Explicit approximate controllability of the Schr\"odinger equation with a polarizability term

We consider a controlled Schr\"odinger equation with a dipolar and a polarizability term, used when the dipolar approximation is not valid. The control is the amplitude of the external electric field, it acts non linearly on the state. We extend in this infinite dimensional framework previous techniques used by Coron, Grigoriu, Lefter and Turinici for stabilization in finite dimension. We consider a highly oscillating control and prove the semi-global weak $H^2$ stabilization of the averaged system using a Lyapunov function introduced by Nersesyan. Then it is proved that the solutions of the Schr\"odinger equation and of the averaged equation stay close on every finite time horizon provided that the control is oscillating enough. Combining these two results, we get approximate controllability to the ground state for the polarizability system

Estimation of parameters in a structured SIR model

[EN] In this paper, an age-structured epidemiological process is considered. The disease model is based on a SIR model with unknown parameters. We addressed two important issues to analyzing the model and its parameters. One issue is concerned with the theoretical existence of unique solution, the identifiability problem. The second issue is how to estimate the parameters in the model. We propose an iterative algorithm to study the identifiability of the system and a method to estimate the parameters which are identifiable. A least squares approach based on a finite set of observations helps us to estimate the initial values of the parameters. Finally, we test the proposed algorithms.The authors would like to thank the referees and the editor for their comments and useful suggestions for improvement of the manuscript. This work has been partially supported by Spanish Grant MTM2013-43678-P.Cantó Colomina, B.; Coll, C.; Sánchez, E. (2017). Estimation of parameters in a structured SIR model. Advances in Difference Equations. 33:1-13. https://doi.org/10.1186/s13662-017-1078-5S11333Strogatz, S, Friedman, M, Mallinck-Rodt, AJ, McKay, S: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Perseus Books, Washington (1994)De La Sen, M, Quesada, A: Some equilibrium, stability, instability and oscillatory results for an extended discrete epidemic model with evolution memory. Adv. Differ. Equ. 2013, 234 (2013)Han, Q, Wang, Z: On extinction of infectious diseases for multi-group SIRS models with satured incidence rate. Adv. Differ. Equ. 2015, 333 (2015)Cantó, B, Coll, C, Sánchez, E: Structural identifiability of a model of dialysis. Math. Comput. Model. 50, 733-737 (2009)Cantó, B, Coll, C, Sánchez, E: Identifiability of a class of discretized linear partial differential algebraic equations. Math. Probl. Eng., 1-12 (2011)Craciun, G, Pantea, C: Identifiability of chemical reaction networks. J. Math. Chem. 44, 244-259 (2008)Malik, MB, Salman, M: State-space least mean square. Digit. Signal Process. 18, 334-345 (2008)Ding, F, Liu, PX, Liu, G: Multiinnovatiovation least-squares identification for system modeling. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 18(3), 767-778 (2010)Ben-Zvi, A, McLellan, PJ, McAuley, KB: Identifiability of linear time-invariant differential-algebraic systems, I. The generalized Markov parameter approach. Ind. Eng. Chem. Res. 42, 6607-6618 (2003)Boyadjiev, C, Dimitrova, E: An iterative method for model parameter identification. Comput. Chem. Eng. 29, 941-948 (2005)Ben-Zvi, A, McLellan, PJ, McAuley, KB: Identifiability of linear time-invariant differential-algebraic systems, 2. The differential-algebraic approach. Ind. Eng. Chem. Res. 43, 1251-1259 (2004)Dion, JM, Commault, C, van der Woude, J: Generic properties and control of linear structured systems: a survey. Automatica 39, 1125-1144 (2003)Chou, IC, Voit, EO: Recent developments in parameter estimation and structure identification of biochemical and genomic systems. Math. Biosci. 219, 57-83 (2009)Schmitz, OJ: Ecology and Ecosystems Conservation. Island Press, Washington (2013

