetected at ?3σ in the stacks, although a 2.5σ signal is observed at 870μm for the z = 2.8 sources. We consider a wide range of far-infrared spectral energy distributions (SEDs), including an M82 and an Sd galaxy template, to determine upper limits on the far-infrared luminosities and far-infrared-derived star formation rates of the LAEs. These star formation rates are then combined with those inferred from the Lyα and UV emission to determine lower limits on the LAEs’ Lyα escape fraction (f esc (Lyα)). For the Sd SED template, the inferred LAEs f esc (Lyα) are ?30% (1σ) at z = 2.8, 3.1, and 4.5, which are all significantly higher than the global f esc (Lyα) at these redshifts. Thus, if the LAEs f esc (Lyα) follows the global evolution, then they have warmer far-infrared SEDs than the Sd galaxy template. The average and M82 SEDs produce lower limits on the LAE f esc (Lyα) of ∼10%–20% (1σ), all of which are slightly higher than the global evolution of f esc (Lyα), but consistent with it at the 2σ–3σ level