Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems

A method for the numerical solution of state-constrained optimal control problems subject to higher-index differential-algebraic equation (DAE) systems is introduced. For a broad and important class of DAE systems (semiexplicit systems with algebraic variables of different index), a direct multiple shooting method is developed. The multiple shooting method is based on the discretization of the optimal control problem and its transformation into a finite-dimensional nonlinear programming problem (NLP). Special attention is turned to the mandatory calculation of consistent initial values at the multiple shooting nodes within the iterative solution process of (NLP). Two different methods are proposed. The projection method guarantees consistency within each iteration, whereas the relaxation method achieves consistency only at an optimal solution. An illustrative example completes this article.     

Linear elliptic boundary value problems in varying domains

The paper is devoted to the study of solutions to linear elliptic boundary value problems in domains depending smoothly on a small perturbation parameter. To this end we transform the boundary value problem onto a fixed reference domain and obtain a problem in a fixed domain but with differential operators depending on the perturbation parameter. Using the Fredholm property of the underlying operator we show the differentiability of the transformed solution under the assumption that the dimension of the kernel does not depend on the perturbation parameter. Furthermore, we obtain an explicit representation for the corresponding derivative.     

AFPP vs FPP

The main theme of this paper is that almost fixed point properties of discrete structures and fixed point properties of (topological) spaces are interdeducible via a suitable category which contains both graphs and spaces as objects. To carry out the program, we have to consider (almost) fixed points of multifunctions, and for this we need a preliminary discussion of power structures for graphs and simplicial complexes. Specific applications developed are: a digital convexity (discrete) version of Kakutani's fixed point theorem for convex-valued multifunctions; and fixed point properties of dendrites in terms of those of finite discrete trees.     

Shape sensitivity of a plane crack front

The 3D‐elasticity model of a solid with a plane crack under the stress‐free boundary conditions at the crack is considered. We investigate variations of a solution and of energy functionals with respect to perturbations of the crack front in the plane. The corresponding expansions at least up to the second‐order terms are obtained. The strong derivatives of the solution are constructed as an iterative solution of the same elasticity problem with specified right‐hand sides. Using the expansion of the potential and surface energy, we consider an approximate quadratic form for local shape optimization of the crack front defined by the Griffith criterion. To specify its properties, a procedure of discrete optimization is proposed, which reduces to a matrix variational inequality. At least for a small load we prove its solvability and find a quasi‐static model of the crack growth depending on the loading parameter. Copyright © 2003 John Wiley & Sons, Ltd.     

荧光粉相对亮度测量的色修正

由于很难将光接收器的相对光谱灵敏度S(λ)调到与CIE标准观察者V(λ)完全一致,不同荧光份又具有不同的相对光谱功率分布,因此测量荧光粉的相对亮度与测量其它光度量一样,必须进行色修正。本工作针对实际使用的光接收器和相对光谱功率分布不同的几种荧光粉的相对亮度计算了色修正系数。     

Nano liquid-metal fluid as ultimate coolant

We proposed for the first time the concept of the nano liquid-metal fluid, aiming to establish an engineering route to make the highest conductive coolant. Using several widely accepted theoretical models for characterizing the nano fluid, the thermal conductivity enhancement of the liquid-metal fluid due to addition of more conductive nano particles was predicted. Further, the effects of particle size, cluster of nano particle, solid-like layer due to adsorption, volume fraction and particle types were evaluated. Having the highest conductivity, being electromagnetically drivable, the liquid metal with low melting point is expected to be an idealistic base fluid for making super conductive solution which may lead to the ultimate coolant in a wide variety of heat transfer enhancement area.     

Enhanced Ratiometric pH Sensing Using SNAFL-2 on Silver Island Films: Metal-enhanced Fluorescence Sensing

We have explored the opportunities for enhanced ratiometric pH sensing using the well-known carboxy seminaphthofluorescein (SNAFL-2) and silver island films (SiFs). Our results show that the metallic surfaces can provide up to a 40-fold increase in probe fluorescence intensity as compared to nonmetallic surfaces with the same probe coverage. However, while the S/N is significantly better for pH sensing, the emission wavelength ratiometric values are similar to that obtained in solution, due to the fact that the emission of both the acidic and basic forms of the probe are enhanced to similar extents. To the best of our knowledge this is the first report of enhanced ratiometric fluorescence sensing on metallic surfaces.     

Gas-phase and catalytic combustion in heat-recirculating burners

An experimental study of a spiral counterflow “Swiss roll” burner was conducted, with emphasis on the determination of extinction limits and comparison of results with and without bare-metal Pt catalyst. A wide range of Reynolds numbers (Re) were tested using propane–air mixtures. Both lean and rich extinction limits were extended with the catalyst, though rich limits were extended much further. With the catalyst, combustion could be sustained at Re as low as 1.2 with peak temperatures as low as 350 K. A heat transfer parameter characterizing the thermal performance of both gas-phase and catalytic combustion at all Re was identified. At low Re, the “lean” extinction limit was actually rich of stoichiometric, and rich-limit had equivalence ratios exceeded 40 in some cases. No corresponding behavior was observed without the catalyst. Gas-phase combustion, in general, occurred in a “flameless” mode near the burner center. With or without catalyst, for sufficiently robust conditions (high Re, near-stoichiometric) not requiring heat recirculation, a visible flame would propagate out of the center, but this flame could only be re-centered if the catalyst were present. Gas chromatography indicated that at low Re, even in extremely rich mixtures, CO and non-propane hydrocarbons did not form. For higher Re, where both gas-phase and catalytic combustion could occur, catalytic limits were slightly broader but had much lower limit temperatures. At sufficiently high Re, catalytic and gas-phase limits merged. It is concluded that combustion at low Re in heat-recirculating burners greatly benefits from catalytic combustion with the proper choice of mixtures that are different from those preferred for gas-phase combustion. In particular, the importance of providing a reducing environment for the catalyst to enhance O₂ desorption, especially at low Re where heat losses are severe thus peak temperatures are low, is noted.     

On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve

In comparison with direct measurements of unsaturated hydraulic conductivity, the methods of calculations from the moisture retention curve are attractive for their fast and simple use and low cost. These are the main reasons for their increasing use, mainly in spatial variability studies. On the other hand, it is known that their applicability is limited. The possibility of the use of the retention curve to indirectly determine hydraulic conductivities is analyzed as follows. The theoretical derivation of the relationK(h) – (h) is briefly discussed with regards to potential sources of inaccuracy. The sensitivity of the algorithm forK(h) calculation is studied as a response to possible inaccuracies in the retention curve determination. Conclusions about the usability of calculated hydraulic conductivities are drawn.