Anti-deSitter gravitational collapse

We describe a formalism for studying spherically symmetric collapse of the massless scalar field in any spacetime dimension, and for any value of the cosmological constant $\Lambda$. The formalism is used for numerical simulations of gravitational collapse in four spacetime dimensions with negative $\Lambda$. We observe critical behaviour at the onset of black hole formation, and find that the critical exponent is independent of $\Lambda$.Comment: 4 pages, 2 figures, revtex4, version to appear in CQ

Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse

We study the critical behaviour of spherically symmetric scalar field collapse to black holes in spacetime dimensions other than four. We obtain reliable values for the scaling exponent in the supercritical region for dimensions in the range $3.5\leq D\leq 14$. The critical exponent increases monotonically to an asymptotic value at large $D$ of $\gamma\sim0.466$. The data is well fit by a simple exponential of the form: $\gamma \sim 0.466(1-e^{-0.408 D})$.Comment: 5 pages, including 7 figures New version contains more data points, one extra graph and more accurate error bars. No changes to result

On the correlation functions of the domain wall six vertex model

We propose an (essentially combinatorial) approach to the correlation functions of the domain wall six vertex model. We reproduce the boundary 1-point function determinant expression of Bogoliubov, Pronko and Zvonarev, then use that as a building block to obtain analogous expressions for boundary 2-point functions. The latter can be used, at least in principle, to express more general boundary (and bulk) correlation functions as sums over (products of) determinants.Comment: LaTeX2e, requires eepic, 25 pages, including 29 figure

Statistics of Magnetic Fields for OB Stars

Based on an analysis of the catalog of magnetic fields, we have investigated the statistical properties of the mean magnetic fields for OB stars. We show that the mean effective magnetic field ${\cal B}$ of a star can be used as a statistically significant characteristic of its magnetic field. No correlation has been found between the mean magnetic field strength ${\cal B}$ and projected rotational velocity of OB stars, which is consistent with the hypothesis about a fossil origin of the magnetic field. We have constructed the magnetic field distribution function for B stars, $F({\cal B})$, that has a power-law dependence on ${\cal B}$ with an exponent of $\approx -1.82$. We have found a sharp decrease in the function $F({\cal B})$F for {\cal B}\lem 400 G that may be related to rapid dissipation of weak stellar surface magnetic fields.Comment: 22 pages, 7 figures, accepted Astronomy Letters, 2010, vol.36, No.5, pp.370-379, contact E-mail: [email protected]

Spots structure and stratification of helium and silicon in the atmosphere of He-weak star HD 21699

The magnetic star HD 21699 possesses a unique magnetic field structure where the magnetic dipole is displaced from the centre by 0.4 +/- 0.1 of the stellar radius (perpendicularly to the magnetic axis), as a result, the magnetic poles are situated close to one another on the stellar surface with an angular separation of 55$^o$ and not 180$^o$ as seen in the case of a centred dipole. Respectively, the two magnetic poles form a large "magnetic spot". High-resolution spectra were obtained allowing He I and Si II abundance variations to be studied as a function of rotational phase. The results show that the helium abundance is concentrated in one hemisphere of the star, near the magnetic poles and it is comparatively weaker in another hemisphere, where magnetic field lines are horizontal with respect to the stellar surface. At the same time, the silicon abundance is greatest between longitudes of 180 - 320$^o$, the same place where the helium abundance is the weakest. These abundance variations (with rotational phase) support predictions made by the theory of atomic diffusion in the presence of a magnetic field. Simultaneously, these result support the possibility of the formation of unusual structures in stellar magnetic fields. Analysis of vertical stratification of the silicon and helium abundances shows that the boundaries of an abundance jump (in the two step model) are similar for each element; $\tau_{5000}$ = 0.8-1.2 for helium and 0.5-1.3 for silicon. The elemental abundances in the layers of effective formation of selected absorption lines for various phases are also correlated with the excitation energies of low transition levels: abundances are enhanced for higher excitation energy and higher optical depth within the applied model atmosphere.Comment: accepted by MN, 7 pagers, 10 figs, 3 table

The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

Nonsingular potentials from excited state factorization of a quantum system with position dependent mass

The modified factorization technique of a quantum system characterized by position-dependent mass Hamiltonian is presented. It has been shown that the singular superpotential defined in terms of a mass function and a excited state wave function of a given position-dependent mass Hamiltonian can be used to construct non-singular isospectral Hamiltonians. The method has been illustrated with the help of a few examples.Comment: Improved version accepted in J. Phys.

An In-Depth Spectroscopic Analysis of the Blazhko Star RR Lyr. I. Characterisation of the star: abundance analysis and fundamental parameters

The knowledge of accurate stellar parameters is a keystone in several fields of stellar astrophysics, such as asteroseismology and stellar evolution. Although the fundamental parameters can be derived both from spectroscopy and multicolour photometry, the results obtained are sometimes affected by systematic uncertainties. In this paper, we present a self-consistent spectral analysis of the pulsating star RR Lyr, which is the primary target for our study of the Blazhko effect. We used high-resolution and high signal-to-noise ratio spectra to carry out a consistent parameter determination and abundance analysis for RR Lyr. We provide a detailed description of the methodology adopted to derive the fundamental parameters and the abundances. Stellar pulsation attains high amplitudes in RR Lyrae stars, and as a consequence the stellar parameters vary significantly over the pulsation cycle. The abundances of the star, however, are not expected to change. From a set of available high-resolution spectra of RR Lyr we selected the phase of maximum radius, at which the spectra are least disturbed by the pulsation. Using the abundances determined at this phase as a starting point, we expect to obtain a higher accuracy in the fundamental parameters determined at other phases. The set of fundamental parameters obtained in this work fits the observed spectrum accurately. Through the abundance analysis, we find clear indications for a depth-dependent microturbulent velocity, that we quantified. We confirm the importance of a consistent analysis of relevant spectroscopic features, application of advanced model atmospheres, and the use of up-to-date atomic line data for the determination of stellar parameters. These results are crucial for further studies, e.g., detailed theoretical modelling of the observed pulsations.Comment: 12 pages, accepted for publication in Astronomy & Astrophysic

Programming Robots With Events

International audienceWe introduce how to use event-based style to program robots through the INI programming language. INI features both built-in and user-defined events, a mechanism to handle various kinds of changes happening in the environment. Event handlers run in parallel either synchronously or asynchronously, and events can be reconfigured at runtime to modify their behavior when needed. We apply INI to the humanoid robot called Nao, for which we develop an object tracking program