Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models

This paper proposes a new method that extends the efficient global optimization to address stochastic black-box systems. The method is based on a kriging meta-model that provides a global prediction of the objective values and a measure of prediction uncertainty at every point. The criterion for the infill sample selection is an augmented expected improvement function with desirable properties for stochastic responses. The method is empirically compared with the revised simplex search, the simultaneous perturbation stochastic approximation, and the DIRECT methods using six test problems from the literature. An application case study on an inventory system is also documented. The results suggest that the proposed method has excellent consistency and efficiency in finding global optimal solutions, and is particularly useful for expensive systems.     

Dynamics of Drop Formation in an Electric Field

The effect of an electric field on the formation of a drop of an inviscid, perfectly conducting liquid from a capillary which protrudes from the top plate of a parallel-plate capacitor into a surrounding dynamically inactive, insulating gas is studied computationally. This free boundary problem which is comprised of the surface Bernoulli equation for the transient drop shape and the Laplace equation for the velocity potential inside the drop and the electrostatic potential outside the drop is solved by a method of lines incorporating the finite element method for spatial discretization. The finite element algorithm employed relies on judicious use of remeshing and element addition to a two-region adaptive mesh to accommodate large domain deformations, and allows the computations to proceed until the thickness of the neck connecting an about to form drop to the rest of the liquid in the capillary is less than 0.1% of the capillary radius. The accuracy of the computations is demonstrated by showing that in the absence of an electric field predictions made with the new algorithm are in excellent agreement with boundary integral calculations (Schulkes, R. M. S. M. J. Fluid Mech. 278, 83 (1994)) and experimental measurements on water drops (Zhang, X., and Basaran, O. A. Phys. Fluids 7(6), 1184 (1995)). In the presence of an electric field, the algorithm predicts that as the strength of the applied field increases, the mode of drop formation changes from simple dripping to jetting to so-called microdripping, in accordance with experimental observations (Cloupeau, M., and Prunet-Foch, B. J. Aerosol Sci. 25(6), 1021 (1994); Zhang, X., and Basaran, O. A. J. Fluid Mech. 326, 239 (1996)). Computational predictions of the primary drop volume and drop length at breakup are reported over a wide range of values of the ratios of electrical, gravitational, and inertial forces to surface tension force. In contrast to previously mentioned cases where both the flow rate in the tube and the electric field strength are nonzero, situations are also considered in which the flow rate is zero and the dynamics are initiated by impulsively changing the field strength from a certain value to a larger value. When the magnitude of the step change in field strength is small, the results of the new transient calculations accord well with those of an earlier stability analysis (Basaran, O. A., and Scriven, L. E. J. Colloid Interface Sci. 140(1), 10 (1990)) and thereby provide yet another testament to the accuracy of the new algorithm. Copyright 1999 Academic Press.     

Serendipitous synthesis of a ditwistane: a one-step access!

4-tert-Butyl-2-cyclohexen-1-one dimerizes in THF solution via its kinetic enolate, leading to di-tert-butylditwistane 8 in up to 36% yield (−78 °C → room temp., protonolysis, flash chromatography). X-ray crystallography shows that 8 incorporates one R and one S enantiomer of the starting ketone; none of the diastereomeric ditwistanes epi-8, epi’-8 or iso-8 was isolated. This means that the formation of 8 proceeds with mutual kinetic resolution and 100% induced diastereoselectivity.     

Zur Natur der Aluminiumsilicatniederschläge aus Na2H2SiO4-und AlCl3-Lösungen bei neutraler Reaktion

On addition, at neutral reaction, of increasing amounts of AlCl₃ solutions to 0.005 m Na-silicate solutions, in which the silicate anions are monomeric, amorphous, almost Na⁺-free precipitates are formed being at first characterised by a higher atomic Al:Si ratio than the total Al:Si mixing ratio. With increasing Al:Si addition, the Al:Si ratio of the precipitates increases until — at a 3:1 ratio in both the liquid and the solid phase — a definite, “saturated” compound, {[(OH)₂AlO]₃SiOH · aq}, is formed. In this compound the silicate anions are monomeric and not condensable at room temperature. This is valid, too, for precipitates from Al:Si > 3 which contain, besides the “saturated” compound, free Al hydroxide. The first-mentioned precipitates with Al:Si < 3, however, contain polymeric Si units which easily condense to more high-polymeric silicate anions.     

Correction to: Fatou closedness under model uncertainty

Positivity - There is an error in Proposition&nbsp;3.10. In fact, the stated proof only shows     

The Bounded Axiom A Forcing Axiom

We introduce the Bounded Axiom A Forcing Axiom (BAAFA). It turns out that it is equiconsistent with the existence of a regular ∑₂‐correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom (BPFA) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct organocatalytic aldol reactions in buffered aqueous media

Organocatalytic cross-aldol reactions catalyzed by cyclic secondary amines in aqueous media provide a direct route to a variety of aldols including carbohydrate derivatives and may warrant consideration as a prebiotic route to sugars.