Optimal Control of 1D Non linear Schrödinger equation

This talk is concerned with the optimal control of a 1D cubic nonlinear Schr\"odinger equation that describes the propagation of optical pulses. We consider the noise on an optical transmission systems as a control variable and study the existence of a minimum norm control such that the pulse is degraded at the end of the transmission (integral restriction on the state). We also give first order necessary conditions for an optimal solution.Non UBCUnreviewedAuthor affiliation: FCEyN, Universidad de Buenos Aires ArgentinaFacult

Optical solitons in nematic liquid crystals: Arbitrary deviation angle model

We study a coupled Schrödinger-elliptic evolution system that describes the propagation of a laser beam in nematic liquid crystals. The elliptic equation describes the effects of the beam electric field on the local orientation (director field) of the nematic liquid crystal and has an important regularizing effect, seen experimentally and understood theoretically in related models. In the present work we propose a new nonlinear elliptic equation for the director field that makes no assumption on the size of the director field angle. The analysis of this elliptic equation leads to an upper bound for the size of the director angle that we believe is optimal and physically relevant, and that implies that the elastic response of the medium prevents a complete alignment between the electric field and the orientation of the liquid crystal. The results on the elliptic problem are combined with arguments from dispersive wave theory to show the local and global well-posedness of the evolution problem and the decay of small initial conditions. We also show the existence of constrained minimizers of the Hamiltonian, assuming sufficiently large optical power ($L^2$-norm of the laser field). These minimizers are solitons with radial, monotonically decreasing profiles.Fil: Borgna, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Martin. Escuela de Ciencia y Tecnología. Centro de Matemática Aplicada; ArgentinaFil: Panayotaros, Panayotis. Universidad Nacional Autónoma de México; MéxicoFil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Sánchez de la Vega, Constanza. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin

Eratosthenes 2009/2010: An Old Experiment in Modern Times

We describe the projects “Eratosthenes 2009” and “Eratosthenes 2010 America,” carried out during the International Year of Astronomy (2009) in Argentina and with almost all the countries in North and South America during 2010. More than 15 000 students at more than 200 schools each year determined the radius of the Earth using the method that Eratosthenes employed more than 2000 years ago. The result obtained was 6290 km in 2009 and 6375 km in 2010, in good agreement with tabulated values of 6371 km [McCarthy and Petit, 2004, “IERS Conventions (2003),” IERS Technical Note No. 32, Frankfurt: Bundesamts für Kartographie und Geodäsie]. These projects involve history, mathematics, and astronomy to create an exciting activity with accurate scientific results

International Nosocomial Infection Control Consortiu (INICC) report, data summary of 43 countries for 2007-2012. Device-associated module

We report the results of an International Nosocomial Infection Control Consortium (INICC) surveillance study from January 2007-December 2012 in 503 intensive care units (ICUs) in Latin America, Asia, Africa, and Europe. During the 6-year study using the Centers for Disease Control and Prevention's (CDC) U.S. National Healthcare Safety Network (NHSN) definitions for device-associated health care–associated infection (DA-HAI), we collected prospective data from 605,310 patients hospitalized in the INICC's ICUs for an aggregate of 3,338,396 days. Although device utilization in the INICC's ICUs was similar to that reported from ICUs in the U.S. in the CDC's NHSN, rates of device-associated nosocomial infection were higher in the ICUs of the INICC hospitals: the pooled rate of central line–associated bloodstream infection in the INICC's ICUs, 4.9 per 1,000 central line days, is nearly 5-fold higher than the 0.9 per 1,000 central line days reported from comparable U.S. ICUs. The overall rate of ventilator-associated pneumonia was also higher (16.8 vs 1.1 per 1,000 ventilator days) as was the rate of catheter-associated urinary tract infection (5.5 vs 1.3 per 1,000 catheter days). Frequencies of resistance of Pseudomonas isolates to amikacin (42.8% vs 10%) and imipenem (42.4% vs 26.1%) and Klebsiella pneumoniae isolates to ceftazidime (71.2% vs 28.8%) and imipenem (19.6% vs 12.8%) were also higher in the INICC's ICUs compared with the ICUs of the CDC's NHSN