Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System

Bifibrations, in symplectic geometry called also dual pairs, play a relevant role in the theory of superintegrable Hamiltonian systems. We prove the existence of an analogous bifibrated geometry in dynamical systems with a symmetry group such that the reduced dynamics is periodic. The integrability of such systems has been proven by M. Field and J. Hermans with a reconstruction technique. We apply the result to the nonholonomic system of a ball rolling on a surface of revolution.Comment: This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

On the number of weakly Noetherian constants of motion of nonholonomic systems

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Cosmogenic 11C production and sensitivity of organic scintillator detectors to pep and CNO neutrinos

Several possible background sources determine the detectability of pep and CNO solar neutrinos in organic liquid scintillator detectors. Among such sources, the cosmogenic 11C nuclide plays a central role. 11C is produced underground in reactions induced by the residual cosmic muon flux. Experimental data available for the effective cross section for 11C by muons indicate that 11C will be the dominant source of background for the observation of pep and CNO neutrinos. 11C decays are expected to total a rate 2.5 (20) times higher than the combined rate of pep and CNO neutrinos in Borexino (KamLAND) in the energy window preferred for the pep measurement, between 0.8 and 1.3 MeV. This study examines the production mechanism of 11C by muon-induced showers in organic liquid scintillators with a novel approach: for the first time, we perform a detailed ab initio calculation of the production of a cosmogenic nuclide, 11C, taking into consideration all relevant production channels. Results of the calculation are compared with the effective cross sections measured by target experiments in muon beams. This paper also discusses a technique for reduction of background from 11C in organic liquid scintillator detectors, which allows to identify on a one-by-one basis and remove from the data set a large fraction of 11C decays. The background reduction technique hinges on an idea proposed by Martin Deutsch, who suggested that a neutron must be ejected in every interaction producing a 11C nuclide from 12C. 11C events are tagged by a three-fold coincidence with the parent muon track and the subsequent neutron capture on protons.Comment: 11 pages, 6 figures; added one section detailing comparison with previous estimates; added reference

The FLUKA code for space applications: recent developments.

The FLUKA Monte Carlo transport code is widely used for fundamental research, radioprotection and dosimetry, hybrid nuclear energy system and cosmic ray calculations. The validity of its physical models has been benchmarked against a variety of experimental data over a wide range of energies, ranging from accelerator data to cosmic ray showers in the earth atmosphere. The code is presently undergoing several developments in order to better fit the needs of space applications. The generation of particle spectra according to up-to-date cosmic ray data as well as the effect of the solar and geomagnetic modulation have been implemented and already successfully applied to a variety of problems. The implementation of suitable models for heavy ion nuclear interactions has reached an operational stage. At medium/high energy FLUKA is using the DPMJET model. The major task of incorporating heavy ion interactions from a few GeV/n down to the threshold for inelastic collisions is also progressing and promising results have been obtained using a modified version of the RQMD-2.4 code. This interim solution is now fully operational, while waiting for the development of new models based on the FLUKA hadron-nucleus interaction code, a newly developed QMD code, and the implementation of the Boltzmann master equation theory for low energy ion interactions. c2004 COSPAR. Published by Elsevier Ltd. All rights reserved