Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution

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

The hadronic models for cosmic ray physics: the FLUKA code solutions

FLUKA is a general purpose Monte Carlo transport and interaction code used for fundamental physics and for a wide range of applications. These include Cosmic Ray Physics (muons, neutrinos, EAS, underground physics), both for basic research and applied studies in space and atmospheric flight dosimetry and radiation damage. A review of the hadronic models available in FLUKA and relevant for the description of cosmic ray air showers is presented in this paper. Recent updates concerning these models are discussed. The FLUKA capabilities in the simulation of the formation and propagation of EM and hadronic showers in the Earth's atmosphere are shown.Comment: 8 pages, 9 figures. Invited talk presented by M.V. Garzelli at ISVHECRI2006, International Symposium on Very High Energy Cosmic Rays, Weihai, China, August 15 - 22 200

Geometrical aspects of integrable systems

We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko-Fomenko theorem on noncommutative integrability, and for each of them we give a version suitable for the noncompact case. We give a possible global version of the previous local results, under certain topological hypotheses on the base space. It turns out that locally affine structures arise naturally in this setting.Comment: It will appear on International Journal of Geometric Methods in Modern Physics vol.5 n.3 (May 2008) issu

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

A Monte Carlo approach to study neutron and fragment emission in heavy-ion reactions

Quantum Molecular Dynamics models (QMD) are Monte Carlo approaches targeted at the description of nucleon-ion and ion-ion collisions. We have developed a QMD code, which has been used for the simulation of the fast stage of ion-ion collisions, considering a wide range of system masses and system mass asymmetries. The slow stage of the collisions has been described by statistical methods. The combination of both stages leads to final distributions of particles and fragments, which have been compared to experimental data available in literature. A few results of these comparisons, concerning neutron double-differential production cross-sections for C, Ne and Ar ions impinging on C, Cu and Pb targets at 290 - 400 MeV/A bombarding energies and fragment isotopic distributions from Xe + Al at 790 MeV/A, are shown in this paper.Comment: 12 pages, 3 figures, submitted for publication in Adv. Space Re

Predicting Neutron Production from Cosmic-ray Muons

Fast neutrons from cosmic-ray muons are an important background to underground low energy experiments. The estimate of such background is often hampered by the difficulty of measuring and calculating neutron production with sufficient accuracy. Indeed substantial disagreement exists between the different analytical calculations performed so far, while data reported by different experiments is not always consistent. We discuss a new unified approach to estimate the neutron yield, the energy spectrum, the multiplicity and the angular distribution from cosmic muons using the Monte Carlo simulation package FLUKA and show that it gives a good description of most of the existing measurements once the appropriate corrections have been applied.Comment: 8 pages, 7 figure

Poisson structures for reduced non-holonomic systems

Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the Hamiltonian function being the reduced energy. We study further the algebraic origin of these Poisson structures, showing that they are of rank two and therefore the mentioned rescaling is not necessary. We show that they are determined, up to a non-vanishing factor function, by the existence of a system of first-order differential equations providing two integrals of motion. We generalize the form of that Poisson structures and extend their domain of definition. We apply the theory to the rolling disk, the Routh's sphere, the ball rolling on a surface of revolution, and its special case of a ball rolling inside a cylinder.Comment: 22 page

Optimal stability and instability for near-linear Hamiltonians

In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover, in the same spirit as the notion of KAM stable integrable Hamiltonians, we will introduce a notion of effectively stable integrable Hamiltonians, conjecture a characterization of these Hamiltonians and show that our result prove this conjecture in the linear case