122 research outputs found
Moving energies as first integrals of nonholonomic systems with affine constraints
In nonholonomic mechanical systems with constraints that are affine (linear
nonhomogeneous) functions of the velocities, the energy is typically not a
first integral. It was shown in [Fass\`o and Sansonetto, JNLS, 26, (2016)]
that, nevertheless, there exist modifications of the energy, called there
moving energies, which under suitable conditions are first integrals. The first
goal of this paper is to study the properties of these functions and the
conditions that lead to their conservation. In particular, we enlarge the class
of moving energies considered in [Fass\`o and Sansonetto, JNLS, 26, (2016)].
The second goal of the paper is to demonstrate the relevance of moving energies
in nonholonomic mechanics. We show that certain first integrals of some well
known systems (the affine Veselova and LR systems), which had been detected on
a case-by-case way, are instances of moving energies. Moreover, we determine
conserved moving energies for a class of affine systems on Lie groups that
include the LR systems, for a heavy convex rigid body that rolls without
slipping on a uniformly rotating plane, and for an -dimensional
generalization of the Chaplygin sphere problem to a uniformly rotating
hyperplane.Comment: 25 pages, 1 figure. Final version prepared according to the
modifications suggested by the referees of Nonlinearit
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
Measuring the Cosmic Ray Muon-Induced Fast Neutron Spectrum by (n,p) Isotope Production Reactions in Underground Detectors
While cosmic ray muons themselves are relatively easy to veto in underground
detectors, their interactions with nuclei create more insidious backgrounds
via: (i) the decays of long-lived isotopes produced by muon-induced spallation
reactions inside the detector, (ii) spallation reactions initiated by fast
muon-induced neutrons entering from outside the detector, and (iii) nuclear
recoils initiated by fast muon-induced neutrons entering from outside the
detector. These backgrounds, which are difficult to veto or shield against, are
very important for solar, reactor, dark matter, and other underground
experiments, especially as increased sensitivity is pursued. We used fluka to
calculate the production rates and spectra of all prominent secondaries
produced by cosmic ray muons, in particular focusing on secondary neutrons, due
to their importance. Since the neutron spectrum is steeply falling, the total
neutron production rate is sensitive just to the relatively soft neutrons, and
not to the fast-neutron component. We show that the neutron spectrum in the
range between 10 and 100 MeV can instead be probed by the (n, p)-induced
isotope production rates 12C(n, p)12B and 16O(n, p)16N in oil- and water-based
detectors. The result for 12B is in good agreement with the recent KamLAND
measurement. Besides testing the calculation of muon secondaries, these results
are also of practical importance, since 12B (T1/2 = 20.2 ms, Q = 13.4 MeV) and
16N (T1/2 = 7.13 s, Q = 10.4 MeV) are among the dominant spallation backgrounds
in these detectors
The weight of water
Leonardo da Vinci’s pioneering work on hydrostatics combined traditional knowledge and innovative empiricism in an attempt to understand an object fraught with paradox: the water-filled container
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
Impact of Uncertainties in Hadron Production on Air-Shower Predictions
At high energy, cosmic rays can only be studied by measuring the extensive
air showers they produce in the atmosphere of the Earth. Although the main
features of air showers can be understood within a simple model of successive
interactions, detailed simulations and a realistic description of particle
production are needed to calculate observables relevant to air shower
experiments. Currently hadronic interaction models are the main source of
uncertainty of such simulations. We will study the effect of using different
hadronic models available in CORSIKA and CONEX on extensive air shower
predictions.Comment: 12 pages, 6 figures, to appear in the proceedings of International
Conference on Interconnection between High Energy Physics and Astroparticle
Physics: From Colliders to Cosmic Rays, Prague, Czech Republic, 7-13 Sep 200
Search for Sub-TeV Gamma Rays Coincident with BATSE Gamma Ray Bursts
Project GRAND is a 100m x 100m air shower array of proportional wire chambers
(PWCs). There are 64 stations each with eight 1.29 m^2 PWC planes arranged in
four orthogonal pairs placed vertically above one another to geometrically
measure the angles of charged secondaries. A steel plate above the bottom pair
of PWCs differentiates muons (which pass undeflected through the steel) from
non-penetrating particles. FLUKA Monte Carlo studies show that a TeV gamma ray
striking the atmosphere at normal incidence produces 0.23 muons which reach
ground level where their angles and identities are measured. Thus,
paradoxically, secondary muons are used as a signature for gamma ray primaries.
The data are examined for possible angular and time coincidences with eight
gamma ray bursts (GRBs) detected by BATSE. Seven of the GRBs were selected
because of their good acceptance by GRAND and high BATSE Fluence. The eighth
GRB was added due to its possible coincident detection by Milagrito. For each
of the eight candidate GRBs, the number of excess counts during the BATSE T90
time interval and within plus or minus five degrees of BATSE's direction was
obtained. The highest statistical significance reported in this paper (2.7
sigma) is for the event that was predicted to be the most likely to be observed
(GRB 971110).Comment: To be presented at the XXVIII International Cosmic Ray Conference,
Tsukuba, Japa
Transition Radiation Spectra of Electrons from 1 to 10 GeV/c in Regular and Irregular Radiators
We present measurements of the spectral distribution of transition radiation
generated by electrons of momentum 1 to 10 GeV/c in different radiator types.
We investigate periodic foil radiators and irregular foam and fiber materials.
The transition radiation photons are detected by prototypes of the drift
chambers to be used in the Transition Radiation Detector (TRD) of the ALICE
experiment at CERN, which are filled with a Xe, CO2 (15 %) mixture. The
measurements are compared to simulations in order to enhance the quantitative
understanding of transition radiation production, in particular the momentum
dependence of the transition radiation yield.Comment: 18 pages, 15 figures, submitted to Nucl. Instr. Meth. Phys. Res.
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