Lyapunov 1-forms for flows

In this paper we find conditions which guarantee that a given flow $\Phi$ on a compact metric space $X$ admits a Lyapunov one-form $\omega$ lying in a prescribed \v{C}ech cohomology class $\xi\in \check H^1(X;\R)$. These conditions are formulated in terms of the restriction of $\xi$ to the chain recurrent set of $\Phi$. 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 $\mu$ of the set $K$ of points with bounded orbits. In [BLS] $\mu$ is also characterized dynamically as the unique measure of maximal entropy. Thus $\mu$ is also an equilibrium measure from the point of view of the thermodynamical formalism. In the present paper we give another dynamical interpretation of $\mu$ as the limit distribution of the periodic points of $f$