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

Conservation of `moving' energy in nonholonomic systems with affine constraints and integrability of spheres on rotating surfaces

Energy is in general not conserved for mechanical nonholonomic systems with affine constraints. In this article we point out that, nevertheless, in certain cases, there is a modification of the energy that is conserved. Such a function coincides with the energy of the system relative to a different reference frame, in which the constraint is linear. After giving sufficient conditions for this to happen, we point out the role of symmetry in this mechanism. Lastly, we apply these ideas to prove that the motions of a heavy homogeneous solid sphere that rolls inside a convex surface of revolution in uniform rotation about its vertical figure axis, are (at least for certain parameter values and in open regions of the phase space) quasi-periodic on tori of dimension up to three

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

Distributions of secondary muons at sea level from cosmic gamma rays below 10 TeV

The FLUKA Monte Carlo program is used to predict the distributions of the muons which originate from primary cosmic gamma rays and reach sea level. The main result is the angular distribution of muons produced by vertical gamma rays which is necessary to predict the inherent angular resolution of any instrument utilizing muons to infer properties of gamma ray primaries. Furthermore, various physical effects are discussed which affect these distributions in differing proportions.Comment: 36 pages, 13 figures, minor revision, new layou

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 $n$-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

To what extent airborne particulate matters are influenced by ammonia and nitrogen oxides?

Intensive farming is known to significantly impact air quality, particularly fine particulate matter (PM$_{2.5}$). Understanding in detial their relation is important for scientific reasons and policy making. Ammonia emissions convey the impact of farming, but are not directly observed. They are computed through emission inventories based on administrative data and provided on a regular spatial grid at daily resolution. In this paper, we aim to validate \textit{lato sensu} the approach mentioned above by considering ammonia concentrations instead of emissions in the Lombardy Region, Italy. While the former are available only in few monitoring stations around the region, they are direct observations. Hence, we build a model explaining PM2.5 based on precursors, ammonia (NH3) and nitrogen oxides (NOX), and meteorological variables. To do this, we use a seasonal interaction regression model allowing for temporal autocorrelation, correlation between stations, and heteroskedasticity. It is found that the sensitivity of PM2.5 to NH3 and NOX depends on season, area, and NOX level. It is recommended that an emission reduction policy should focus on the entire manure cycle and not only on spread practices

Wire scanners in low energy accelerators

Fast wire scanners are today considered as part of standard instrumentation in high energy synchrotrons. The extension of their use to synchrotrons working at lower energies, where Coulomb scattering can be important and the transverse beam size is large, introduces new complications considering beam heating of the wire, composition of the secondary particle shower and geometrical consideration in the detection set-up. A major problem in treating these effects is that the creation of secondaries in a thin carbon wire by a energetic primary beam is difficult to describe in an analytical way. We are here presenting new results from a full Monte Carlo simulation of this process yielding information on heat deposited in the wire, particle type and energy spectrum of secondaries and angular dependence as a function of primary beam energy. The results are used to derive limits for the use of wire scanners in low energy accelerators.Comment: 20 pages, 8 Postscript figures, uses elsart.cl

Comparing air quality among Italy, Germany and Poland using BC indexes

In this paper we discuss air quality assessment in three Italian, German and Polish regions using the index methodology proposed in Bruno and Cocchi (2002, 2007). This analysis focuses first of all on the quality of the air in each of the countries being taken into consideration, and then adopts a more general approach in order to compare pollution severity and toxicity. This is interesting in a global European perspective where all countries are commonly involved in assessing air quality and taking proper measures for improving it. In this context, air quality indexes are a powerful data-driven tool which are easily calculated and summarize a complex phenomenon, such as air pollution, in indicators which are immediately understandable. In particular, the main objective of this work is to evaluate the index performances in distinguishing different air pollution patterns. This kind of analysis can be particularly useful, for example, in the perspective of constructing an indicator of air pollution. --