Derivative based global sensitivity measures

The method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a strong link with the Morris screening method and Sobol' sensitivity indices and has several advantages over them. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is generally much lower than that for estimation of Sobol' sensitivity indices. This paper presents a survey of recent advances in DGSM concerning lower and upper bounds on the values of Sobol' total sensitivity indices $S\_{i}^{tot}$. Using these bounds it is possible in most cases to get a good practical estimation of the values of $S\_{i}^{tot}$. Several examples are used to illustrate an application of DGSM

Influence of backreaction of electric fields and Schwinger effect on inflationary magnetogenesis

We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling $f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ of the electromagnetic field to the inflaton field $\phi$. We consider the case where the coupling function $f(\phi)$ decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The backreaction occurs when the electric energy density becomes as large as the product of the slow-roll parameter $\epsilon$ and inflaton energy density, $\rho_{E}\sim \epsilon \rho_{\rm inf}$. It affects the inflaton field evolution and leads to the scale-invariant electric power spectrum and the magnetic one which is blue with the spectral index $n_{B}=2$ for any decreasing coupling function. This gives an upper limit on the present-day value of observed magnetic fields below $10^{-22}\,{\rm G}$. It is worth emphasizing that since the effective electric charge of particles $e_{\rm eff}=e/f$ is suppressed by the coupling function, the Schwinger effect becomes important only at the late stages of inflation when the inflaton field is close to the minimum of its potential. The Schwinger effect abruptly decreases the value of the electric field, helping to finish the inflation stage and enter the stage of preheating. It effectively produces the charged particles, implementing the Schwinger reheating scenario even before the fast oscillations of the inflaton. The numerical analysis is carried out in the Starobinsky model of inflation for the powerlike $f\propto a^{\alpha}$ and Ratra-type $f=\exp(\beta\phi/M_{p})$ coupling functions.Comment: 21 pages, 8 figure

Schwinger production of scalar particles during and after inflation from the first principles

By using the first-principles approach, we derive a system of three quantum kinetic equations governing the production and evolution of charged scalar particles by an electric field in an expanding universe. Analyzing the ultraviolet asymptotic behavior of the kinetic functions, we found the divergent parts of the electric current and the energy-momentum tensor of the produced particles and determined the corresponding counterterms. The renormalized system of equations is used to study the generation of electromagnetic fields during and after inflation in the kinetic coupling model $\mathcal{L}_{\rm EM}=-(1/4)f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ with the Ratra coupling function $f=\exp(\beta\phi/M_{p})$. It is found that the electric current of created particles is retarded with respect to the electric field. This leads to an oscillatory behavior of both quantities in agreement with the results obtained previously in phenomenological kinetic and hydrodynamical approaches.Comment: 22 pages, 4 figure

Derivative based global sensitivity measures

International audienceThe method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a strong link with the Morris screening method and Sobol' sensitivity indices and has several advantages over them. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is generally much lower than that for estimation of Sobol' sensitivity indices. This paper presents a survey of recent advances in DGSM concerning lower and upper bounds on the values of Sobol' total sensitivity indices $S_{i}^{tot}$. Using these bounds it is possible in most cases to get a good practical estimation of the values of $S_{i}^{tot}$. Several examples are used to illustrate an application of DGSM

Quantum dynamics in canonical and micro-canonical ensembles. Part I. Anderson localization of electrons

The new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner representation of quantum statistical mechanics has been developed. The time correlation functions have been presented in the form of the integral of the Weyl's symbol of considered operators and the Fourier transform of the product of matrix elements of the dynamic propagators. For the last function the integral Wigner- Liouville's type equation has been derived. The numerical procedure for solving this equation combining both molecular dynamics and Monte Carlo methods has been developed. For electrons in disordered systems of scatterers the numerical results have been obtained for series of the average values of the quantum operators including position and momentum dispersions, average energy, energy distribution function as well as for the frequency dependencies of tensor of electron conductivity and permittivity according to quantum Kubo formula. Zero or very small value of static conductivity have been considered as the manifestation of Anderson localization of electrons in 1D case. Independent evidence of Anderson localization comes from the behaviour of the calculated time dependence of position dispersion.Comment: 8 pages, 10 figure

