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

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure

Longitudinal double-spin asymmetry and cross section for inclusive neutral pion production at midrapidity in polarized proton collisions at sqrt(s) = 200 GeV

We report a measurement of the longitudinal double-spin asymmetry A_LL and the differential cross section for inclusive Pi0 production at midrapidity in polarized proton collisions at sqrt(s) = 200 GeV. The cross section was measured over a transverse momentum range of 1 < p_T < 17 GeV/c and found to be in good agreement with a next-to-leading order perturbative QCD calculation. The longitudinal double-spin asymmetry was measured in the range of 3.7 < p_T < 11 GeV/c and excludes a maximal positive gluon polarization in the proton. The mean transverse momentum fraction of Pi0's in their parent jets was found to be around 0.7 for electromagnetically triggered events.Comment: 6 pages, 3 figures, submitted to Phys. Rev. D (RC

Measurement of the Bottom contribution to non-photonic electron production in p+pp+p collisions at s\sqrt{s} =200 GeV

The contribution of $B$ meson decays to non-photonic electrons, which are mainly produced by the semi-leptonic decays of heavy flavor mesons, in $p+p$ collisions at $\sqrt{s} =$ 200 GeV has been measured using azimuthal correlations between non-photonic electrons and hadrons. The extracted $B$ decay contribution is approximately 50% at a transverse momentum of $p_{T} \geq 5$ GeV/$c$. These measurements constrain the nuclear modification factor for electrons from $B$ and $D$ meson decays. The result indicates that $B$ meson production in heavy ion collisions is also suppressed at high $p_{T}$.Comment: 6 pages, 4 figures, accepted by PR

Mid-rapidity anti-proton to proton ratio from Au+Au collisions at sNN=130 \sqrt{s_{NN}} = 130 GeV

We report results on the ratio of mid-rapidity anti-proton to proton yields in Au+Au collisions at \rts = 130 GeV per nucleon pair as measured by the STAR experiment at RHIC. Within the rapidity and transverse momentum range of $|y|<0.5$ and 0.4 $<p_t<$ 1.0 GeV/$c$, the ratio is essentially independent of either transverse momentum or rapidity, with an average of $0.65\pm 0.01_{\rm (stat.)} \pm 0.07_{\rm (syst.)}$ for minimum bias collisions. Within errors, no strong centrality dependence is observed. The results indicate that at this RHIC energy, although the $p$-\pb pair production becomes important at mid-rapidity, a significant excess of baryons over anti-baryons is still present.Comment: 5 pages, 3 figures, accepted by Phys. Rev. Let

Strange anti-particle to particle ratios at mid-rapidity in sqrt(s_NN)= 130 GeV Au+Au Collisions

Values of the ratios in the mid-rapidity yields of anti-Lambda/Lambda = 0.71 +/- 0.01(stat.) +/- 0.04(sys.), anti-Xi+/Xi- = 0.83 +/- 0.04(stat.) +/- 0.05 (sys.), anti-Omega+/Omega- = 0.95 +/- 0.15(stat) +/- 0.05(sys.) and K+/K- 1.092 +/- 0.023(combined) were obtained in central sqrt(s_NN) = 130 GeV Au+Au collisions using the STAR detector. The ratios indicate that a fraction of the net-baryon number from the initial system is present in the excess of hyperons over anti-hyperons at mid-rapidity. The trend in the progression of the baryon ratios, with increasing strange quark content, is similar to that observed in heavy-ion collisions at lower energies. The value of these ratios may be related to the charged kaon ratio in the framework of simple quark-counting and thermal models.Comment: 6 pages, 3 figures, revtex4, now accepted by Physics Letters B. All figures improved for clarity, fig. 2 now has kaon ratio separated by technique, fig. 3 now has additional other RHIC data points. Minor clarifications in text in response to referee comments. Updated ref

System size dependence of associated yields in hadron-triggered jets

We present results on the system size dependence of high transverse momentum di-hadron correlations at $\sqrt{s_{NN}}$ = 200 GeV as measured by STAR at RHIC. Measurements in d+Au, Cu+Cu and Au+Au collisions reveal similar jet-like correlation yields at small angular separation ($\Delta\phi\sim0$, $\Delta\eta\sim0$) for all systems and centralities. Previous measurements have shown that the away-side yield is suppressed in heavy-ion collisions. We present measurements of the away-side suppression as a function of transverse momentum and centrality in Cu+Cu and Au+Au collisions. The suppression is found to be similar in Cu+Cu and Au+Au collisions at a similar number of participants. The results are compared to theoretical calculations based on the parton quenching model and the modified fragmentation model. The observed differences between data and theory indicate that the correlated yields presented here will provide important constraints on medium density profile and energy loss model parameters.Comment: 12 pages, 5 figure