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

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

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

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

The FLUKA Code: Developments and Challenges for High Energy and Medical Applications

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Cosmic-ray interactions with the Sun

The solar disk is a bright gamma-ray source in the sky. The interactions of cosmic rays with the solar atmosphere produce secondary particles which can reach the Earth. In this work we present a comprehensive calculation of the yields of secondary particles such as gamma-rays, electrons, positrons, neutrons and neutrinos, performed with the FLUKA code. We also estimate the intensity at the Sun and the fluxes at the Earth of these secondary particles by folding their yields with the intensities of cosmic rays impinging on the solar surface. The results are sensitive to the assumptions on the magnetic field near the Sun and to the cosmic-ray transport in the magnetic field in the inner solar system