25 research outputs found

    Computational study of three numerical methods for some linear and nonlinear advection-diffusion-reaction problems

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    In this paper, we use three existing schemes namely, Upwind Forward Euler, Non-Standard Finite Difference (NSFD) and Unconditionally Positive Finite Difference (UPFD) schemes to solve two numerical experiments described by a linear and a non-linear advection-diffusion-reaction equation with constant coefficients. These equations model exponential travelling waves and biofilm growth on a medical implant respectively. We study the exact and numerical dissipative and dispersive properties of the three schemes for both problems. Moreover, L1 error, dispersion and dissipation errors, at some values of temporal and spatial step sizes have been computed for the three schemes for both problems.DST/NRF SARChI chair in Mathematical Models and Methods in Bioengineering and BioSciences of the University of Pretoria.http://www.inderscience.com/jhome.php?jcode=PCFD2017-08-31hb2017Mathematics and Applied Mathematic

    Giant magnons of string theory in the lambda background

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    The analogues of giant magnon configurations are studied on the string world sheet in the lambda background. This is a discrete deformation of the AdS(5)xS(5) background that preserves the integrability of the world sheet theory. Giant magnon solutions are generated using the dressing method and their dispersion relation is found. This reduces to the usual dyonic giant magnon dispersion relation in the appropriate limit and becomes relativistic in another limit where the lambda model becomes the generalized sine-Gordon theory of the Pohlmeyer reduction. The scattering of giant magnons is then shown in the semi-classical limit to be described by the quantum S-matrix that is a quantum group deformation of the conventional giant magnon S-matrix. It is further shown that in the small g limit, a sector of the S-matrix is related to the XXZ spin chain whose spectrum matches the spectrum of magnon bound states.Comment: 53 pages, 6 figures, final version to appear in JHE

    Beta function of k deformed AdS5 × S 5 string theory

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    We calculate the one loop beta function for the would-be marginal coupling on the world sheet of the k deformed sigma models associated to a quantum group with q=exp(i pi/k). This includes the bosonic principal chiral models and symmetric space sigma models but also the k deformed semi-symmetric space sigma model describing strings in a deformation of AdS_5 x S^5. The world sheet sigma model is a current-current deformation of the gauged WZW model for the supergroup PSU(2,2|4) with level k. In the string theory context the beta function is shown to vanish because of the vanishing of the Killing form of PSU(2,2|4) which is another piece of evidence that the k deformed theories define consistent string theories.Comment: 26 pages, some typos correcte

    Temporal changes in the epidemiology, management, and outcome from acute respiratory distress syndrome in European intensive care units: a comparison of two large cohorts

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    Background: Mortality rates for patients with ARDS remain high. We assessed temporal changes in the epidemiology and management of ARDS patients requiring invasive mechanical ventilation in European ICUs. We also investigated the association between ventilatory settings and outcome in these patients. Methods: This was a post hoc analysis of two cohorts of adult ICU patients admitted between May 1–15, 2002 (SOAP study, n = 3147), and May 8–18, 2012 (ICON audit, n = 4601 admitted to ICUs in the same 24 countries as the SOAP study). ARDS was defined retrospectively using the Berlin definitions. Values of tidal volume, PEEP, plateau pressure, and FiO2 corresponding to the most abnormal value of arterial PO2 were recorded prospectively every 24 h. In both studies, patients were followed for outcome until death, hospital discharge or for 60 days. Results: The frequency of ARDS requiring mechanical ventilation during the ICU stay was similar in SOAP and ICON (327[10.4%] vs. 494[10.7%], p = 0.793). The diagnosis of ARDS was established at a median of 3 (IQ: 1–7) days after admission in SOAP and 2 (1–6) days in ICON. Within 24 h of diagnosis, ARDS was mild in 244 (29.7%), moderate in 388 (47.3%), and severe in 189 (23.0%) patients. In patients with ARDS, tidal volumes were lower in the later (ICON) than in the earlier (SOAP) cohort. Plateau and driving pressures were also lower in ICON than in SOAP. ICU (134[41.1%] vs 179[36.9%]) and hospital (151[46.2%] vs 212[44.4%]) mortality rates in patients with ARDS were similar in SOAP and ICON. High plateau pressure (> 29 cmH2O) and driving pressure (> 14 cmH2O) on the first day of mechanical ventilation but not tidal volume (> 8 ml/kg predicted body weight [PBW]) were independently associated with a higher risk of in-hospital death. Conclusion: The frequency of and outcome from ARDS remained relatively stable between 2002 and 2012. Plateau pressure > 29 cmH2O and driving pressure > 14 cmH2O on the first day of mechanical ventilation but not tidal volume > 8 ml/kg PBW were independently associated with a higher risk of death. These data highlight the continued burden of ARDS and provide hypothesis-generating data for the design of future studies

    D-branes in λ-deformations

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    We show that the geometric interpretation of D-branes in WZW models as twisted conjugacy classes persists in the λ\lambda--deformed theory. We obtain such configurations by demanding that a monodromy matrix constructed from the Lax connection of the λ\lambda--deformed theory continues to produce conserved charges in the presence of boundaries. In this way the D-brane configurations obtained correspond to ``integrable'' boundary configurations. We illustrate this with examples based on SU(2)SU(2) and SL(2,R)SL(2,\mathbb{R}), and comment on the relation of these D-branes to both non-Abelian T-duality and Poisson-Lie T-duality. We show that the D2 supported by D0 charge in the λ\lambda--deformed theory map, under analytic continuation together with Poisson-Lie T-duality, to D3 branes in the η\eta-deformation of the principal chiral model
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