Multiparticle azimuthal correlations for extracting event-by-event elliptic and triangular flow in Au + Au collisions at sNN =200 GeV

We present measurements of elliptic and triangular azimuthal anisotropy of charged particles detected at forward rapidity 1<|η|<3 in Au + Au collisions at sNN=200 GeV, as a function of centrality. The multiparticle cumulant technique is used to obtain the elliptic flow coefficients v2{2},v2{4},v2{6}, and v2{8}, and triangular flow coefficients v3{2} and v3{4}. Using the small-variance limit, we estimate the mean and variance of the event-by-event v2 distribution from v2{2} and v2{4}. In a complementary analysis, we also use a folding procedure to study the distributions of v2 and v3 directly, extracting both the mean and variance. Implications for initial geometrical fluctuations and their translation into the final-state momentum distributions are discussed

Nonperturbative transverse-momentum-dependent effects in dihadron and direct photon-hadron angular correlations in p+p collisions at s =200 GeV

Dihadron and isolated direct photon-hadron angular correlations are measured in p+p collisions at s=200 GeV. The correlations are sensitive to nonperturbative initial-state and final-state transverse momenta kT and jT in the azimuthal nearly back-to-back region Δφ∼π. To have sensitivity to small transverse momentum scales, nonperturbative momentum widths of pout, the out-of-plane transverse-momentum component perpendicular to the trigger particle, are measured. In this region, the evolution of pout can be studied when several different hard scales are measured. These widths are used to investigate possible effects from transverse-momentum-dependent factorization breaking. When accounting for the longitudinal-momentum fraction of the away-side hadron with respect to the near-side trigger particle, the widths are found to increase with the hard scale; this is qualitatively similar to the observed behavior in Drell-Yan and semi-inclusive deep-inelastic scattering interactions, where factorization is predicted to hold. The momentum widths are also studied as a function of center-of-mass energy by comparing to previous measurements at s=510 GeV. The nonperturbative jet widths also appear to increase with s at a similar xT, which is qualitatively consistent to similar measurements in Drell-Yan interactions. Future detailed global comparisons between measurements of processes where transverse-momentum-dependent factorization is predicted to hold and be broken will provide further insight into the role of color in hadronic interactions

Nonperturbative-transverse-momentum broadening in dihadron angular correlations in sNN =200 GeV proton-nucleus collisions

The PHENIX collaboration has measured high-pT dihadron correlations in p+p, p+Al, and p+Au collisions at sNN=200 GeV. The correlations arise from inter- and intrajet correlations and thus have sensitivity to nonperturbative effects in both the initial and final states. The distributions of pout, the transverse-momentum component of the associated hadron perpendicular to the trigger hadron, are sensitive to initial- and final-state transverse momenta. These distributions are measured multidifferentially as a function of xE, the longitudinal momentum fraction of the associated hadron with respect to the trigger hadron. The near-side pout widths, sensitive to fragmentation transverse momentum, show no significant broadening between p+Au, p+Al, and p+p. The away-side nonperturbative pout widths are found to be broadened in p+Au when compared to p+p; however, there is no significant broadening in p+Al compared to p+p collisions. The data also suggest that the away-side pout broadening is a function of Ncoll, the number of binary nucleon-nucleon collisions, in the interaction. The potential implications of these results with regard to initial- and final-state transverse-momentum broadening and energy loss of partons in a nucleus, among other nuclear effects, are discussed

Pseudorapidity Dependence of Particle Production and Elliptic Flow in Asymmetric Nuclear Collisions of p+Al, p+Au, d+Au, and ^{3}He+Au at sqrt[s_{NN}]=200 GeV.

