Second-variation methods in dynamic optimization

An entire class of rapid-convergence algorithms, called second-variation methods, is developed for the solution of dynamic optimization problems. Several well-known numerical optimization techniques included in this class are developed from a unified point of view. The generalized Riccati transformation can be applied in conjunction with any second-variation method. This fact is demonstrated for the Newton-Raphson or quasilinearization technique.This work was supported by the National Research Council of Canada under Grant No. 67-3134 and is based on investigations described in more detail in Ref. 1.     

An electro-analogue of the oxyhaemoglobin dissociation curve

Summary A method for obtaining an electro-analogue of the oxyhaemoglobin dissociation curve is described. There are two variables involved: the partial pressure of oxygen of the haemoglobin solution or red cell suspension and the percentage saturation of the haemoglobin with oxygen. The partial pressure of oxygen is converted to a current by means of a polarographic electrode system, and the percentage saturation to coulombs by means of oxygen generating or consuming electrodes. Some possible applications of this electro-analogue are mentioned.

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Zusammenfassung Es wird ein Verfahren beschrieben, das es ermöglicht, ein elektrochemisches Analogon für die Dissoziationskurve des Oxyhämoglobins zu erhalten. Hierbei werden die beiden Variablen, der Sauerstoff-Partialdruck der Hämoglobinlösung oder Erythrocytensuspension und die prozentuale Sauerstoffsättigung des Hämoglobins, in elektrische Meßgrößen umgesetzt und zwar ersterer in eine Stromstärke (mit Hilfe eines polarographischen Elektrodensystems) und letztere in eine Strommenge (Coulombs) (mit Hilfe Sauerstoff erzeugender oder verbrauchender Elektroden). Einige Anwendungsbeispiele werden erwähnt.

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Dedicated to Prof. Dr. M. von Stackelberg on his 70th birthday.     

A practical guide to the staggered herringbone mixer

An analytical model of mixing in the staggered herringbone mixer (SHM) was derived to estimate mixing parameters and provide practical expressions to guide mixer design and operation for a wide range of possible solutes and flow conditions. Mixing in microfluidic systems has historically been characterized by the mixing of a specific solute system or by the redistribution of flow streams; this approach does not give any insight into the ideal operational parameters of the mixer with an arbitrary real system. For Stokes-flow mixers, mixing can be computed from a relationship between solute diffusivity, flow rate, and mixer length. Confocal microscopy and computational fluid dynamics (CFD) modeling were used to directly determine the extent of mixing for several solutes in the staggered herringbone mixer over a range of Reynolds numbers (Re) and Péclet numbers (Pe); the results were used to develop and evaluate an analytical model of its behavior. Mixing was found to be a function of only Pe and downstream position in the mixer. Required mixer length was proportional to log(Pe); this analytical model matched well with the confocal data and CFD model for Pe<5 x 10(4), at which point the experiments reached the limit of resolution. For particular solutes, required length and mixing time depend upon Re and diffusivity. This analytical model is applicable to other solute systems, and possibly to other embodiments of the mixer, to enable optimal design, operation, and estimation of performance.