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.

Simulation of three-dimensional viscous flow in turbomachinery geometries using a solution-adaptive unstructured mesh methodology

This paper presents a numerical method for the simulation of flow in turbomachinery blade rows using a solution-adaptive mesh methodology. The fully three-dimensional, compressible, Reynolds-averaged Navier-Stokes equations with k-ε turbulence modeling (and low Reynolds number damping terms) are solved on an unstructured mesh formed from tetrahedral finite volumes. At stages in the solution, mesh refinement is carried out based on flagging cell faces with either a fractional variation of a chosen variable (like Mach number) greater than a given threshold or with a mean value of the chosen variable within a given range. Several solutions are presented, including that for the highly three-dimensional flow associated with the corner stall and secondary flow in a transonic compressor cascade, to demonstrate the potential of the new method.

Deposition of diamond-like carbon films by photon-enhanced chemical vapour deposition of methane using a windowless hydrogen lamp

Thin films of diamond-like carbon (DLC) have been deposited using a novel photon-enhanced chemical vapour deposition (photo-CVD) method. This low energy method may be a way to produce better interfaces in electronic devices by reducing damage due to ion bombardment. Methane requires high energy photons for photolysis to take place and these are not transmitted in most photo-CVD methods owing to the presence of a window between the lamp and the deposition environment. In our photo-CVD system there is no window and all the high energy photons are transmitted into the reaction gas. Initial work has proved promising and this paper presents recent results. Films have been characterized by measuring electron energy loss spectra, by ellipsometry and by fabricating and testing diode structures. Results indicate that the films are of a largely amorphous nature and are semiconducting. Diode structures have on/off current ratios of up to 106.

Distribution and length-weight relationship of tunas and tuna-like fishes around Ceylon

Tunas and tuna-like fishes have contributed considerably towards the increase in fish production from Ceylon's coastal waters, during the last five years and in this blood fish group lies a potential resource for a further increase in production. Consequently considerable attention is being paid to the study of these species. Length frequency sampling of these species are being carried out and quite often it becomes necessary to convert catch in terms of weight to catch in terms of number, when estimating apparent abundance of the stock. The length-weight relationship in addition to its usefulness in converting length frequency data to weight frequency data for such purpose is of general value to biologists and even to fishermen. The six species studied are yellowfin tuna (Thunnus alacares, Bonneterre), skipjack tuna (Katsuwonus pelamis, Linnaeus), mackerel tuna (Buthynnus affinis, Cantor), frigate mackerel (narrow corseleted Auxis thazard, Lacepede and broad corseleted A. rochie, Risso) and bonito (Saida orientalis, T&S).

Variability of nanoindentation responses of bone and artificial bone-like composites

Nanoindentation is a popular technique for measuring the intrinsic mechanical response of bone and has been used to measure a single-valued elastic modulus. However, bone is a composite material with 20-80 nm hydroxyapatite plates embedded in a collagen matrix, and modern instrumentation allows for measurements at these small length scales. The present study examines the indentation response of bone and artificial gelatin-apatite nanocomposite materials across three orders of magnitude of lengthscale, from nanometers to micrometers, to isolate the composite phase contributions to the overall response. The load-displacement responses were variable and deviated from the quadratic response of homogeneous materials at small depths. The distribution of apparent elastic modulus values narrowed substantially with increasing indentation load. Indentation of particulate nanocomposites was simulated using finite element analysis. Modeling results replicated the convergence in effective modulus seen in the experiments. It appears that the apatite particles are acting as the continuous ("matrix") phase in bone and nanocomposites. Copyright © 2004 by ASME.