Asymmetric nuclear collisions of p+Al, p+Au, d+Au, and ^{3}He+Au at sqrt[s_{NN}]=200  GeV provide an excellent laboratory for understanding particle production, as well as exploring interactions among these particles after their initial creation in the collision. We present measurements of charged hadron production dN_{ch}/dη in all such collision systems over a broad pseudorapidity range and as a function of collision multiplicity. A simple wounded quark model is remarkably successful at describing the full data set. We also measure the elliptic flow v_{2} over a similarly broad pseudorapidity range. These measurements provide key constraints on models of particle emission and their translation into flow

Measurements of μμ pairs from open heavy flavor and Drell-Yan in p+p collisions at s =200 GeV

PHENIX reports differential cross sections of μμ pairs from semileptonic heavy-flavor decays and the Drell-Yan production mechanism measured in p+p collisions at s=200 GeV at forward and backward rapidity (1.2<|η|<2.2). The μμ pairs from cc, bb, and Drell-Yan are separated using a template fit to unlike- and like-sign muon pair spectra in mass and pT. The azimuthal opening angle correlation between the muons from cc and bb decays and the pair-pT distributions are compared to distributions generated using pythia and powheg models, which both include next-to-leading order processes. The measured distributions for pairs from cc are consistent with pythia calculations. The cc data present narrower azimuthal correlations and softer pT distributions compared to distributions generated from powheg. The bb data are well described by both models. The extrapolated total cross section for bottom production is 3.75±0.24(stat)±0.500.35(syst)±0.45(global) [μb], which is consistent with previous measurements at the Relativistic Heavy Ion Collider in the same system at the same collision energy and is approximately a factor of 2 higher than the central value calculated with theoretical models. The measured Drell-Yan cross section is in good agreement with next-to-leading-order quantum-chromodynamics calculations

Long term follow up results of sequential left internal thoracic artery grafts on severe left anterior descending artery disease

<p>Abstract</p> <p>Purpose</p> <p>Several alternative procedures have been proposed to achieve complete revascularization in the presence of diffuse left anterior descending coronary artery (LAD) disease. With the extensive use of internal thoracic artery grafts in coronary artery bypass procedures, sequential anastomosis of the left internal thoracic artery (LITA) to LAD has gained popularity in these challenging cases. The long term results of sequential LITA to LAD anstomosis were examined in this study.</p> <p>Patients and Methods</p> <p>In order to determine the long term results of the sequential revascularization of LAD by LITA graft, 41 out of 49 patients operated between January 2001 and December 2005 were selected for control coronary arteriography. The median period for control coronary arteriography was 64 months.</p> <p>Results</p> <p>Seventy five anastomoses were found to be fully patent (91,46%) among the 82 sequential LITA anastomoses (41 LITA grafts) on the LAD at a median follow-up period of 64 months (53 to 123 months). Among the 41 LITA grafts used for this purpose, 36 were found intact (complete patency of the proximal and distal anastomoses) (87,8%). Two LITA grafts (4 anastomoses) were found to be totally occluded (4,87%). The proximal anastomosis of the LITA graft was observed to be 90% stenotic in one patient (1,21%). In one patient tight stenosis of the distal anastomosis line was observed (1,21%), while in another patient 70% narrowing of LITA lumen after the proximal anastomosis was detected (1,21%).</p> <p>Conclusion</p> <p>We strongly beleive that sequential LITA grafting of LAD is a safe alternative in the presence of severe LAD disease to achieve complete revascularization of the anterior myocardium with patency rates not much differing from conventional single LITA to LAD anastomosis.</p

Measurement of charm and bottom production from semileptonic hadron decays in p+p collisions at s =200 GeV

Measurements of the differential production of electrons from open-heavy-flavor hadrons with charm- and bottom-quark content in p+p collisions at s=200 GeV are presented. The measurements proceed through displaced-vertex analyses of electron tracks from the semileptonic decay of charm and bottom hadrons using the PHENIX silicon-vertex detector. The relative contribution of electrons from bottom decays to inclusive heavy-flavor-electron production is found to be consistent with fixed-order-plus-next-to-leading-log perturbative-QCD calculations within experimental and theoretical uncertainties. These new measurements in p+p collisions provide a precision baseline for comparable forthcoming measurements in A+A collisions