A pointwise constrained version of the Liapunov convexity theorem for single integrals

Given any AC solution ${\overline{x} : [a,b] \rightarrow \mathbb{R}^{n}}$ to the convex ordinary differential inclusion $$x^{\prime} ( t) \in co\{v^{1} ( t), \ldots, v^{m} ( t)\} \qquad a.e. on [ a,b], \qquad \qquad (^{*})$$ we aim at solving the associated nonconvex inclusion $$x^{\prime} ( t) \in \{v^{1} ( t), \ldots, v^{m} ( t)\} \qquad a.e.,x( a) = \overline{x} ( a), x( b) = \overline{x} ( b), \qquad \qquad (^{**})$$ under an extra pointwise constraint (e.g. on the first coordinate): $$x_{1} ( t) \leq \overline{x}_{1} ( t) \qquad \forall t \in [ a,b]. \qquad \qquad \qquad (^{***})$$ While the unconstrained inclusion (**) had been solved already in 1940 by Liapunov, its constrained version, with (***), was solved in 1994 by Amar and Cellina in the scalar n = 1 case. In this paper we add an extra geometrical hypothesis which is necessary and sufficient, in the vector n > 1 case, for it existence of solution to the constrained inclusion (**) and (***). We also present many examples and counterexamples to the 2 × 2 case.     

Classical versus Bayesian risks in acceptance sampling: a sensitivity analysis

Assuming a beta prior distribution on the fraction defective, $p$ , failure-censored sampling plans for Weibull lifetime models using classical (or average) and Bayesian (or posterior) producer’s and consumer’s risks are designed to determine the acceptability of lots of a given product. The average risk criterion provides a certain assurance that good (bad) lots will be accepted (rejected), whereas the posterior risk criterion provides a determined confidence that an accepted (rejected) lot is indeed good (bad). The performance of classical and Bayesian risks are analyzed in developing sampling plans when the lifetime variable follows the Weibull distribution. Several figures and tables illustrate the sensitivity of the risks and optimal sample sizes for selected censoring levels and specifications according to the available prior information on $p$ . The analysis clarifies the distinction among the different risks for a given sampling plan, and the effect of the prior knowledge on the required sample size. The study shows that, under uncertainty in the prior variance of $p$ , the designs using Bayesian risks are more appropriate.     

Optimization methodology assessment for the inlet velocity profile of a hydraulic turbine draft tube: part II—performance evaluation of draft tube model

Computational Fluids Dynamics (CFD) tools guide engineers and designers to estimate the performance of new designs. However, a CFD analysis can be very time-consuming depending mainly on the grid size and domain complexity. Thus, this paper aims to describe the tools used to evaluate and compare the performance of different 3D draft tube models for reducing the time-effort needed in an optimization procedure. The results presented here, are the second part of an overall research to establish a global optimization methodology to improve the performance of an hydraulic draft tube through the inlet velocity profile. Previously, three steps of optimization methodology to minimize the energy losses were studied: the inlet velocity profile parameterization, the numerical optimization set-up and the objective function validation. In the latter step, a global optimization method called Multi Island Genetic Algorithm (MIGA) was considered, which requires a large number of iterations before producing a reliable result. This step is able to identify an efficient inlet velocity profile to minimize the energy losses through the draft tube model. However, each iteration is expensive in terms of computational time due to the need for 3D Navier–Stokes (NS) computations to evaluate each profile’s fitness. Thus, in this work the methodology attempts to accelerate the optimization process with accurate results. In order to achieve the goal, the grid size of the 3D draft tube model was minimized, resulting in a much lower computational cost. Specifically, the draft tube calculations were performed on a sequence of five different grids each having approximately twice the number of elements compared to the previous. The measurements of the sensitivity of the draft tube performance quantities to the change of the inlet velocity parameters during the process showed that, in spite of the numerical difference between its performance, the results have the same tendency. Consequently, the 3D draft tube numerical model with a minimal grid size, is reliable and left record of its capabilities for being integrated in the optimization process.     

Negative differential conductance in nano-scale normal metal/superconductor/normal metal junctions featuring Fe1 + y Te1 − x Se x

Iron-based superconductors have been the subject of intensive study due to their high transition temperature and intriguing physical mechanisms. We describe a unique experimental approach to fabricate nano-scale normal metal/superconductor/normal metal junctions involving microcrystals of Fe₁ ?₊?_y Te₁ ?_??_x Se _x , for which we have observed a distinct phenomenon of negative differential conductance (NDC) dips along with multiple plateau features in differential conductance spectra. The evolution of the NDC dips and the plateau features is further explored as a function of both temperature and magnetic field, and their physical origin is discussed.     

Crystal plasticity modeling of irradiation growth in Zircaloy-2

Abstract

A physically based reaction-diffusion model is implemented in the visco-plastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. The reaction-diffusion model accounts for the defects produced by the cascade of displaced atoms, their diffusion to lattice sinks and the contribution to crystallographic strain at the level of single crystals. The VPSC framework accounts for intergranular interactions and irradiation creep, and calculates the strain in the polycrystalline ensemble. A novel scheme is proposed to model the simultaneous evolution of both, number density and radius, of irradiation-induced dislocation loops directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behaviour of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture and external stress on the coupled irradiation growth and creep behaviour are also studied and compared with available experimental data.     

Microscopic study of neutron-rich dysprosium isotopes

Microscopic studies in heavy nuclei are very scarce due to large valence spaces involved. This computational problem can be avoided by means of the use of symmetry-based models. Ground-state, γ and β bands, and their B(E2) transition strengths in ^160–168Dy isotopes, are studied in the framework of the pseudo-SU(3) model which includes the preserving symmetry Q · Q term and the symmetry-breaking Nilsson and pairing terms, systematically parametrized. Additionally, three rotor-like terms are considered, whose free parameters, fixed for all members of the chain, are used to fine tune the moment of inertia of rotational bands and the band head of γ and β bands. The model succesfully describes in a systematic way rotational features in these nuclei and allows to extrapolate toward the midshell nucleus ¹⁷⁰Dy. The results presented show that it is possible to study a full chain of isotopes or isotones in the region with the present model.     

Paraxial designing of planar waveguide variable-index focusing elements: Part 1—lenses of circular symmetry

A paraxial ray equation is used to evaluate refractive index profiles for a family of radially symmetric planar waveguide lenses. Two cases are considered: the (theoretically) full-aperture solution, and the solution with smooth index variation (non-full-aperature case). In deriving the latter case a new method has been applied that consists of the proper choice of a continuous deflection function. Both types of index profiles are described by exceptionally simple formulas.