55,933 research outputs found
A stability property of a force-free surface bounding a vacuum gap
A force-free surface (FFS) 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 a simple
relation between the charge density 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
on , this relation implies that a FFS has a general
stability property, already conjectured by Michel (1979, ApJ 227, 579): turns out to attract charges placed on the vacuum side if they are of the
same sign as . 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)
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