Sensitivity analysis methods for uncertainty budgeting in system design

Quantification and management of uncertainty are critical in the design of engineering systems, especially in the early stages of conceptual design. This paper presents an approach to defining budgets on the acceptable levels of uncertainty in design quantities of interest, such as the allowable risk in not meeting a critical design constraint and the allowable deviation in a system performance metric. A sensitivity-based method analyzes the effects of design decisions on satisfying those budgets, and a multi-objective optimization formulation permits the designer to explore the tradespace of uncertainty reduction activities while also accounting for a cost budget. For models that are computationally costly to evaluate, a surrogate modeling approach based on high dimensional model representation (HDMR) achieves efficient computation of the sensitivities. An example problem in aircraft conceptual design illustrates the approach.United States. National Aeronautics and Space Administration. Leading Edge Aeronautics Research Program (Grant NNX14AC73A)United States. Department of Energy. Applied Mathematics Program (Award DE-FG02-08ER2585)United States. Department of Energy. Applied Mathematics Program (Award DE-SC0009297

X-ray line formation in the spectrum of SS 433

The mechanisms for the formation of X-ray lines in the spectrum of SS 433 are investigated by taking into account the radiative transfer inside the jets. The results of Monte Carlo numerical simulations are presented. The effect of a decrease in line intensity due to scattering inside the jet turns out to be pronounced, but it does not exceed 60% in magnitude on the entire grid of parameters. The line broadening due to scattering, nutational motion, and the contribution of satellites can lead to overestimates of the jet opening angle $\Theta$ from the line widths in Chandra X-ray observations. The fine structure of the lines turns out to be very sensitive to the scattering effects. This makes its investigation by planned X-ray observatories equipped with high-resolution spectrometers (primarily Astro-H) a powerful tool for diagnosing the parameters of the jets in SS 433.Comment: 23 pages, 14 figures, to be published in Astronomy Letters, v. 38, n. 7, p. 443 (2012

Copolyamide-clay nanotube polymer composite nanofiber membranes: Preparation, characterization and its asymmetric wettability driven oil/water emulsion separation towards sewage remediation

To address the problem of ever-increasing oily wastewater management, due to its directional liquid transport property, membranes with asymmetric wettability can be effectively used for emulsion separation. This study reports the synthesis of electrospun polymer?clay nanocomposite nanofibers, using co-polyamide polymer (COPA) and halloysite nanotubes (HA) as filler. The influence of clay content on the morphological, thermal and dielectric properties of the polymer composite nanofiber was investigated comprehensively to address the material characteristics of the developed system. The surface structure analysis and contact angle measurements of the electrospun composite nanofibers confirms the change in surface roughness and wettability when the fillers are added to the polymer. The porosity of the composite electrospun nanofiber membrane was found to be 85% with an oil adsorption capacity of 97% and water permeability of 6265 L/m2 h. Furthermore, the asymmetric wettability-driven oil/water emulsion separation abilities of the as-synthesized membranes shows that the separation efficiency of the composite fiber membrane is 10% improved compared to that of the neat fiber membrane, with improved separation time.Scopu

A study of the etapipi channel produced in central pp interactions at 450 GeV/c

The reaction pp -> pf (eta pi pi) ps has been studied at 450 GeV/c. There is clear evidence for an a2(1320)pi decay mode of the eta2(1645) and eta2(1870). In addition, there is evidence for an a0(980)pi$ decay mode of both resonances and an f2(1270)eta decay mode of the eta2(1870). No evidence is found for a JPC = 2++ a2(1320)pi wave.Comment: 15 pages, Latex, 4 Figures Branching ratio a2pi /f2 eta correcte

A phase II trial of bendamustine in combination with rituximab in older patients with previously untreated diffuse large B-cell lymphoma

Bendamustine in combination with rituximab (BR) has been associated with high response rates and acceptable toxicity in older patients with relapsed/refractory diffuse large B-cell lymphoma (DLBCL). Evaluation of BR is warranted in the front-line setting for DLBCL patients not eligible for anthracyclines or for the elderly. In this phase II study, we enrolled DLBCL patients aged ≥65 years who were poor candidates for R-CHOP (rituximab, cyclophosphamide, doxorubicin, vincristine, prednisone) to determine the efficacy and safety of BR in previously untreated stage II–IV DLBCL. Twenty-three patients were enrolled with a median age of 80 years. 52% of patients presented with poor functional status (Eastern Cooperative Oncology Group performance score of ≥2). The overall response rate was 78% with 12 complete responses (52%). At a median follow up of 29 months, the median overall survival was 10.2 months and the median progression-free survival was 5.4 months. The most common grade 3/4 adverse events were haematological. Combination therapy with BR demonstrates high response rates as front-line therapy in frail older patients with DLBCL, but survival rates were low. BR should be used with caution in future clinical trials involving older DLBCL patients with poor functional status