Relative periodic orbits in point vortex systems

We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is applied to point vortices systems on a sphere and on the plane, but works for other surfaces with isotropy (cylinder, ellipsoid, ...). The method permits also to determine some relative equilibria and heteroclinic cycles connecting these relative equilibria.Comment: 27 pages, 17 figure

CII in the Interstellar Medium: Excitation by H2 Revisited

C$^+$ is a critical constituent of many regions of the interstellar medium, as it can be a major reservoir of carbon and, under a wide range of conditions, the dominant gas coolant. Emission from its 158$\mu$m fine structure line is used to trace the structure of photon dominated regions in the Milky Way and is often employed as a measure of the star formation rate in external galaxies. Under most conditions, the emission from the single [CII] line is proportional to the collisional excitation rate coefficient. We here used improved calculations of the deexcitation rate of [CII] by collisions with H$_2$ to calculate more accurate expressions for interstellar C$^+$ fine structure emission, its critical density, and its cooling rate. The collision rates in the new quantum calculation are $\sim$ 25% larger than those previously available, and narrow the difference between rates for excitation by atomic and molecular hydrogen. This results in [CII] excitation being quasi-independent of the molecular fraction and thus dependent only on the total hydrogen particle density. A convenient expression for the cooling rate at temperatures between 20 K and 400 K, assuming an LTE H$_2$ ortho to para ration is $\Lambda ({\rm LTE~OPR}) = \left(11.5 + 4.0\,e^{-100\,\mathrm K/T^{\rm kin}}\right)\;e^{-91.25\,\mathrm K/T^{\rm kin}}\,n ({\rm C}^{+})\,n({\rm H}_2)\times 10^{-24}\;{\rm ergs}~{\rm cm}^{-3}~{\rm s}^{-1}$. The present work should allow more accurate and convenient analysis of the [\CII] line emission and its cooling

Inflation from Supersymmetric Quantum Cosmology

We derive a special scalar field potential using the anisotropic Bianchi type I cosmological model from canonical quantum cosmology under determined conditions in the evolution to anisotropic variables $\beta_\pm$. In the process, we obtain a family of potentials that has been introduced by hand in the literature to explain cosmological data. Considering supersymmetric quantum cosmology, this family is scanned, fixing the exponential potential as more viable in the inflation scenario $\rm V (\phi) = V_0 \,e^{-\sqrt{3}\phi}$.Comment: 14 pages, latex2e, To appear in Phys. Rev.

Matrix probing and its conditioning

When a matrix A with n columns is known to be well approximated by a linear combination of basis matrices B_1,..., B_p, we can apply A to a random vector and solve a linear system to recover this linear combination. The same technique can be used to recover an approximation to A^-1. A basic question is whether this linear system is invertible and well-conditioned. In this paper, we show that if the Gram matrix of the B_j's is sufficiently well-conditioned and each B_j has a high numerical rank, then n {proportional} p log^2 n will ensure that the linear system is well-conditioned with high probability. Our main application is probing linear operators with smooth pseudodifferential symbols such as the wave equation Hessian in seismic imaging. We demonstrate numerically that matrix probing can also produce good preconditioners for inverting elliptic operators in variable media

The IBIS view of the galactic centre: INTEGRAL's imager observations simulations

The Imager on Board Integral Satellite (IBIS) is the imaging instrument of the INTEGRAL satellite, the hard-X/soft-gamma ray ESA mission to be launched in 2001. It provides diagnostic capabilities of fine imaging (12' FWHM), source identification and spectral sensitivity to both continuum and broad lines over a broad (15 keV--10 MeV) energy range. It has a continuum sensitivity of 2~10^{-7} ph cm^{-2} s^{-1} at 1 MeV for a 10^6 seconds observation and a spectral resolution better than 7 % at 100 keV and of 6 % at 1 MeV. The imaging capabilities of the IBIS are characterized by the coupling of the above quoted source discrimination capability with a very wide field of view (FOV), namely 9 x 9 degrees fully coded, 29 x 29 degrees partially coded FOV. We present simulations of IBIS observations of the Galactic Center based on the results of the SIGMA Galactic Center survey. They show the capabilities of this instrument in discriminating between different sources while at the same time monitoring a huge FOV. It will be possible to simultaneously take spectra of all of these sources over the FOV even if the sensitivity decreases out of the fully coded area. It is envisaged that a proper exploitation of both the FOV dimension and the source localization capability of the IBIS will be a key factor in maximizing its scientific output.Comment: 5 pages, LaTeX, to be published in the 4th Compton Symposium Conference Proceedings, uses aipproc.cls, aipproc.sty (included