Nilpotent normal form for divergence-free vector fields and volume-preserving maps

We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vector field in $\mathbb{R}^3$ has nilpotent linearization with maximal Jordan block then, to arbitrary degree, coordinates can be chosen so that the nonlinear terms occur as a single function of two variables in the third component. The analogue for volume-preserving diffeomorphisms gives an optimal normal form in which the truncation of the normal form at any degree gives an exactly volume-preserving map whose inverse is also polynomial inverse with the same degree.Comment: laTeX, 20 pages, 1 figur

The Destruction of Tori in Volume-Preserving Maps

Invariant tori are prominent features of symplectic and volume preserving maps. From the point of view of chaotic transport the most relevant tori are those that are barriers, and thus have codimension one. For an $n$-dimensional volume-preserving map, such tori are prevalent when the map is nearly "integrable," in the sense of having one action and $n-1$ angle variables. As the map is perturbed, numerical studies show that the originally connected image of the frequency map acquires gaps due to resonances and domains of nonconvergence due to chaos. We present examples of a three-dimensional, generalized standard map for which there is a critical perturbation size, $\epsilon_c$, above which there are no tori. Numerical investigations to find the "last invariant torus" reveal some similarities to the behavior found by Greene near a critical invariant circle for area preserving maps: the crossing time through the newly destroyed torus appears to have a power law singularity at $\epsilon_c$, and the local phase space near the critical torus contains many high-order resonances.Comment: laTeX, 16 figure

Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

The ANTARES Optical Beacon System

ANTARES is a neutrino telescope being deployed in the Mediterranean Sea. It consists of a three dimensional array of photomultiplier tubes that can detect the Cherenkov light induced by charged particles produced in the interactions of neutrinos with the surrounding medium. High angular resolution can be achieved, in particular when a muon is produced, provided that the Cherenkov photons are detected with sufficient timing precision. Considerations of the intrinsic time uncertainties stemming from the transit time spread in the photomultiplier tubes and the mechanism of transmission of light in sea water lead to the conclusion that a relative time accuracy of the order of 0.5 ns is desirable. Accordingly, different time calibration systems have been developed for the ANTARES telescope. In this article, a system based on Optical Beacons, a set of external and well-controlled pulsed light sources located throughout the detector, is described. This calibration system takes into account the optical properties of sea water, which is used as the detection volume of the ANTARES telescope. The design, tests, construction and first results of the two types of beacons, LED and laser-based, are presented.Comment: 21 pages, 18 figures, submitted to Nucl. Instr. and Meth. Phys. Res.

Search for the glueball candidates f0(1500) and fJ(1710) in gamma gamma collisions

Data taken with the ALEPH detector at LEP1 have been used to search for gamma gamma production of the glueball candidates f0(1500) and fJ(1710) via their decay to pi+pi-. No signal is observed and upper limits to the product of gamma gamma width and pi+pi- branching ratio of the f0(1500) and the fJ(1710) have been measured to be Gamma_(gamma gamma -> f0(1500)). BR(f0(1500)->pi+pi-) < 0.31 keV and Gamma_(gamma gamma -> fJ(1710)). BR(fJ(1710)->pi+pi-) < 0.55 keV at 95% confidence level.Comment: 10 pages, 3 figure

Search for supersymmetry with a dominant R-parity violating LQDbar couplings in e+e- collisions at centre-of-mass energies of 130GeV to 172 GeV

A search for pair-production of supersymmetric particles under the assumption that R-parity is violated via a dominant LQDbar coupling has been performed using the data collected by ALEPH at centre-of-mass energies of 130-172 GeV. The observed candidate events in the data are in agreement with the Standard Model expectation. This result is translated into lower limits on the masses of charginos, neutralinos, sleptons, sneutrinos and squarks. For instance, for m_0=500 GeV/c^2 and tan(beta)=sqrt(2) charginos with masses smaller than 81 GeV/c^2 and neutralinos with masses smaller than 29 GeV/c^2 are excluded at the 95% confidence level for any generation structure of the LQDbar coupling.Comment: 32 pages, 30 figure

First results of the Instrumentation Line for the deep-sea ANTARES neutrino telescope

In 2005, the ANTARES Collaboration deployed and operated at a depth of 2500 m a so-called Mini Instrumentation Line equipped with Optical Modules (MILOM) at the ANTARES site. The various data acquired during the continuous operation from April to December 2005 of the MILOM confirm the satisfactory performance of the Optical Modules, their front-end electronics and readout system. as well as the calibration devices of the detector. The in situ measurement of the Optical Module time response yields a resolution better than 0.5 ns. The performance of the acoustic positioning system, which enables the spatial reconstruction of the ANTARES detector with a precision of about 10 cm, is verified. These results demonstrate that with the full ANTARES neutrino telescope the design angular resolution of better than 0.3 degrees can be realistically achieved

Study of large hemispherical photomultiplier tubes for the ANTARES neutrino telescope

The ANTARES neutrino telescope, to be immersed depth in the Mediterranean Sea, will consist of a 3 dimensional matrix of 900 large area photomultiplier tubes housed in pressure resistant glass spheres. The selection of the optimal photomultiplier was a critical step for the project and required an intensive phase of tests and developments carried out in close collaboration with the main manufacturers worldwide. This paper provides an overview of the tests performed by the collaboration and describes in detail the features of the PMT chosen for ANTARES

Constraints on anomalous QGC's in e+e−e^{+}e^{-} interactions from 183 to 209 GeV

The acoplanar photon pairs produced in the reaction e(+) e(-) - → vvyy are analysed in the 700 pb(-1) of data collected by the ALEPH detector at centre-of-mass energies between 183 and 209 GeV. No deviation from the Standard Model predictions is seen in any of the distributions examined. The resulting 95% C.L. limits set on anomalous QGCs, a(0)(Z), a(c)(Z), a(0)(W) and a(c)(W), are -0.012 lt a(0)(Z)/Lambda(2) lt +0.019 GeV-2, -0.041 lt a(c)(Z)/Lambda(2) lt +0.044 GeV-2, -0.060 lt a(0)(W)/Lambda(2) lt +0.055 GeV-2, -0.099 lt a(c)(W)/Lambda(2) lt +0.093 GeV-2, where Lambda is the energy scale of the new physics responsible for the anomalous couplings