Optimal H2 order-one reduction by solving eigenproblems for polynomial equations

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based search, and hence avoids the usual problems of local minima. We examine mostly the case when the model order is reduced by one, and when the original system has distinct poles. This case exhibits special structure which allows us to provide a complete solution. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations, following the methods developed by Stetter and Moeller. The use of Buchberger's algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Groebner basis is immediately available. Compared with our previous work the method presented here has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. In addition, some hypotheses which were required in the previous work have been removed. Some examples are included.

Defect and disorder reduction by annealing in hydrogenated tetrahedral amorphous carbon

Hydrogenated tetrahedral amorphous carbon (ta-C:H) is a form of diamond-like carbon with a high sp3 content (>60%), grown here using a plasma beam source. Information on the behaviour of hydrogen upon annealing is obtained from effusion measurements, which show that hydrogen does not effuse significantly at temperatures less than 500 °C in films grown using methane and 700 °C in films grown using acetylene. Raman measurements show no significant structural changes at temperatures up to 300 °C. At higher temperatures, corresponding to the onset of effusion, the Raman spectra show a clustering of the sp2 phase. The density of states of ta-C:H is directly measured using scanning tunnelling spectroscopy. The measured gradients of the conduction and valence band tails increase up to 300 °C, confirming the occurrence of band tail sharpening. Examination of the photoluminescence background in the Raman spectra shows an increase in photoluminescence intensity with decreasing defect density, providing evidence that paramagnetic defects are the dominant non-radiative recombination centres in ta-C:H.

Reduction of porosity in RE1Ba2Cu3Oy pseudo crystals

The distribution of porosity in Y1Ba2Cu3Oy (Y-123) pseudo-crystals prepared by hot seeded melt growth of precursor pellet samples pre-sintered at elevated temperatures in air or vacuum has been investigated. The results demonstrate that the porosity within the Y-123 pseudo-crystal matrix could be reduced dramatically by pre-sintering in vacuum, compared with that for precursor pellets processed in air.

Evaluation of wave drag reduction by flow control

An analytical expression is proposed to estimate the wave drag of an aerofoil equipped with shock control. The analysis extends the conventional approach for a single normal shock wave, based on the knowledge that all types of successful shock control on transonic aerofoils cause bifurcated λ-shock structures. The influence of surface curvature on the λ-shock structure has been taken into account. The extended method has been found to produce fairly good agreement with the results obtained by CFD methods while requiring negligible computational effort. This new formulation is expected to be beneficial in the industrial design process of transonic aerofoils and wings where a large number of computational simulations have to be performed.

A new alternative for reduction of secondary flows in low pressure turbines

This paper describes a new flow mechanism for the reduction of secondary flows in Low Pressure Turbines using the benefit of contoured endwalls. The extensive application of contoured endwalls in recent years has provided a deeper understanding of the physical phenomenon that governs the reduction of secondary flows. Based on this understanding, the endwall geometry of a linear cascade of solid-thin profiles typical of Low Pressure Turbines has been redesigned. Experimental data are presented for the validation of this new solution. Based on these data, a reduction of 72% in the SKEH and 20% in the mixed-out endwall losses can be obtained. CFD simulations are also presented to illustrate the effect of the new endwall on the secondary flows. Furthermore, an explanation of the flow mechanism that governs the reduction of the SKEH and the losses is given. Copyright © 2006 by ASME.

Refractive index evaluation of multi-walled carbon nanotube arrays

Transmission terahertz time-domain spectroscopy (THz-TDS) measurements of carbon nanotube arrays are presented. A relatively thin film with vertically aligned multi-walled carbon nanotubes has been prepared and measured using THz-TDS. Experimental results were obtained from 80GHz to 2.5THz, and the sample has been characterized by extracting the relative permittivity of the carbon nanotubes. A combination of the Maxwell-Garnett and Drude models within the frequency range provide a good fit to the measured permittivity.

Assessing the potential of yield improvements, through process scrap reduction, for energy and CO2 abatement in the steel and aluminium sectors

Targets to cut 2050 CO2 emissions in the steel and aluminium sectors by 50%, whilst demand is expected to double, cannot be met by energy efficiency measures alone, so options that reduce total demand for liquid metal production must also be considered. Such reductions could occur through reduced demand for final goods (for instance by life extension), reduced demand for material use in each product (for instance by lightweight design) or reduced demand for material to make existing products. The last option, improving the yield of manufacturing processes from liquid metal to final product, is attractive in being invisible to the final customer, but has had little attention to date. Accordingly this paper aims to provide an estimate of the potential to make existing products with less liquid metal production. Yield ratios have been measured for five case study products, through a series of detailed factory visits, along each supply chain. The results of these studies, presented on graphs of cumulative energy against yield, demonstrate how the embodied energy in final products may be up to 15 times greater than the energy required to make liquid metal, due to yield losses. A top-down evaluation of the global flows of steel and aluminium showed that 26% of liquid steel and 41% of liquid aluminium produced does not make it into final products, but is diverted as process scrap and recycled. Reducing scrap substitutes production by recycling and could reduce total energy use by 17% and 6% and total CO 2 emissions by 16% and 7% for the steel and aluminium industries respectively, using forming and fabrication energy values from the case studies. The abatement potential of process scrap elimination is similar in magnitude to worldwide implementation of best available standards of energy efficiency and demonstrates how decreasing the recycled content may sometimes result in emission reductions. Evidence from the case studies suggests that whilst most companies are aware of their own yield ratios, few, if any, are fully aware of cumulative losses along their whole supply chain. Addressing yield losses requires this awareness to motivate collaborative approaches to improvement. © 2011 Elsevier B.V. All rights reserved.