Solid‐State Gas Sensors Developed from Functional Difluoroboradiazaindacene Dyes

This article describes the synthesis and characterization of several new difluoroboradiazaindacene (BODIPY?) dyes functionalized at the central 8‐position by a phenyliodo, phenylheptynoate or phenylheptynoic fragment and at the 3‐ or 3/5‐position(s) by 4‐dimethylaminophenylstyryl residue(s). Single‐crystal structural determinations confirm the planarity of the dyes, while the absorption and fluorescence spectroscopic properties are highly sensitive to the state of protonation (or alkylation) of the terminal anilino donor group(s). Reversible color tuning from green to blue for absorption and from colorless (i.e., near‐IR region) to red for fluorescence is obtained on successive addition of acid and base. The difunctionalized derivative is especially interesting in this respect and shows two well‐resolved pK_a values of 5.10 and 3.04 in acetonitrile. Addition of the first proton causes only small spectral changes and deactivates the molecule towards addition of the second proton. It is this latter step that accommodates the large change in absorption and emission properties, due to the reversible extinction of the intramolecular charge‐transfer character inherent to this type of dye. The main focus of the work is the covalent anchoring of the dyes to inert, porous polyacrylate beads so as to form a solid‐state sensor suitable for analysis of gases or flowing liquids. The final material is highly stable—its performance is undiminished after more than one year—and fully reversible over many cycles. The sensitivity is such that reactions can be followed by the naked eye and the detection limit is about 600 ppb for HCl and about 80 ppb for ammonia. Trace amounts of diphosgene can be detected, as can alkylating agents. The sensing action is indiscriminate and also operates when the beads are dispersed in aqueous media.     

Numerical experiments with several variant WENO schemes for the Euler equations

Numerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126 :202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamics Aggregation in Stochastic Control Problems

For stochastic control problems with mixed state-control constraints, we develop a dynamics aggregation method which replaces the stochastic differential or difference equation with a simpler constraint. Solutions of such simplified problems are used to construct a sequence of approximations to the original problem. Convergence properties of the method for both discrete-time and continuous-time models are analyzed in detail.     

Identification of ground water flow patterns using particle models

Particle models are often used to simulate transport processes in ground water. The ground water flow pattern is one of the driving parameters of the transport model. In this paper a parameter identification algorithm is developed for particle type models to identify the underlying flow pattern from concentration measurements. The estimation problem is solved with a gradient based algorithm. For each generated particle track, the adjoint track is determined to efficiently compute gradient of the criterion.     

A multigrid procedure for Cartesian ghost‐cell methods

This paper proposes a multigrid technique for Cartesian grid flow solvers. A recently developed ghost body‐cell method for inviscid flows is combined with a nested‐level local refinement procedure, which employs multigrid to accelerate convergence to steady state. Different from standard multigrid applications for body‐fitted grids, a fictitious residual needs to be defined in the ghost cells to perform a correct residual collection and thus to avoid possible stalling of the multigrid procedure. The efficiency of the proposed local refinement multigrid Cartesian method is demonstrated for the case of the inviscid subsonic flow past a circular body. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive finite element methods for the identification of distributed parameters in elliptic equation

In this paper, adaptive finite element method is developed for the estimation of distributed parameter in elliptic equation. Both upper and lower error bound are derived and used to improve the accuracy by appropriate mesh refinement. An efficient preconditioned project gradient algorithm is employed to solve the nonlinear least-squares problem arising in the context of parameter identification problem. The efficiency of our error estimators is demonstrated by some numerical experiments.      

Convergence of Conjugate Gradient Methods with a Closed-Form Stepsize Formula

Conjugate gradient methods are efficient methods for minimizing differentiable objective functions in large dimension spaces. However, converging line search strategies are usually not easy to choose, nor to implement. Sun and colleagues (Ann. Oper. Res. 103:161–173, 2001; J. Comput. Appl. Math. 146:37–45, 2002) introduced a simple stepsize formula. However, the associated convergence domain happens to be overrestrictive, since it precludes the optimal stepsize in the convex quadratic case. Here, we identify this stepsize formula with one iteration of the Weiszfeld algorithm in the scalar case. More generally, we propose to make use of a finite number of iterates of such an algorithm to compute the stepsize. In this framework, we establish a new convergence domain, that incorporates the optimal stepsize in the convex quadratic case. The authors thank the associate editor and the reviewer for helpful comments and suggestions. C. Labat is now in postdoctoral position, Johns Hopkins University, Baltimore, MD, United States.     

Making decisions in the absence of clear facts

Bennis and O’Toole [Bennis, W.G., O’Toole, J., 2005. How business schools lost their way. Harvard Business Review 83, 96–104] have recently argued that decision makers need guidance in ‘making decisions in the absence of clear facts’. As such, decision makers must be able to resourcefully use whatever limited information is available and advantageously portray its implications. Based on recently published theory which directly addresses this requirement, this paper demonstrates, through a practical example, how decision makers can make systemic decisions in situations characterized by extremely limited information and, furthermore, what form such decisions can take. Evidence is provided, therefore, that operational research can effectively address what appears to be a gap in management training.     

Sequential stopping rules for the multistart algorithm in global optimisation

In this paper a sequential stopping rule is developed for the Multistart algorithm. A statistical model for the values of the observed local maxima of an objective function is introduced in the framework of Bayesian non-parametric statistics. A suitablea-priori distribution is proposed which is general enough and which leads to computationally manageable expressions for thea-posteriori distribution. Sequential stopping rules of thek-step look-ahead kind are then explicitly derived, and their numerical effectiveness compared.