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

Doppler images and the underlying dynamo. The case of AF Leporis

The (Zeeman-)Doppler imaging studies of solar-type stars very often reveal large high-latitude spots. This also includes F stars that possess relatively shallow convection zones, indicating that the dynamo operating in these stars differs from the solar dynamo. We aim to determine whether mean-field dynamo models of late-F type dwarf stars can reproduce the surface features recovered in Doppler maps. In particular, we wish to test whether the models can reproduce the high-latitude spots observed on some F dwarfs. The photometric inversions and the surface temperature maps of AF Lep were obtained using the Occamian-approach inversion technique. Low signal-to-noise spectroscopic data were improved by applying the least-squares deconvolution method. The locations of strong magnetic flux in the stellar tachocline as well as the surface fields obtained from mean-field dynamo solutions were compared with the observed surface temperature maps. The photometric record of AF Lep reveals both long- and short-term variability. However, the current data set is too short for cycle-length estimates. From the photometry, we have determined the rotation period of the star to be 0.9660+-0.0023 days. The surface temperature maps show a dominant, but evolving, high-latitude (around +65 degrees) spot. Detailed study of the photometry reveals that sometimes the spot coverage varies only marginally over a long time, and at other times it varies rapidly. Of a suite of dynamo models, the model with a radiative interior rotating as fast as the convection zone at the equator delivered the highest compatibility with the obtained Doppler images.Comment: accepted for publication in Astronomy & Astrophysic

Discrete Nonholonomic LL Systems on Lie Groups

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.Comment: 32 pages, 13 figure

On the use of projectors for Hamiltonian systems and their relationship with Dirac brackets

The role of projectors associated with Poisson brackets of constrained Hamiltonian systems is analyzed. Projectors act in two instances in a bracket: in the explicit dependence on the variables and in the computation of the functional derivatives. The role of these projectors is investigated by using Dirac's theory of constrained Hamiltonian systems. Results are illustrated by three examples taken from plasma physics: magnetohydrodynamics, the Vlasov-Maxwell system, and the linear two-species Vlasov system with quasineutrality

The solar wind in time – II. 3D stellar wind structure and radio emission

In this work, we simulate the evolution of the solar wind along its main-sequence lifetime and compute its thermal radio emission. To study the evolution of the solar wind, we use a sample of solar mass stars at different ages. All these stars have observationally reconstructed magnetic maps, which are incorporated in our 3D magnetohydrodynamic simulations of their winds. We show that angular-momentum loss and mass-loss rates decrease steadily on evolutionary time-scales, although they can vary in a magnetic cycle time-scale. Stellar winds are known to emit radiation in the form of thermal bremsstrahlung in the radio spectrum. To calculate the expected radio fluxes from these winds, we solve the radiative transfer equation numerically from first principles. We compute continuum spectra across the frequency range 100 MHz to 100 GHz and find maximum radio flux densities ranging from 0.05 to 2.2 μJy. At a frequency of 1 GHz and a normalized distance of d = 10 pc, the radio flux density follows 0.24 (Ω/Ω☉)0.9 (d/[10pc])-2μJy, where Ω is the rotation rate. This means that the best candidates for stellar wind observations in the radio regime are faster rotators within distances of 10 pc, such as κ1 Ceti (0.73 μJy) and χ1 Ori (2.2 μJy). These flux predictions provide a guide to observing solar-type stars across the frequency range 0.1-100 GHz in the future using the next generation of radio telescopes, such as ngVLA and Square Kilometre Array

C^{2} formulation of Euler fluid

The Hamiltonian formalism for the continuous media is constructed using the representation of Euler variables in $\mathcal{C}^{2}\times \infty$ phase space.Comment: 8 page

Covariant gauge fixing and Kuchar decomposition

The symplectic geometry of a broad class of generally covariant models is studied. The class is restricted so that the gauge group of the models coincides with the Bergmann-Komar group and the analysis can focus on the general covariance. A geometrical definition of gauge fixing at the constraint manifold is given; it is equivalent to a definition of a background (spacetime) manifold for each topological sector of a model. Every gauge fixing defines a decomposition of the constraint manifold into the physical phase space and the space of embeddings of the Cauchy manifold into the background manifold (Kuchar decomposition). Extensions of every gauge fixing and the associated Kuchar decomposition to a neighbourhood of the constraint manifold are shown to exist.Comment: Revtex, 35 pages, no figure