147 research outputs found
Moving constraints as stabilizing controls in classical mechanics
The paper analyzes a Lagrangian system which is controlled by directly
assigning some of the coordinates as functions of time, by means of
frictionless constraints. In a natural system of coordinates, the equations of
motions contain terms which are linear or quadratic w.r.t.time derivatives of
the control functions. After reviewing the basic equations, we explain the
significance of the quadratic terms, related to geodesics orthogonal to a given
foliation. We then study the problem of stabilization of the system to a given
point, by means of oscillating controls. This problem is first reduced to the
weak stability for a related convex-valued differential inclusion, then studied
by Lyapunov functions methods. In the last sections, we illustrate the results
by means of various mechanical examples.Comment: 52 pages, 4 figure
L^2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method
We consider scalar nonviscous conservation laws with strictly convex flux in
one spatial dimension, and we investigate the behavior of bounded L^2
perturbations of shock wave solutions to the Riemann problem using the relative
entropy method. We show that up to a time-dependent translation of the shock,
the L^2 norm of a perturbed solution relative to the shock wave is bounded
above by the L^2 norm of the initial perturbation.Comment: 17 page
Stellar evolution and modelling stars
In this chapter I give an overall description of the structure and evolution
of stars of different masses, and review the main ingredients included in
state-of-the-art calculations aiming at reproducing observational features. I
give particular emphasis to processes where large uncertainties still exist as
they have strong impact on stellar properties derived from large compilations
of tracks and isochrones, and are therefore of fundamental importance in many
fields of astrophysics.Comment: Lecture presented at the IVth Azores International Advanced School in
Space Sciences on "Asteroseismology and Exoplanets: Listening to the Stars
and Searching for New Worlds" (arXiv:1709.00645), which took place in Horta,
Azores Islands, Portugal in July 201
Geometric Approach to Pontryagin's Maximum Principle
Since the second half of the 20th century, Pontryagin's Maximum Principle has
been widely discussed and used as a method to solve optimal control problems in
medicine, robotics, finance, engineering, astronomy. Here, we focus on the
proof and on the understanding of this Principle, using as much geometric ideas
and geometric tools as possible. This approach provides a better and clearer
understanding of the Principle and, in particular, of the role of the abnormal
extremals. These extremals are interesting because they do not depend on the
cost function, but only on the control system. Moreover, they were discarded as
solutions until the nineties, when examples of strict abnormal optimal curves
were found. In order to give a detailed exposition of the proof, the paper is
mostly self\textendash{}contained, which forces us to consider different areas
in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page
Gluon polarization in the nucleon from quasi-real photoproduction of high-pT hadron pairs
We present a determination of the gluon polarization Delta G/G in the
nucleon, based on the helicity asymmetry of quasi-real photoproduction events,
Q^2<1(GeV/c)^2, with a pair of large transverse-momentum hadrons in the final
state. The data were obtained by the COMPASS experiment at CERN using a 160 GeV
polarized muon beam scattered on a polarized 6-LiD target. The helicity
asymmetry for the selected events is = 0.002 +- 0.019(stat.) +-
0.003(syst.). From this value, we obtain in a leading-order QCD analysis Delta
G/G=0.024 +- 0.089(stat.) +- 0.057(syst.) at x_g = 0.095 and mu^2 =~ 3
(GeV}/c)^2.Comment: 10 pages, 3 figure
Spin asymmetry A_1^d and the spin-dependent structure function g_1^d of the deuteron at low values of x and Q^2
We present a precise measurement of the deuteron longitudinal spin asymmetry
A_1^d and of the deuteron spin-dependent structure function g_1^d at Q^2 < 1
GeV^2 and 4*10^-5 < x < 2.5*10^-2 based on the data collected by the COMPASS
experiment at CERN during the years 2002 and 2003. The statistical precision is
tenfold better than that of the previous measurement in this region. The
measured A_1^d and g_1^d are found to be consistent with zero in the whole
range of x.Comment: 17 pages, 10 figure
A new measurement of the Collins and Sivers asymmetries on a transversely polarised deuteron target
New high precision measurements of the Collins and Sivers asymmetries of
charged hadrons produced in deep-inelastic scattering of muons on a
transversely polarised 6LiD target are presented. The data were taken in 2003
and 2004 with the COMPASS spectrometer using the muon beam of the CERN SPS at
160 GeV/c. Both the Collins and Sivers asymmetries turn out to be compatible
with zero, within the present statistical errors, which are more than a factor
of 2 smaller than those of the published COMPASS results from the 2002 data.
The final results from the 2002, 2003 and 2004 runs are compared with naive
expectations and with existing model calculations.Comment: 40 pages, 28 figure
Measurement of the Spin Structure of the Deuteron in the DIS Region
We present a new measurement of the longitudinal spin asymmetry A_1^d and the
spin-dependent structure function g_1^d of the deuteron in the range 1 GeV^2 <
Q^2 < 100 GeV^2 and 0.004< x <0.7. The data were obtained by the COMPASS
experiment at CERN using a 160 GeV polarised muon beam and a large polarised
6-LiD target. The results are in agreement with those from previous experiments
and improve considerably the statistical accuracy in the region 0.004 < x <
0.03.Comment: 10 pages, 6 figures, subm. to PLB, revised: author list, Fig. 4,
details adde
The Deuteron Spin-dependent Structure Function g1d and its First Moment
We present a measurement of the deuteron spin-dependent structure function
g1d based on the data collected by the COMPASS experiment at CERN during the
years 2002-2004. The data provide an accurate evaluation for Gamma_1^d, the
first moment of g1d(x), and for the matrix element of the singlet axial
current, a0. The results of QCD fits in the next to leading order (NLO) on all
g1 deep inelastic scattering data are also presented. They provide two
solutions with the gluon spin distribution function Delta G positive or
negative, which describe the data equally well. In both cases, at Q^2 = 3
(GeV/c)^2 the first moment of Delta G is found to be of the order of 0.2 - 0.3
in absolute value.Comment: fits redone using MRST2004 instead of MRSV1998 for G(x), correlation
matrix adde
The COMPASS Experiment at CERN
The COMPASS experiment makes use of the CERN SPS high-intensitymuon and
hadron beams for the investigation of the nucleon spin structure and the
spectroscopy of hadrons. One or more outgoing particles are detected in
coincidence with the incoming muon or hadron. A large polarized target inside a
superconducting solenoid is used for the measurements with the muon beam.
Outgoing particles are detected by a two-stage, large angle and large momentum
range spectrometer. The setup is built using several types of tracking
detectors, according to the expected incident rate, required space resolution
and the solid angle to be covered. Particle identification is achieved using a
RICH counter and both hadron and electromagnetic calorimeters. The setup has
been successfully operated from 2002 onwards using a muon beam. Data with a
hadron beam were also collected in 2004. This article describes the main
features and performances of the spectrometer in 2004; a short summary of the
2006 upgrade is also given.Comment: 84 papes, 74 figure
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