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.

Preparation of tetrahedral amorphous carbon films by filtered cathodic vacuum arc deposition

Tetrahedrally bonded amorphous carbon (ta-C) and nitrogen doped (ta-C:N) films were obtained at room temperature in a filtered cathodic vacuum arc (FCVA) system incorporating an off-plane double bend (S-bend) magnetic filter. The influence of the negative bias voltage applied to substrates (from -20 to -350 V) and the nitrogen background pressure (up to 10-3 Torr) on film properties was studied by scanning electron microscopy (SEM), electron energy loss spectroscopy (EELS), Raman spectroscopy, X-ray photoemission spectroscopy (XPS), secondary ion mass spectroscopy (SIMS) and X-ray reflectivity (XRR). The ta-C films showed sp3 fractions between 84% and 88%, and mass densities around 3.2 g/cm3 in the wide range of bias voltage studied. In contrast, the compressive stress showed a maximum value of 11 GPa for bias voltages around -90 V, whereas for lower and higher bias voltages the stress decreased to 6 GPa. As for the ta-C:N films grown at bias voltages below -200 V and with N contents up to 7%, it has been found that the N atoms were preferentially sp3 bonded to the carbon network with a reduction in stress below 8 GPa. Further increase in bias voltage or N content increased the sp2 fraction, leading to a reduction in film density to 2.7 g/cm3.

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.