A combinatorial smoothness criterion for spherical varieties

We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces, generalizing an earlier result of Camus for spherical varieties of type $A$.Comment: 14 pages, 2 table

Charge, Orbital and Magnetic Order in Nd0.5Ca0.5MnO3

In the manganite Nd0.5Ca0.5MnO3, charge ordering occurs at much higher temperature than the antiferromagnetic order (TCO=250K,TN=160K). The magnetic behavior of the phase TN<T<TCO is puzzling: its magnetization and susceptibility are typical of an antiferromagnet while no magnetic order is detected by neutron diffraction.We have undertaken an extensive study of the cristallographic, electric and magnetic properties of Nd0.5Ca0.5MnO3 and established its phase diagram as a function of temperature and magnetic field. The charge disordered, paramagnetic phase above TCO present ferromagnetic correlations. An antiferromagnetic CE phase prevails below TN, with complete charge and orbital ordering. In the intermediate temperature range, charge ordering occurs while orbital ordering sets in progressively, with no magnetic order. Strong magnetic fields destroy the charge ordered phases in a fisrt order transition towards a ferromagnetic state.Comment: 17 pages, 11 Figures to appear in Phys. Rev.

Spherical orbit closures in simple projective spaces and their normalizations

Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its closure, then we describe the orbits of X and those of its normalization. If moreover the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup.Comment: 24 pages, LaTeX. v4: Final version, to appear in Transformation Groups. Simplified some proofs and corrected minor mistakes, added references. v3: major changes due to a mistake in previous version

The X-ray flaring activity of the galactic nucleus observed with XMM-Newton

We report the results of XMM-Newton observations of Sgr A*, the radiative counterpart of the massive black hole at the nucleus of our Galaxy, performed in the frame of the guaranteed time survey program of the Galactic Center region. The discovery of bright X-ray flares from Sgr A* with Chandra in October 2000 have opened new perspectives to understand the processes at work in this object and in general in black holes accreting at low accretion rates. We report here the important results obtained with XMM-Newton on the Sgr A* high-energy flaring activity and we discuss the implications on the models and the future observational perspectives.Comment: 4 pages, 3 figures, proc. of the SF2A conf. held in Bordeaux, France, June 2003, eds.: F. Combes, D. Barret and T. Contini, EdP-Sciences Conf. Serie

Effect of magnesium doping on the orbital and magnetic order in LiNiO2

In LiNiO2, the Ni3+ ions, with S=1/2 and twofold orbital degeneracy, are arranged on a trian- gular lattice. Using muon spin relaxation (MuSR) and electron spin resonance (ESR), we show that magnesium doping does not stabilize any magnetic or orbital order, despite the absence of interplane Ni2+. A disordered, slowly fluctuating state develops below 12 K. In addition, we find that magnons are excited on the time scale of the ESR experiment. At the same time, a g factor anisotropy is observed, in agreement with $| 3z^{2}-r^{2}>$ orbital occupancy

Mechatronic design of a fast and long range 4 degrees of freedom humanoid neck

This paper describes the mechatronic design of a humanoid neck. To research human machine interaction, the head and neck combination should be able to approach the human behavior as much as possible. We present a novel humanoid neck concept that is both fast, and has a long range of motion in 4 degrees of freedom (DOFs). This enables the head to track fast objects, and the neck design is suitable for mimicking expressions. The humanoid neck features a differential drive design for the lower 2 DOFs resulting in a low moving mass and the ability to use strong actuators. The performance of the neck has been\ud optimized by minimizing backlash in the mechanisms, and by using gravity compensation. Two cameras in the head are used for scanning and interaction with the environment