1,581 research outputs found
Lyapunov 1-forms for flows
In this paper we find conditions which guarantee that a given flow on
a compact metric space admits a Lyapunov one-form lying in a
prescribed \v{C}ech cohomology class . These
conditions are formulated in terms of the restriction of to the chain
recurrent set of . The result of the paper may be viewed as a
generalization of a well-known theorem of C. Conley about the existence of
Lyapunov functions.Comment: 27 pages, 3 figures. This revised version incorporates a few minor
improvement
Nonsolar astronomy with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI)
The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is a NASA Small Explorer satellite designed to study hard x-ray and gamma-ray emission from solar flares. In addition, its high-resolution array of germanium detectors can see photons from high-energy sources throughout the Universe. Here we discuss the various algorithms necessary to extract spectra, lightcurves, and other information about cosmic gamma-ray bursts, pulsars, and other astrophysical phenomena using an unpointed, spinning array of detectors. We show some preliminary results and discuss our plans for future analyses. All RHESSI data are public, and scientists interested in participating should contact the principal author
Polarization from GRB021206: No constraints from reanalysis of RHESSI data
The determination of a polarization signal in Gamma Ray Bursts (GRBs) would give new information about their nature and mechanism. Using the RHESSI satellite as a Compton polarimeter, Coburn W. and Boggs S. E. (Nature, 423 (2003) 415) reported that GRB021206 was highly linearly polarized. This was contradicted by Rutledge R. E. and Fox D. B. (Mon. Not. R. Astron. Soc., 350 (2004) 1288) who found about 10 times less scattering events suitable for measuring
polarization. Applying our own method to thesamedata weconfirm them uch lower number of suitable scattering events. But we obtain three times smaller errors by using better selection criteria. Comparison with our Monte Carlo simulations shows that from the RHESSI data of GRB021206 we cannot distinguish between no and full polarization within less than 2 standard deviations. We also applied our method
to other GRBs observed by RHESSI. This shows that the probability to observe a GRB suitable for polarization search with such an instrument is small
Phase detection at the quantum limit with multi-photon Mach-Zehnder interferometry
We study a Mach-Zehnder interferometer fed by a coherent state in one input
port and vacuum in the other. We explore a Bayesian phase estimation strategy
to demonstrate that it is possible to achieve the standard quantum limit
independently from the true value of the phase shift and specific assumptions
on the noise of the interferometer. We have been able to implement the protocol
using parallel operation of two photon-number-resolving detectors and
multiphoton coincidence logic electronics at the output ports of a
weakly-illuminated Mach-Zehnder interferometer. This protocol is unbiased and
saturates the Cramer-Rao phase uncertainty bound and, therefore, is an optimal
phase estimation strategy.Comment: 4 pages, 5 figures replaced fig. 1 to correct graphics bu
Measuring Optical Properties On Rough And Liquid Metal Surfaces
For understanding and optimizing laser processing of metals and alloys the optical properties, especially the absorption of the work piece in function of the temperature up to the liquid phase have to be known [1]. There are several approaches to extend the Drude-Model [2] for optical properties of metal to temperature dependence [3, 4, 5]. However, a verification of these models is difficult due to the lack of sufficient experimental data. Even though measuring optical properties with ellipsometry is well established, such measurements on metals and alloys at elevated temperatures up to the liquid state are very challenging. To collect the optical properties of different metals and alloys like Al, Ti, Ag, Cu and steel in the solid and liquid state a custom-made high-temperature ellipsometer was used. The instrument is also used to investigate the influence of curved and rough surfaces which may occur due to the heating of the samples during the ellipsometric measurements
Distribution of periodic points of polynomial diffeomorphisms of C^2
This paper deals with the dynamics of a simple family of holomorphic
diffeomorphisms of \C^2: the polynomial automorphisms. This family of maps
has been studied by a number of authors. We refer to [BLS] for a general
introduction to this class of dynamical systems. An interesting object from the
point of view of potential theory is the equilibrium measure of the set
of points with bounded orbits. In [BLS] is also characterized
dynamically as the unique measure of maximal entropy. Thus is also an
equilibrium measure from the point of view of the thermodynamical formalism. In
the present paper we give another dynamical interpretation of as the
limit distribution of the periodic points of
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