Third‐order sensitivity analysis for robust aerodynamic design using continuous adjoint

Robust design problems in aerodynamics are associated with the design variables, which control the shape of an aerodynamic body, and also with the so‐called environmental variables, which account for uncertainties. In this kind of problems, the set of design variables, which leads to optimal performance, taking into account possible variations in the environmental variables, is sought. One of the possible ways to solve this problem is by means of the second‐order second‐moment approach, which requires first‐order and second‐order derivatives of the objective function with respect to the environmental variables. Should the minimization problem be solved using a gradient‐based method, algorithms for the computation of up to third‐order sensitivity derivatives (twice with respect to the environmental variables and once with respect to the shape controlling design variables) must be devised. In this paper, a combination of the continuous adjoint variable method and direct differentiation to compute the third‐order sensitivities is proposed. This is shown to be the most efficient among all alternative methods provided that the environmental variables are much less than the design ones. Apart from presenting the method formulation, this paper focuses on the assessment of the so‐computed up‐to third‐order mixed derivatives through comparison with costly finite‐difference schemes. To this end, the robust design of a two‐dimensional duct is performed. Then, using the validated method, the robust design of a two‐dimensional cascade airfoil is demonstrated. Although both cases are handled as inverse design problems, the method can be extended to other objective functions or three‐dimensional problems in a straightforward manner. Copyright © 2012 John Wiley & Sons, Ltd.     

Reactivity of B‐Xanthyl N‐Heterocyclic Carbene‐Boranes

The synthesis and reactivity of mono‐ and bis‐S‐xanthyl NHC‐boranes is reported. The new NHC‐boranes are prepared through nucleophilic exchange at boron from either mono‐ or bis‐triflyl NHC‐boranes, themselves obtained by protolysis of the NHC‐BH₃ starting compounds. The B?H bond of the S‐xanthyl NHC‐boranes can be cleaved both homolytically and heterolytically, albeit the latter is more synthetically useful. The S‐xanthyl NHC‐boranes can reduce both aldehydes and imines. The B?S bond can also be cleaved homolytically. Under UV irradiation, the S‐xanthyl NHC‐boranes generate NHC‐boryl radicals that can initiate radical polymerizations of acrylates.     

Structural and phase characteristics of the diamond/matrix interfacial zone in high-resistant diamond composites

The structural-phase state of the contact zone and the factors that influence on the strength of diamond retention in the diamond carbide composites were determined. Composites were obtained by the new hybrid technology that eliminates the reheating of the metalized coating. The elaborated technology combines the thermal diffusion metallization of a diamond and the sintering by the scheme of self-dosed impregnation in a one-stage technological cycle. By the methods of electron microscopy, X-ray diffraction analysis, and Raman spectroscopy the structural and phase characteristics of the interphase boundary were investigated. The improvement of chemical and mechanical adhesion between the diamond and carbide matrix was obtained. It was shown that the specific productivity of the samples with a metalized diamond component is 39% higher than those without metallization.     

Highly Selective Zeolite Topologies for Flue Gas Separation

The separation of carbon dioxide from flue gas is essential for the reduction of greenhouse gas emissions. In adsorptive methods, the challenge lies in the choice of suitable porous materials. Among all zeolite topologies, a number of adsorbents with pore dimensions in the range of the guest molecules were identified to allow an excellent separation by diffusion, and MRE and AFO zeolite topologies appear to be the best candidates based on equilibrium adsorption. Also, it was found that the behavior of this gas mixture in DFT and APD zeolites differed from the normal behavior.     

CoII Cryptates Convert CO2 into CO and CH4 under Visible Light

Three Co^II octaazacryptates, with different substituents on the aromatic rings (Br, NO₂, CCH), were synthesised and characterised. These and the already published non-substituted cryptate catalysed CO₂ photoreduction to CO and CH₄ under blue visible light at room temperature. Although CO was observed after short irradiation times and a large range of catalyst concentrations, CH₄ was only observed after longer irradiation periods, such as 30 h, but with a small catalyst concentration (25 nm ). Experiments with ¹³C labelled CO₂ showed that CO is formed and reacts further when the reaction time is long. The CCH catalyst is deactivated faster than the others and the more efficient catalyst for CH₄ production is the one with Br. This reactivity trend was explained by an energy decomposition analysis based on DFT calculations.     

Trichloro(Dinitrogen)Platinate(II)

Zeise's salt, [PtCl₃(H₂C=CH₂)]⁻_, is the oldest known organometallic complex, featuring ethylene strongly bound to a platinum salt. Many derivatives are known, but none involving dinitrogen, and indeed dinitrogen complexes are unknown for both platinum and palladium. Electrospray ionization mass spectrometry of K₂[PtCl₄] solutions generate strong ions corresponding to [PtCl₃(N₂)]⁻, the identity of which was confirmed through ion-mobility spectrometry and MS/MS experiments that proved it to be distinct from its isobaric counterparts [PtCl₃(C₂H₄)]⁻ and [PtCl₃(CO)]⁻. Computational analysis established a gas-phase platinum–dinitrogen bond strength of 116 kJ mol⁻¹, substantially weaker than the ethylene and carbon monoxide analogues but stronger than for polar solvents such as water, methanol and dimethylformamide, and strong enough that the calculated N−N bond length of 1.119 Å represents weakening to a degree typical of isolated dinitrogen complexes.     

Hidden Markov models revealing the stress field underlying the earthquake generation

The application of the hidden Markov models (HMMs) is attempted for revealing key features for the earthquake generation which are not accessible to direct observation. Considering that the states of the HMM correspond to levels of the stress field, our objective is to identify these states. The observations are considered after grouping earthquake magnitudes and the cases of different number of states are examined. The problems of HMMs theory are solved and the ensuing HMMs are compared on the basis of Akaike and Bayesian information criteria. A new insight on the evaluation of future seismic hazard is given by calculating the mean number of steps for the first visit to a particular state, along with the respective variance. We further calculate an estimator of the mean number of steps for the first visit to a particular state and we construct its confidence interval. Additionally, a second approach to the problem is followed by assuming a different determination of observations. The HMMs applied to both approaches, contribute significantly to seismic hazard assessment via revealing the number of the stress levels as well as the way in which these levels are associated with certain earthquake occurrence.     

Phase modulation and ellipticity of the light transmitted through a smectic C* layer with short helix pitch

A chiral ferroelectric smectic C* liquid crystal (FLC) with the helix pitch p ₀?=?330 nm was developed to avoid any scattering of visible light when the helix is not unwound over a certain limit. Planar cells with different FLC layer thickness (16 and 44 μm) have been assembled with helix axis parallel to the glass plates and aligned along the rubbing direction. The ellipticity of the light passing through the cells vs. the electric field was investigated, and a method for evaluating the electrically controlled birefringence via ellipticity measurements has been established. We have found that the FLC cell is an optical retardation layer driven by the electric field, the effective birefringence being proportional to the square electric field. The physical origin of the electrically controlled phase shift of the light passing through the FLC layer has been analysed.