A stability property of a force-free surface bounding a vacuum gap

A force-free surface (FFS) ${\cal S}$ is a sharp boundary separating a void from a region occupied by a charge-separated force-free plasma. It is proven here under very general assumptions that there is on ${\cal S}$ a simple relation between the charge density $\mu$ on the plasma side and the derivative of \delta=\E\cdot\B along \B on the vacuum side (with \E denoting the electric field and \B the magnetic field). Combined with the condition $\delta=0$ on ${\cal S}$, this relation implies that a FFS has a general stability property, already conjectured by Michel (1979, ApJ 227, 579): ${\cal S}$ turns out to attract charges placed on the vacuum side if they are of the same sign as $\mu$. In the particular case of a FFS existing in the axisymmetric stationary magnetosphere of a "pulsar", the relation is given a most convenient form by using magnetic coordinates, and is shown to imply an interesting property of a gap. Also, a simple proof is given of the impossibility of a vacuum gap forming in a field \B which is either uniform or radial (monopolar)

Complements on disconnected reductive groups

We present various results on disconnected reductive groups, in particular about the characteristic 0 representation theory of such groups over finite fields.Comment: This version takes into account improvements suggested by G. Mall

Causal conditioning and instantaneous coupling in causality graphs

The paper investigates the link between Granger causality graphs recently formalized by Eichler and directed information theory developed by Massey and Kramer. We particularly insist on the implication of two notions of causality that may occur in physical systems. It is well accepted that dynamical causality is assessed by the conditional transfer entropy, a measure appearing naturally as a part of directed information. Surprisingly the notion of instantaneous causality is often overlooked, even if it was clearly understood in early works. In the bivariate case, instantaneous coupling is measured adequately by the instantaneous information exchange, a measure that supplements the transfer entropy in the decomposition of directed information. In this paper, the focus is put on the multivariate case and conditional graph modeling issues. In this framework, we show that the decomposition of directed information into the sum of transfer entropy and information exchange does not hold anymore. Nevertheless, the discussion allows to put forward the two measures as pillars for the inference of causality graphs. We illustrate this on two synthetic examples which allow us to discuss not only the theoretical concepts, but also the practical estimation issues.Comment: submitte

Photometry of the eclipsing cataclysmic variable SDSS J152419.33+220920.0

Aims. We present new photometry of the faint and poorly studied cataclysmic variable SDSS J152419.33+220920.0, analyze its light curve and provide an accurate ephemeris for this system. Methods. Time-resolved CCD differential photometry was carried out using the 1.5m and 0.84m telescopes at the Observatorio Astronomico Nacional at San Pedro Martir. Results. From time-resolved photometry of the system obtained during six nights (covering more than twenty primary eclipse cycles in more than three years), we show that this binary presents a strong primary and a weak secondary modulation. Our light curve analysis shows that only two fundamental frequencies are present, corresponding to the orbital period and a modulation with twice this frequency. We determine the accurate ephemeris of the system to be HJD(eclipse)= 2454967.6750(1) + 0.06531866661(1) E. A double-hump orbital period modulation, a standing feature in several bounce-back systems at quiescence, is present at several epochs. However, we found no other evidence to support the hypothesis that this system belongs to the post-minimum orbital-period systems

Maharam's problem

We construct an exhaustive submeasure that is not equivalent to a measure. This solves problems of J. von Neumann (1937) and D. Maharam (1947)