Low-rank optimization on the cone of positive semidefinite matrices

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. © 2010 Society for Industrial and Applied Mathematics.

Optimization of burnable poison design for Pu incineration in fully fertile free PWR core

The design challenges of the fertile-free based fuel (FFF) can be addressed by careful and elaborate use of burnable poisons (BP). Practical fully FFF core design for PWR reactor has been reported in the past [1]. However, the burnable poison option used in the design resulted in significant end of cycle reactivity penalty due to incomplete BP depletion. Consequently, excessive Pu loading were required to maintain the target fuel cycle length, which in turn decreased the Pu burning efficiency. A systematic evaluation of commercially available BP materials in all configurations currently used in PWRs is the main objective of this work. The BP materials considered are Boron, Gd, Er, and Hf. The BP geometries were based on Wet Annular Burnable Absorber (WABA), Integral Fuel Burnable Absorber (IFBA), and Homogeneous poison/fuel mixtures. Several most promising combinations of BP designs were selected for the full core 3D simulation. All major core performance parameters for the analyzed cases are very close to those of a standard PWR with conventional UO2 fuel including possibility of reactivity control, power peaking factors, and cycle length. The MTC of all FFF cores was found at the full power conditions at all times and very close to that of the UO2 core. The Doppler coefficient of the FFF cores is also negative but somewhat lower in magnitude compared to UO2 core. The soluble boron worth of the FFF cores was calculated to be lower than that of the UO2 core by about a factor of two, which still allows the core reactivity control with acceptable soluble boron concentrations. The main conclusion of this work is that judicial application of burnable poisons for fertile free fuel has a potential to produce a core design with performance characteristics close to those of the reference PWR core with conventional UO2 fuel.

A self-adaptive genetic algorithm applied to multi-objective optimization of an airfoil

Genetic algorithms (GAs) have been used to tackle non-linear multi-objective optimization (MOO) problems successfully, but their success is governed by key parameters which have been shown to be sensitive to the nature of the particular problem, incorporating concerns such as the numbers of objectives and variables, and the size and topology of the search space, making it hard to determine the best settings in advance. This work describes a real-encoded multi-objective optimizing GA (MOGA) that uses self-adaptive mutation and crossover, and which is applied to optimization of an airfoil, for minimization of drag and maximization of lift coefficients. The MOGA is integrated with a Free-Form Deformation tool to manage the section geometry, and XFoil which evaluates each airfoil in terms of its aerodynamic efficiency. The performance is compared with those of the heuristic MOO algorithms, the Multi-Objective Tabu Search (MOTS) and NSGA-II, showing that this GA achieves better convergence.

Fracture energy of the concrete-FRP interface in strengthened beams

To determine the load at which FRPs debond from concrete beams using global-energy-balance-based fracture mechanics concepts, the single most important parameter is the fracture energy of the concrete-FRP interface, which is easy to define but difficult to determine. Debonding propagates in the narrow zone of concrete, between the FRP and the (tension) steel reinforcement bars in the beam, and the presence of nearby steel bars prevents the fracture process zone, which in concrete is normally extensive, from developing fully. The paper presents a detailed discussion of the mechanism of the FRP debonding, and shows that the initiation of debonding can be regarded as a Mode I (tensile) fracture in concrete, despite being loaded primarily in shear. It is shown that the incorporation of this fracture energy in the debonding model developed by the authors, details of which are presented elsewhere, gives predictions that match the test results reported in the literature. © 2013 Elsevier Ltd.

The use of non-dimensional parameters to study stress in lithiumion battery electrode storage particles

Mechanical degradation is thought to be one of the causes of capacity fade within Lithium-Ion batteries. In this work we develop a coupled stress-diffusion model for idealized spherical storage particles, which is analogous to the development of thermal strains. We then non-dimensionalize the model and identify three important parameters that control the development of stress within these particles. We can therefore use a wide number of values for these parameters to make predictions about the stress responses of different materials. The maximum stress developed within the particle for different values of these parameters are plotted as stress maps. A two dimensional model of a battery was then developed, in order to study the effect of particle morphology. Copyright © 2012 by ASME.

