Low-cost control problems on perforated and non-perforated domains

We study the homogenization of a class of optimal control problems whose state equations are given by second order elliptic boundary value problems with oscillating coefficients posed on perforated and non-perforated domains. We attempt to describe the limit problem when the cost of the control is also of the same order as that describing the oscillations of the coefficients. We study the situations where the control and the state are both defined over the entire domain or when both are defined on the boundary.     

An Experimental Technique to Assess the Compactness of Slurry-Fuel Sediments

Experimental Techniques -     

Preparation of advanced intermediates for the synthesis of both methyllycaconitine and racemulsonine via a common intermediate

Polycyclic precursors to 1 and 2 have been prepared via a common intermediate. The key steps include the intramolecular alkylation of a phenol and a selective metal-ammonia reduction.     

Enantioselective synthesis of linear polypropionate arrays using anthracene-tagged organosilanes

[reaction: see text] Preparation and use of anthracene-tagged organosilanes in an iterative, resin-capture-release protocol for the stereocontrolled synthesis of polypropionate arrays are described.     

Homogenization of elliptic eigenvalue problems: Part 2

The aim of this paper is to study the homogenization of elliptic eigenvalue problems, with a second order homogeneous Dirichlet problem as an example. The main homogenization theorem states that the same operator which serves to homogenize the corresponding static problem works for the eigenvalue problem as well and that the structure of eigenvalues and eigenvectors is in some sense preserved. Formulae for first and second order correctors for eigenvalues are proposed and error estimates are obtained. These results are applied to the case of coefficients with a periodic structure and a simple numerical example is presented. Extensions to other types of boundary conditions and to higher order equations are indicated.

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Resume Le but de cet article est d'étudier l'homogénéisation du problème de valeurs propres pour des opérateurs elliptiques. On prend comme exemple un problème de second-ordre avec des conditions de Dirichlet homogènes au bord. Le Théorème principal d'homogénéisation dit que le même opérateur qui homogénéise le problème stationnaire correspondant sert également à homogénéiser ce problème de valeurs propres et que la structure des valeurs et vecteurs propres est, grosso modo, préservée. On propose des formules pour calculer les correcteurs de premier et second ordre pour les valeurs propres et on obtient des estimations d'erreur. Ces résultats sont appliqués à un cas particulier où les coefficients sònt périodiques et des résultats numériques sont présentés. On indique des extensions possibles du point de vue conditions aux limites, et des problèmes de quatrième ordre.

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Part 1 of Dr. Kesavan's article appeared in Appl. Math. Optim. 5, Number 2.     

Homogenization of elliptic eigenvalue problems: Part 1

The aim of this paper is to study the homogenization of elliptic eigenvalue problems, with a second order homogeneous Dirichlet problem as an example. The main homogenization theorem states that the same operator which serves to homogenize the corresponding static problem works for the eigenvalue problem as well and that the structure of eigenvalues and eigenvectors is in some sense preserved. Formulae for first and second order correctors for eigenvalues are proposed and error estimates are obtained. These results are applied to the case of coefficients with a periodic structure and a simple numerical example is presented. Extensions to other types of boundary conditions and to higher order equations are indicated.

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Resume Le but de cet article est d'étudier l'homogénéisation du problème de valeurs propres pour des opérateurs elliptiques. On prend comme exemple un problème de second-ordre avec des conditions de Dirichlet homogènes au bord. Le Thèoréme principal d'homogénéisation dit que le même opérateur qui homogénéise le problème stationnaire correspondant sert également à homogénéiser ce problème de valeurs propres et que la structure des valeurs et vecteurs propres est, grosso modo, préservée. On propose des formules pour calculer les correcteurs de premier et second ordre pour les valeurs propres et on obtient des estimations d'erreur. Ces résultats sont appliqués à un cas particulier où les coefficients sont périodiques et des résultats numériques sont présentés. On indique des extensions possibles du point de vue conditions aux limites, et des problèmes de quatrième ordre.

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Part 2 of Dr. Kesavan's article will appear inAppl. Math. Opt. 5, Number 3.     

Substituted phenothiaziiies as indicators in the ferrocyanide titration of zinc

Chlorpromazine, promethazine and diethazine hydrochlorides and prochlorperazine maleate have been tested as indicators in the ferrocyanide titration of zinc. Only the first and last are useful, giving a sharp reversible colour change in both the direct and reverse titrations, but the results are negatively biased by 0.2-1.3%.     

Outer approximation algorithms for separable nonconvex mixed-integer nonlinear programs

A rigorous decomposition approach to solve separable mixed-integer nonlinear programs where the participating functions are nonconvex is presented. The proposed algorithms consist of solving an alternating sequence of Relaxed Master Problems (mixed-integer linear program) and two nonlinear programming problems (NLPs). A sequence of valid nondecreasing lower bounds and upper bounds is generated by the algorithms which converge in a finite number of iterations. A Primal Bounding Problem is introduced, which is a convex NLP solved at each iteration to derive valid outer approximations of the nonconvex functions in the continuous space. Two decomposition algorithms are presented in this work. On finite termination, the first yields the global solution to the original nonconvex MINLP and the second finds a rigorous bound to the global solution. Convergence and optimality properties, and refinement of the algorithms for efficient implementation are presented. Finally, numerical results are compared with currently available algorithms for example problems, illuminating the potential benefits of the proposed algorithm.     

Synthesis,Photophysical Properties and Computational Studies of beta‐Substituted Porphyrin Dyads

Beta‐pyrrole‐substituted porphyrin dyads connected by ethynyl linkage to N‐butylcarbazole or triphenylamine donors are reported. Donor‐π‐acceptor type beta‐substituted porphyrin dyads and their Zn(II) and Pd(II) complexes were characterized by MALDI‐MS, NMR, UV‐vis absorption, fluorescence and cyclic voltammetry techniques. The S₁ emission dynamics were analyzed by time‐resolved spectroscopy (TCSPC); dyads exhibited efficient energy transfer up to 93% from beta‐donors (N‐butylcarbazole or triphenylamine group) to the porphyrin core. The efficiency of energy transfer for the beta‐substituted porphyrin dyads were much higher than those of the corresponding meso‐substituted porphyrin dyads, reflecting enhanced communications between the beta‐donors and the porphyrin core. The Pd(II) dyads, showed characteristic phosphorescence in the near IR region and very efficient singlet oxygen quantum yields (53–60%); these dyads are promising candidates for photocatalytic oxidations of organic compounds. The donor‐acceptor interaction between the porphyrin core and the beta‐donors was supported by the DFT studies in the porphyrin dyads.     

Homogenization of periodic optimal control problems via multi-scale convergence

The aim of this paper is to provide an alternate treatment of the homogenization of an optimal control problem in the framework of two-scale (multi-scale) convergence in the periodic case. The main advantage of this method is that we are able to show the convergence of cost functionals directly without going through the adjoint equation. We use a corrector result for the solution of the state equation to achieve this.