On the convergence of successive Galerkin approximation for nonlinear output feedback <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

Although the formulation of the nonlinear theory of H _∞ control has been well developed, solving the Hamilton–Jacobi–Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H _∞ control via output feedback are presented. An example is presented illustrating the application of the algorithm.     

Iridium Cluster Chemistry: The Synthesis and the Solid State Structures of [HIr5(CO)12]2− and [HIr4(CO)10PPh3]−

The cluster [HIr₅(CO)₁₂]^2- (1) was prepared by condensation of [HIr₄(CO)₁₁]^- and [Ir(CO)₄]^- (molar ratio 1:1) in refluxing THF, with almost quantitative yields. Its solid state structure was determined by X-ray diffraction at low temperature on the salt [PPh₃CH₂Ph]₂[HIr₅(CO)₁₂]. The metal atoms define a trigonal bipyramidal arrangement. The hydride ligand was located indirectly as a bridge between apical and equatorial metal atoms. The phosphine-substituted cluster [HIr₄(CO)₁₀PPh₃]^- (2) was synthetized by CO displacement on [HIr₄(CO)₁₁]^-, in THF at room temperature. This reaction is selective, with no traces of polysubstitution products. In the solid state, the hydride and the triphenylphosphine are axially bound on basal iridium atoms; the terminal hydrogen atom was directly located by X-ray analysis at a Ir–H distance of 1.57(9) Å. On the contrary, two isomers are present in THF solution, and they interconvert rapidly at room temperature, as shown by¹H and ³¹P NMR spectra.     

Effect of agitation and aeration on production of hexokinase by Saccharomyces cerevisiae

A batch culture of Saccharomyces cerevisiae for the production of hexokinase was carried out in a 5-L fermentor containing 3 L of culture medium, which was in oculated with cell suspension (about 0.7 g/L), and left ferm entingat 35°C and pH 4.0. The aeration and agitation were adjusted to attain k _La values of 15, 60, 135, and 230 h⁻¹. The highest hexokinase productivity (754.6 U/[L h]) and substrate-cell conversion yield (0.21 g/g) occurred for a k _La of 60 h⁻¹. Moreover, the formation of hexokinase and cell growth are coupled events, which is in accordance with the constitutive character of this enzyme. Hexokinase formation for k _La>60 h⁻¹ was not enhanced probably owing to saturation of the respiratory pathway by oxygen.     

Kinetic and mass transfer parameters of maltotriose hydrolysis catalyzed by glucoamylase immobilized on macroporous silica and wrapped in pectin gel

Applied Biochemistry and Biotechnology - Kinetic and mass transport parameters were estimated for maltotriose hydrolysis using glucoamylase immobilized on macroporous silica and wrapped in pectin...     

Homogenization of Polycrystalline¶Aggregates

The effective elastic properties of a polycrystalline material depend on the single crystal elastic constants of the crystallites comprising the polycrystal and on the manner in which the crystallites are arranged. In this paper we apply the techniques of homogenization to put the problem of determining effective elastic constants in a precise mathematical framework that permits us to derive an expression for the effective elasticity tensor. We also study how the homogenized elasticity tensor changes as the probability characterizing the ensemble changes. Under the assumption that the field of orientations of the crystallographic axes of the crystallites is an independent random field, we show that our theory is compatible with the formulation used in texture analysis. In particular, we are able to prove that the physical assumption made by [10] in his study of weakly-textured polycrystals holds true. In addition, we establish some elementary bounds on the material constants that characterize the effective elasticity tensor of weakly-textured orthorhombic aggregates of cubic crystallites. Accepted: (June 15, 1999)     

Activity and Osmotic Coefficients from the Emf of Liquid Membrane Cells. VIII. K.3[Co(CN)6], Mg3[Co(CN)6]2, and Ca3[Co(CN)6]2

The activity coefficients of K₃[Co(CN)₆], Mg₃[Co(CN)₆]₂, and Ca₃[Co(CN)₆]₂,are examined. The results highlight close similarity with the correspondinghexacyanoferrate (III) salts. On dilution, K₃[Co(CN)₆], like K₃[Fe(CN)₆], approachesthe limiting law from the upper side, while Mg₃[Co(CN)₆]₂ and Ca₃[Co(CN)₆]₂tend to the limiting law from the opposite side, like Mg₃[Fe(CN)₆]₂,Ca₃[Fe(CN)₆]₂, Sr₃[Fe(CN)₆]₂, and Ba₃[Fe(CN)₆]₂. Both kinds of behavior agreewith theory for a model of hard spheres bearing electric charges +1 and –3 or+2 and –3, respectively. The paramater values of the Pitzer equation for activityand osmotic coefficients are reported.     

On the Nitroxide Quasi‐Equilibrium in the Alkoxyamine‐Mediated Radical Polymerization of Styrene

Summary: The range of validity of two popular versions of the nitroxide quasi‐equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, k_c[P][N] = k_d[P N], where P, N and P N are living, nitroxide radicals and dormant species respectively, with kinetic constants k_c and k_d, is found valid only for small values of the equilibrium constant K (10⁻¹¹–10⁻¹² mol · L⁻¹) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, k_c[P][N] = k_d[P N]₀ was found to be remarkably good up to values of K around 10⁻⁸ mol · L⁻¹. This upper bound is numerically found to be 2–3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physico‐chemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested.

Validity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.     

Turbulent Flow and Dispersion of Inertial Particles in a Confined Jet Issued by a Long Cylindrical Pipe

In this work we examine first the flow field of a confined jet produced by a turbulent flow in a long cylindrical pipe issuing in an abrupt angle diffuser. Second, we examine the dispersion of inertial micro-particles entrained by the turbulent flow. Specifically, we examine how the particle dispersion field evolves in the multiscale flow generated by the interactions between the large-scale structures, which are geometry dependent, with the smaller turbulent scales issued by the pipe which are advected downstream. We use Large-Eddy-Simulation (LES) for the flow field and Lagrangian tracking for particle dispersion. The complex shape of the domain is modelled using the immersed-boundaries method. Fully developed turbulence inlet conditions are derived from an independent LES of a spatially periodic cylindrical pipe flow. The flow field is analyzed in terms of local velocity signals to determine spatial coherence and decay rate of the coherent K–H vortices and to make quantitative comparisons with experimental data on free jets. Particle dispersion is analyzed in terms of statistical quantities and also with reference to the dynamics of the coherent structures. Results show that the particle dynamics is initially dominated by the Kelvin–Helmholtz (K–H) rolls which form at the expansion and only eventually by the advected smaller turbulence scales.     

Applications of homogenization techniques to the electrical conduction in biological tissues

We study a family of problems set in a finely mixed periodic medium, modelling electrical conduction in biological tissues. We prove a unified derivation of these different schemes from the Maxwell equations in the quasi-stationary approximation and we investigate the behaviour of the corresponding macroscopic models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)