Optimization of an effective extraction procedure for the analysis of microcystins in soils and lake sediments

Microcystin analysis in sediments and soils is considered very difficult due to low recovery for extraction. This is the primary limiting factor for understanding the fate of toxins in the interface between water and sediment in both the aquatic ecosystem as well as in soils. In the present study, a wide range of extraction solvents were evaluated over a wide range of pH, extraction approaches and equilibration time to optimize an effective extraction procedure for the analysis of microcystins in soils and lake sediments. The number of extractions required and acids in extraction solutions were also studied. In this procedure, EDTA-sodium pyrophosphate solution was selected as an extraction solvent based on the adsorption mechanism study. The optimized procedure proved to be highly efficient and achieved over 90% recovery. Finally, the developed procedure was applied to field soil and sediment sample collected from Chinese lakes during bloom seasons and microcystins were determined in six of ten samples. (c) 2005 Elsevier Ltd. All rights reserved.

Optimization by orthogonal array design and humoral immunity of the bivalent vaccine against Aeromonas hydrophila and Vibrio fluvialis infection in crucian carp (Carassius auratus L.)

Aeromonas hydrophila and Vibrio fluvialis are the causative agents of a serious haemorrhagic septicaemia that affects a wide range of freshwater fish in China. In order to develop a bivalent anti-A. hydrophila and anti-V. fluvialis formalin-killed vaccine to prevent this disease, an orthogonal array design (OAD) method was used to optimize the production conditions, using three factors, each having three levels. The effects of these factors and levels on the relative per cent survival for crucian carp were quantitatively evaluated by analysis of variance. The final optimized formulation was established. The data showed that inactivation temperature had a significant effect on the potency of vaccine, but formalin concentration did not. The bivalent vaccine could elicit a strong humoral response in crucian carp (Carassius auratus L.) against both A. hydrophila and V. fluvialis simultaneously, which peaked at 3 or 5 weeks respectively. Antibody titres remained high until week 12, the end of the experiment, after a single intraperitoneal injection. The verification experiment confirmed that an optimized preparation could provide protection for fish at least against A. hydrophila infection, and did perform better than the non-optimized vaccine judged by the antibody levels and protection rate, suggesting that OAD is of value in the development of improved vaccine formulations.

The optimization of high performance liquid chromatographic method for analysis of trace microcystins in natural water bodies

The ratio of methanol., water and trifluoroacetic acid ( TFA) was regulated to change the polarity and the pH of the rinse solution and the eluent, so as to improve the high performance liquid chromatography HPLC) detection method for trace microcystines (MCs) in natural water bodies. The results showed that 40 % similar to 45 % methanol-water solution containing 0. 1 % TFA could get good effects on the rinse of impurity, and 70% methanol-water solution containing 0. 1% TFA could elute all the MCs in solid phase extraction ( SPE) cartridge ( C-18), In this way. it is suggested that, in analysis of environmental samples with high concentration of impurity, impurity should be washed with 40% similar to 45% methanol-water solution containing 0. 1% TFA, and MCs should be eluted with 70% similar to 100% methanol-water solution containing 0. 1% TFA.

Fracture Properties of LPCVD Silicon Nitride and Thermally Grown Silicon Oxide Thin Films From the Load-Deflection of Long Si3N4 and SiO2/Si3N4 Diaphragms

