A dynamic motion simulator for future European docking systems

Europe's first confrontation with docking in space will require extensive testing to verify design and performance and to qualify hardware. For this purpose, a Docking Dynamics Test Facility (DDTF) was developed. It allows reproduction on the ground of the same impact loads and relative motion dynamics which would occur in space during docking. It uses a 9 degree of freedom, servo-motion system, controlled by a real time computer, which simulates the docking spacecraft in a zero-g environment. The test technique involves and active loop based on six axis force and torque detection, a mathematical simulation of individual spacecraft dynamics, and a 9 degree of freedom servomotion of which 3 DOFs allow extension of the kinematic range to 5 m. The configuration was checked out by closed loop tests involving spacecraft control models and real sensor hardware. The test facility at present has an extensive configuration that allows evaluation of both proximity control and docking systems. It provides a versatile tool to verify system design, hardware items and performance capabilities in the ongoing HERMES and COLUMBUS programs. The test system is described and its capabilities are summarized

Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case

In this article, we show that the double scaling limit correlation functions of a random matrix model when two cuts merge with degeneracy $2m$ (i.e. when $y\sim x^{2m}$ for arbitrary values of the integer $m$) are the same as the determinantal formulae defined by conformal $(2m,1)$ models. Our approach follows the one developed by Berg\`{e}re and Eynard in \cite{BergereEynard} and uses a Lax pair representation of the conformal $(2m,1)$ models (giving Painlev\'e II integrable hierarchy) as suggested by Bleher and Eynard in \cite{BleherEynard}. In particular we define Baker-Akhiezer functions associated to the Lax pair to construct a kernel which is then used to compute determinantal formulae giving the correlation functions of the double scaling limit of a matrix model near the merging of two cuts.Comment: 37 pages, 4 figures. Presentation improved, typos corrected. Published in Journal Of Statistical Mechanic

Hard probes in heavy ion collisions at the LHC: heavy flavour physics

We present the results from the heavy quarks and quarkonia working group. This report gives benchmark heavy quark and quarkonium cross sections for $pp$ and $pA$ collisions at the LHC against which the $AA$ rates can be compared in the study of the quark-gluon plasma. We also provide an assessment of the theoretical uncertainties in these benchmarks. We then discuss some of the cold matter effects on quarkonia production, including nuclear absorption, scattering by produced hadrons, and energy loss in the medium. Hot matter effects that could reduce the observed quarkonium rates such as color screening and thermal activation are then discussed. Possible quarkonium enhancement through coalescence of uncorrelated heavy quarks and antiquarks is also described. Finally, we discuss the capabilities of the LHC detectors to measure heavy quarks and quarkonia as well as the Monte Carlo generators used in the data analysis.Comment: 126 pages Latex; 96 figures included. Subgroup report, to appear in the CERN Yellow Book of the workshop: Hard Probes in Heavy Ion Collisions at the LHC. See also http://a.home.cern.ch/f/frixione/www/hvq.html for a version with better quality for a few plot

Large deviations of the maximal eigenvalue of random matrices

We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not restricted to the standard values beta = 1 (hermitian matrices), beta = 1/2 (symmetric matrices), beta = 2 (quaternionic self-dual matrices). This model allows to study the statistic of the maximum eigenvalue of random matrices. We compute the large deviation function to the left of the expected maximum. We specialize our results to the gaussian beta-ensembles and check them numerically. Our method is based on general results and procedures already developed in the literature to solve the Pastur equations (also called "loop equations"). It allows to compute the left tail of the analog of Tracy-Widom laws for any beta, including the constant term.Comment: 62 pages, 4 figures, pdflatex ; v2 bibliography corrected ; v3 typos corrected and preprint added ; v4 few more numbers adde

Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field