The unsatisfiability threshold revisited

The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the experimentally observed abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to the actual threshold value. In this paper, we consider the problem of bounding the threshold value from above using methods that, we believe, are of interest on their own right. More specifically, we show how the method of local maximum satisfying truth assignments can be combined with results for the occupancy problem in schemes of random allocation of balls into bins in order to achieve an upper bound for the unsatisfiability threshold less than 4.571. In order to obtain this value, we establish a bound on the q-binomial coefficients (a generalization of the binomial coefficients). No such bound was previously known, despite the extensive literature on q-binomial coefficients. Finally, to prove our result we had to establish certain relations among the conditional probabilities of an event in various probabilistic models for random formulas. It turned out that these relations were considerably harder to prove than the corresponding ones for unconditional probabilities, which were previously known.     

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.     

Rate constants from the reaction path Hamiltonian. I. Reactive flux simulations for dynamically correct rates

As ab initio electronic structure calculations become more accurate, inherent sources of error in classical transition state theory such as barrier recrossing and tunneling may become major sources of error in calculating rate constants. This paper introduces a general method for diabatically constructing the transverse eigensystem of a reaction path Hamiltonian in systems with many degenerate transverse frequencies. The diabatically constructed reaction path Hamiltonian yields smoothly varying coupling constants that, in turn, facilitate reactive flux calculations. As an example we compute the dynamically corrected rate constant for the chair to boat interconversion of cyclohexane, a system with 48 degrees of freedom and a number of degenerate frequencies. The transmission coefficients obtained from the reactive flux simulations agree with previous results that have been calculated using an empirical potential. Furthermore, the calculated rate constants agree with experimental values. Comparison to variational transition state theory shows that, despite finding the true bottleneck along the reaction pathway, variational transition state theory only accounts for half of the rate constant reduction due to recrossing trajectories.     

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.

     

In situ UV-visible spectroscopic measurements of kinetic parameters and active sites for catalytic oxidation of alkanes on vanadium oxides

In situ diffuse reflectance UV-visible spectroscopy was used to measure the dynamics of catalyst reduction and oxidation during propane oxidative dehydrogenation (ODH) on VOx/gamma-Al2O3. Transients in UV-visible intensity in the near-edge region were analyzed using a mechanistic model of ODH reactions. Rate constants per site for the kinetically relevant reduction step (C-H bond activation) measured using this analysis are slightly larger than those obtained from steady-state ODH rates normalized by surface V. The ratio of these values provides a measure of the fraction of the V surface sites that are active for ODH (0.6-0.7, for V surface densities of 2.3-34 V nm(-2)). This suggests that some of the V atoms are either inaccessible or inactive. Reoxidation rate constants, which cannot be obtained from steady-state analysis, are 10(3)-10(5) times larger than those for the C-H bond activation reduction step.     

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.     

Regioselective palladium-catalyzed phenylation of ethyl 4-oxazolecarboxylate

The efficient and regioselective palladium-catalyzed C-2 arylation of ethyl 4-oxazolecarboxylate 1 with phenyliodide is described. The different parameters (solvent, base, ligand and catalyst) for the optimal conditions of this arylation process have been screened.     

A growing string method for determining transition states: comparison to the nudged elastic band and string methods

Interpolation methods such as the nudged elastic band and string methods are widely used for calculating minimum energy pathways and transition states for chemical reactions. Both methods require an initial guess for the reaction pathway. A poorly chosen initial guess can cause slow convergence, convergence to an incorrect pathway, or even failed electronic structure force calculations along the guessed pathway. This paper presents a growing string method that can find minimum energy pathways and transition states without the requirement of an initial guess for the pathway. The growing string begins as two string fragments, one associated with the reactants and the other with the products. Each string fragment is grown separately until the fragments converge. Once the two fragments join, the full string moves toward the minimum energy pathway according to the algorithm for the string method. This paper compares the growing string method to the string method and to the nudged elastic band method using the alanine dipeptide rearrangement as an example. In this example, for which the linearly interpolated guess is far from the minimum energy pathway, the growing string method finds the saddle point with significantly fewer electronic structure force calculations than the string method or the nudged elastic band method.