The bulge test is successfully extended to the determination of the fracture properties of silicon nitride and oxide thin films. This is achieved by using long diaphragms made of silicon nitride single layers and oxide/nitride bilayers, and applying comprehensive mechanical model that describes the mechanical response of the diaphragms under uniform differential pressure. The model is valid for thin films with arbitrary z-dependent plane-strain modulus and prestress, where z denotes the coordinate perpendicular to the diaphragm. It takes into account the bending rigidity and stretching stiffness of the layered materials and the compliance of the supporting edges. This enables the accurate computation of the load-deflection response and stress distribution throughout the composite diaphragm as a function of the load, in particular at the critical pressure leading to the fracture of the diaphragms. The method is applied to diaphragms made of single layers of 300-nm-thick silicon nitride deposited by low-pressure chemical vapor deposition and composite diaphragms of silicon nitride grown on top of thermal silicon oxide films produced by wet thermal oxidation at 950 degrees C and 1050 degrees C with target thicknesses of 500, 750, and 1000 mn. All films characterized have an amorphous structure. Plane-strain moduli E-ps and prestress levels sigma(0) of 304.8 +/- 12.2 GPa and 1132.3 +/- 34.4 MPa, respectively, are extracted for Si3N4, whereas E-ps = 49.1 +/- 7.4 GPa and sigma(0) = -258.6 +/- 23.1 MPa are obtained for SiO2 films. The fracture data are analyzed using the standardized form of the Weibull distribution. The Si3N4 films present relatively high values of maximum stress at fracture and Weibull moduli, i.e., sigma(max) = 7.89 +/- 0.23 GPa and m = 50.0 +/- 3.6, respectively, when compared to the thermal oxides (sigma(max) = 0.89 +/- 0.07 GPa and m = 12.1 +/- 0.5 for 507-nm-thick 950 degrees C layers). A marginal decrease of sigma(max) with thickness is observed for SiO2, with no significant differences between the films grown at 950 degrees C and 1050 degrees C. Weibull moduli of oxide thin films are found to lie between 4.5 +/- 1.2 and 19.8 +/- 4.2, depending on the oxidation temperature and film thickness.

Optimization of metamorphic InGaAs quantum wells on GaAs grown by molecular beam epitaxy

We investigate the molecular beam epitaxy growth of metamorphic InxGa(1-x)As materials (x up to 0.5) on GaAs substrates systematically. Optimization of structure design and growth parameters is aimed at obtaining smooth surface and high optical quality. The optimized structures have an average surface roughness of 0.9-1.8 nm. It is also proven by PL measurements that the optical properties of high indium content (55%) InGaAs quantum wells are improved apparently by defect reduction technique and by introducing Sb as a surfactant. These provide us new ways for growing device quality metamorphic structures on GaAs substrates with long-wavelength emissions.

Optimization of GaInNAs(Sb)/GaAs quantum wells at 1.3-1.55 mu m grown by molecular beam epitaxy

The InGaNAs(Sb)/(GaNAs)/GaAs quantum wells (QWs) emitting at 1.3-1.55 mu m have been grown by molecular beam epitaxy (MBE). The parameters of the radio frequency (RF) such as RF power and flow rate are optimized to reduce the damages from the ions or energetic species. The growth temperature is carefully controlled to prevent the phase segregation and strain relaxation. The effects of Sb on the wavelength and quality are investigated. The GaNAs barrier is used to extend the wavelength and reduce the strain. A 1.5865 mu m InGaNAs(Sb)/GaNAs SQW edge emitting laser lasing at room temperature at continuous wave operation mode is demonstrated. (c) 2006 Elsevier B.V. All rights reserved.

Structure optimization of field-plate AlGaN/GaN HEMTs

AlGaN/GaN high electron mobility transistors (HEMTs) on 6H-SiC with varying field-plate length and gate-drain spacing were fabricated and analyzed. The classical small signal FET model and the well-known ColdFET method were used to extract the small signal parameters of the devices. Though the devices with field plates exhibited lower better f(T) characteristic, they did demonstrate better f(max), MSG and power density performances than the conventional devices without field plate. Besides, no independence of DC characteristic on field-plate length was observed. With the increase of the field-plate length and the gate-drain spacing, the characteristic of f(T) and f(max), degraded due to the large parasitic effects. Loadpull method was used to measure the microwave power performance of the devices. Under the condition of continuous wave at 5.4 GHz, an output power density of 4.69 W/mm was obtained for device with field-plate length of 0.5 mu m and gate-drain length of 2 mu m. (c) 2006 Elsevier Ltd. All rights reserved.

Geometry parameter optimization of large cross-sectional S-shaped bent rib waveguides for silicon based optical switches

地址: Chinese Acad Sci, Inst Semicond, State Key Lab Integrated Optoelect, Beijing 100083, Peoples R China