Some Applications of the Extended Bendixson-Dulac Theorem

During the last years the authors have studied the number of limit cycles of several families of planar vector fields. The common tool has been the use of an extended version of the celebrated Bendixson-Dulac Theorem. The aim of this work is to present an unified approach of some of these results, together with their corresponding proofs. We also provide several applications.Comment: 19 pages, 3 figure

Strange particle production in proton-proton collisions at s=0.9\sqrt{s}=0.9 TeV with ALICE at the LHC

The production of mesons containing strange quarks (K$^0_s$, $\phi$) and both singly and doubly strange baryons ($\Lambda$, Anti-$\Lambda$, and $\Xi$+Anti-$\Xi$) are measured at central rapidity in pp collisions at $\sqrt{s}$ = 0.9 TeV with the ALICE experiment at the LHC. The results are obtained from the analysis of about 250 k minimum bias events recorded in 2009. Measurements of yields (dN/dy) and transverse momentum spectra at central rapidities for inelastic pp collisions are presented. For mesons, we report yields () of 0.184 $\pm$ 0.002 stat. $\pm$ 0.006 syst. for K$^0_s$ and 0.021 $\pm$ 0.004 stat. $\pm$ 0.003 syst. for $\phi$. For baryons, we find = 0.048 $\pm$ 0.001 stat. $\pm$ 0.004 syst. for $\Lambda$, 0.047 $\pm$ 0.002 stat. $\pm$ 0.005 syst. for Anti-$\Lambda$ and 0.0101 $\pm$ 0.0020 stat. $\pm$ 0.0009 syst. for $\Xi$+Anti-$\Xi$. The results are also compared with predictions for identified particle spectra from QCD-inspired models and provide a baseline for comparisons with both future pp measurements at higher energies and heavy-ion collisions.Comment: 33 pages, 21 captioned figures, 10 tables, authors from page 28, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/387

Suppression of charged particle production at large transverse momentum in central Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}} = 2.76 TeV

Inclusive transverse momentum spectra of primary charged particles in Pb-Pb collisions at $\sqrt{s_{_{\rm NN}}}$ = 2.76 TeV have been measured by the ALICE Collaboration at the LHC. The data are presented for central and peripheral collisions, corresponding to 0-5% and 70-80% of the hadronic Pb-Pb cross section. The measured charged particle spectra in $|\eta|<0.8$ and $0.3 < p_T < 20$ GeV/$c$ are compared to the expectation in pp collisions at the same $\sqrt{s_{\rm NN}}$, scaled by the number of underlying nucleon-nucleon collisions. The comparison is expressed in terms of the nuclear modification factor $R_{\rm AA}$. The result indicates only weak medium effects ($R_{\rm AA} \approx$ 0.7) in peripheral collisions. In central collisions, $R_{\rm AA}$ reaches a minimum of about 0.14 at $p_{\rm T}=6$-7GeV/$c$ and increases significantly at larger $p_{\rm T}$. The measured suppression of high-$p_{\rm T}$ particles is stronger than that observed at lower collision energies, indicating that a very dense medium is formed in central Pb-Pb collisions at the LHC.Comment: 15 pages, 5 captioned figures, 3 tables, authors from page 10, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/98

Two-pion Bose-Einstein correlations in central Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV

The first measurement of two-pion Bose-Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC.Comment: 17 pages, 5 captioned figures, 1 table, authors from page 12, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/388