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Aguilar, M.,Ali Cavasonza, L.,Ambrosi, G.,Arruda, L.,Attig, N.,Aupetit, S.,Azzarello, P.,Bachlechner, A.,Barao, F.,Barrau, A.,Barrin, L.,Bartoloni, A.,Basara, L.,Baş,ex11f,mez-du Pree, S.,Batta American Physical Society 2016 Physical review letters Vol.117 No.23
<P>Knowledge of the rigidity dependence of the boron to carbon flux ratio (B/C) is important in understanding the propagation of cosmic rays. The precise measurement of the B/C ratio from 1.9 GV to 2.6 TV, based on 2.3 million boron and 8.3 million carbon nuclei collected by AMS during the first 5 years of operation, is presented. The detailed variation with rigidity of the B/C spectral index is reported for the first time. The B/C ratio does not show any significant structures in contrast to many cosmic ray models that require such structures at high rigidities. Remarkably, above 65 GV, the B/C ratio is well described by a single power law R. with index. Delta = -0.333 +/- 0.014(fit) +/- 0.005(syst), in good agreement with the Kolmogorov theory of turbulence which predicts. Delta = -1/3 asymptotically.</P>
Properties of Cosmic Helium Isotopes Measured by the Alpha Magnetic Spectrometer
Aguilar, M.,Ali Cavasonza, L.,Ambrosi, G.,Arruda, L.,Attig, N.,Bachlechner, A.,Barao, F.,Barrau, A.,Barrin, L.,Bartoloni, A.,Baş,ex11f,mez-du Pree, S.,Battiston, R.,Becker, U.,Behlmann, M.,Beis American Physical Society 2019 Physical Review Letters Vol.123 No.18
Linear quadratic mean field Stackelberg differential games
Moon, Jun,Baş,ar, Tamer Elsevier 2018 Automatica Vol.97 No.-
<P><B>Abstract</B></P> <P>We consider linear–quadratic mean field Stackelberg differential games with the adapted open-loop information structure of the leader. There are one leader and N followers, where N is arbitrarily large. The leader holds a dominating position in the game in the sense that the leader first chooses and then announces the optimal strategy to which the N followers respond by playing a Nash game, i.e., choosing their optimal strategies noncooperatively and simultaneously based on the leader’s observed strategy. In our setting, the followers are coupled with each other through the mean field term included in their cost functions, and are strongly influenced by the leader’s open-loop strategy included in their cost functions and dynamics. From the leader’s perspective, he is coupled with the N followers through the mean field term included in his cost function. To circumvent the complexity brought about by the coupling nature among the leader and the followers with large N , which makes the use of the direct approach almost impossible, our approach in this paper is to characterize an approximated stochastic mean field process by solving a local optimal control problem of the followers with leader’s control taken as an exogenous stochastic process. We show that for each fixed strategy of the leader, the followers’ local optimal decentralized strategies lead to an ϵ -Nash equilibrium. The paper then solves the leader’s local optimal control problem, as a nonstandard constrained optimization problem, with constraints being induced by the approximated mean field process determined by Nash followers (which also depend on the leader’s control). We show that the local optimal decentralized controllers for the leader and the followers constitute an ( <SUB> ϵ 1 </SUB> , <SUB> ϵ 2 </SUB> ) -Stackelberg–Nash equilibrium for the original game, where <SUB> ϵ 1 </SUB> and <SUB> ϵ 2 </SUB> both converge to zero as N → ∞ . Numerical examples are provided to illustrate the theoretical results.</P>
Aguilar, M.,Ali Cavasonza, L.,Alpat, B.,Ambrosi, G.,Arruda, L.,Attig, N.,Aupetit, S.,Azzarello, P.,Bachlechner, A.,Barao, F.,Barrau, A.,Barrin, L.,Bartoloni, A.,Basara, L.,Baş,ex11f,mez-du Pree American Physical Society 2017 Physical Review Letters Vol.119 No.25
<P>We report the observation of new properties of primary cosmic rays He, C, and O measured in the rigidity (momentum/charge) range 2 GV to 3 TV with 90 x 10(6) helium, 8.4 x 10(6) carbon, and 7.0 x 10(6) oxygen nuclei collected by the Alpha Magnetic Spectrometer ( AMS) during the first five years of operation. Above 60 GV, these three spectra have identical rigidity dependence. They all deviate from a single power law above 200 GV and harden in an identical way.</P>
Aguilar, M.,Ali Cavasonza, L.,Ambrosi, G.,Arruda, L.,Attig, N.,Aupetit, S.,Azzarello, P.,Bachlechner, A.,Barao, F.,Barrau, A.,Barrin, L.,Bartoloni, A.,Basara, L.,Baş,ex11f,mez-du Pree, S.,Batta American Physical Society 2018 Physical Review Letters Vol.120 No.2
<P>We report on the observation of new properties of secondary cosmic rays Li, Be, and B measured in the rigidity (momentum per unit charge) range 1.9 GV to 3.3 TV with a total of 5.4 x 10(6) nuclei collected by AMS during the first five years of operation aboard the International Space Station. The Li and B fluxes have an identical rigidity dependence above 7 GV and all three fluxes have an identical rigidity dependence above 30 GV with the Li/Be flux ratio of 2.0 +/- 0.1. The three fluxes deviate from a single power law above 200 GV in an identical way. This behavior of secondary cosmic rays has also been observed in the AMS measurement of primary cosmic rays He, C, and O but the rigidity dependences of primary cosmic rays and of secondary cosmic rays are distinctly different. In particular, above 200 GV, the secondary cosmic rays harden more than the primary cosmic rays.</P>