How electrons guard the space: shape optimization with probability distribution criteria

Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume ³ for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue     

Static micromixers based on large-scale industrial mixer geometry

Mixing liquids at the micro-scale is difficult because the low Reynolds numbers in microchannels and in microreactors prohibit the use of conventional mixing techniques based on mechanical actuators and induce turbulence. Static mixers can be used to solve this mixing problem. This paper presents micromixers with geometries very close to conventional large-scale static mixers used in the chemical and food-processing industry. Two kinds of geometries have been studied. The first type is composed of a series of stationary rigid elements that form intersecting channels to split, rearrange and combine component streams. The second type is composed of a series of short helix elements arranged in pairs, each pair comprised of a right-handed and left-handed element arranged alternately in a pipe. Micromixers of both types have been designed by CAD and manufactured with the integral microstereolithography process, a new microfabrication technique that allows the manufacturing of complex three-dimensional objects in polymers. The realized mixers have been tested experimentally. Numerical simulations of these micromixers using the computational fluid dynamics (CFD) program FLUENT are used to evaluate the mixing efficiency. With a low pressure drop and good mixing efficiency these truly three-dimensional micromixers can be used for mixing of reactants or liquids containing cells in many microTAS applications.     

Enantioselective Diels-Alder reactions with N-hydroxy-N-phenylacrylamide

[reaction: see text] The use of hydroxamic acids as templates for Lewis acid catalyzed enantioselective Diels-Alder reactions has been examined. A very simple chiral Lewis acid, prepared by mixing optically pure binaphthol with 3 equiv of trimethylaluminum, catalyzes the [4 + 2] cycloaddition of N-hydroxy-N-phenylacrylamide with cyclopentadiene at 0 degrees C in high yield (>96%) and with a fairly good level of enantioselectivity (91% ee). Facile conversion of the products to the corresponding alcohols or aldehydes makes the hydroxamic acid intermediates particularly useful.     

Quantifying uncertainty with ensembles of surrogates for blackbox optimization

Blackbox optimization tackles problems where the functions are expensive to evaluate and where no analytical information is available. In this context, a tried and tested technique is to build surrogates of the objective and the constraints in order to conduct the optimization at a cheaper computational cost. This work introduces an extension to a specific type of surrogates: ensembles of surrogates, enabling them to quantify the uncertainty on the predictions they produce. The resulting extended ensembles of surrogates behave as stochastic models and allow the use of efficient Bayesian optimization tools. The method is incorporated in the search step of the mesh adaptive direct search (MADS) algorithm to improve the exploration of the search space. Computational experiments are conducted on seven analytical problems, two multi-disciplinary optimization problems and two simulation problems. The results show that the proposed approach solves expensive simulation-based problems at a greater precision and with a lower computational effort than stochastic models.

     

Higher Coverings of Racks and Quandles—Part II

Applied Categorical Structures - This article is the second part of a series of three articles, in which we develop a higher covering theory of racks and quandles. This project is rooted in...     

High Performance Varistor Discs Obtained from Chemically Synthesized Doped Zinc Oxide Powder

The ceramic microstructure, the chemical homogeneity of specific dopants and the mechanical integrity of a varistor disc are critical parameters in determining the transient voltage suppression features of these devices. The material properties and overall quality of the starting ceramic powders used to produce such components are essential in achieving the desired properties. The present work describes a novel chemical method developed to produce doped zinc oxide powders and an industrial scale manufacturing process for the production of final varistor blocks for surge arrester applications. The results are compared with those obtained when using standard varistor powder made by the mixed oxide route is used. All the fundamental electrical properties of the discs have been determined and correlated with the relevant manufacturing steps.     

Facile Preparation of (±)-12-Epiprostaglandins from 7-Oxabicyclo[2.2.1]hept-5-en-2-one via an all-cis-formyllactone related to Corey lactone

The bicyclic monoselenoacetal 7 , easily obtained from (±)-7-oxabicyclo[2.2.1]hept-5-en-2-one ( 6 ) via a radical addition-acyl migration sequence, was converted to racemic 12-epiprostaglandins 3 and 4 . The key intermediate was the all-cis-formyllactone 2b related to Corey lactone (see 12 ; Scheme 1). The presence of a (tert-butyl)-dimethylsilyl protective group for the 11-OH substituent (prostaglandin numbering) was found to be crucial in avoidingβ -elimination and epimerization during the Wittig-Horner reaction (Scheme 2). Epimerization at C(12) at the formyllactone stage (see 2b ) was also possible and gave the known precursor 1b of naturally occurring prostaglandins and analogs.     

Adsorption of barium and calcium chloride onto negatively charged alpha-Fe(2)O(3) particles

Adsorption of cations (Na(+), Ca(2+), Ba(2+)) onto negatively charged (pH 10.4) hematite (alpha-Fe(2)O(3)) particles has been studied. The oxide material was carefully prepared in order to obtain monodisperse suspensions of well-crystallized, quasi-spherical particles (50 nm in diameter). The isoelectric point (IEP) is located at pH 8.5. Adsorption of barium ions onto oxide particles was carried out and the electrophoretic mobility was measured throughout the adsorption experiment. Comparison with calcium adsorption at full coverage reveals a higher uptake of Ba(2+). In both cases it shows also that chloride ions coadsorb with M(2) ions. Simultaneous uptake of the positive and negative ions explains why the electrophoretic mobility does not reverse to cationic migration. A theoretical study of the surface speciation has been carried out, using the MuSiC model. It reveals the presence of negative as well as positive sites on both sides of the point of zero charge (PZC) of the hematite particles, which may explain the coadsorption of Ba(2+) and Cl(-) at pH 10.4. The effective charge of the oxide particles, calculated from the electrophoretic mobility, is in very good agreement with the results found with the MuSiC modelization and the chloride/barium adsorption ratio. It also verifies the theory of ionic condensation. Calorimetric measurements gave a negative heat for the overall reaction occurring when Ba(2+)/Cl(-) ions adsorb onto hematite. Despite the fact that anions (Cl(-) and OH(-)) adsorption onto mineral oxides is an exothermic phenomenon, it is likely that barium and calcium adsorption is endothermic, denoting the formation of an inner-sphere complex as reported in the literature.