Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.     

Mono-cyclopentadienyl complexes of lanthanum: synthesis and characterization of anilido derivatives

Use of the bulky cyclopentadienyl ligand [η⁵-C₅H₂(SiMe₃)₃-1,2,4]⁻ (Cp?) allows for the isolation of monomeric, mono-ring lanthanide species. As previously reported, (Cp?)K reacts with LaI₃(THF)₄ (THF=tetrahydrofuran) in THF/pyridine to form the mono-ring complex (Cp?)LaI₂(py)₃ (1) (py=pyridine); a minor product of this reaction is the bis-ring species (Cp?)₂LaI(py) (2). The solid state structure of 2 reveals a monomeric compound containing a pseudo-tetrahedral metal center exhibiting no unusual intramolecular contacts. Addition of one equiv of KNHAr (Ar=2,6-ⁱPr₂C₆H₃) to complex 1 in THF generates the mono-anilido compound (Cp?)LaI(NHAr)(THF)₂ (3), which may be converted to the more stable pyridine adduct (Cp?)LaI(NHAr)(py)₂ (4) by the addition of pyridine to 3. An X-ray crystal structure of 3 indicated a trigonal bipyramidal metal center with the anilido group oriented trans to the iodide atom (N1-La1-I1=123.1(3)°). A structural study on the bis-pyridine adduct 4 revealed a similar C_s-symmetric structure with a slightly increased N_anilido-La-I angle of 132.1(2)°. Addition of KNHAr to the di-iodo bipyridine adduct (Cp?)LaI₂(bipy)(py) (5), in which the two iodide atoms are cis-disposed, yields the mono-anilido complex (Cp?)LaI(NHAr)(bipy)(py) (6) (bipy=2,2^′-bipyridine); this compound may also be prepared by the addition of bipy to (Cp?)LaI(NHAr)(py)₂ (4). An X-ray diffraction study shows that the lanthanum center in 6 is octahedrally coordinated by a Cp? ring, an iodide, an anilido group, a pyridine molecule and two nitrogens of a bipy molecule. In this case, the anilido moiety and the iodide ligand are arranged in a cis fashion (N_anilido-La-I=111.2(2)°), resulting in a complex with C₁ symmetry. Both (Cp?)LaI(NHAr)(py)₂ (4) and (Cp?)LaI(NHAr)(bipy)(py) (6) are inactive as catalysts for the hydroamination/cyclization of 2-amino-hex-5-ene.     

New synthetic pathways into dithiazolyl radicals: Preparation and characterisation of 3′-methyl-benzo-1,3,2-dithiazolyl, M’BDTA

A general three-step synthesis to a range of benzo-fused-1,3,2-dithiazolylium salts bearing both electron-withdrawing (CN) and electron-donating (Me) groups is described. This methodology has also been extended to pyridyl derivatives and offers a potential route to a diversity of 1,3,2-dithiazolylium rings and their corresponding 1,3,2-dithiazolyl free radicals. The key steps in the reaction are treatment of a substituted 1,2,-dichlorobenzene with two equivalents of [^tBuS]Na, followed by chlorination to yield the corresponding bis(sulfenyl chloride). Subsequent ring closure with Me₃SiN₃ yields the target 1,3,2-dithiazolylium ring system in good yield. The preparation and crystal structures of 3′-methyl-benzo-1,3,2-dithiazolylium chloride and 3′-methyl-benzo-1,3,2-dithiazolyl are described and the electronic properties of the radical examined through EPR spectroscopy, DFT calculations and variable temperature magnetic susceptibility measurements.     

Preparative isolation of (+)-beta-eudesmol fromAmyris balsamifera

Summary Optically pure (+)-beta-eudesmol is a possible starting material for the synthesis of several termite defense compounds. A two step procedure for the isolation of gram quantities of (+)-beta-eudesmol from commercially availableAmyris balsamifera oil (syn. West Indian sandalwood oil), containing 8% beta-eudesmol, was developed. Step one consisted of an efficient vacuum distillation of the total oil. Step two was a medium pressure LC separation with an AgNO₃ impregnated silica gel stationary phase. Several other separation procedures failed due to the presence of many closely related sesquiterpene alcohols (75% of the oil).     

The design and synthesis of porphyrin/oligiothiophene hybrid monomers

In an effort to build effective photovoltaic cells based on porphyrin-functionalised polythiophenes we have focused on synthetic routes to three monomer types. By controlling the geometric structure of the monomer, oxidation of these materials should produce polymers with different architectural structures, and as a result, different opto-electronic properties. Employing Wittig protocols allowed access to monomers in which the porphyrin moiety is connected to the beta-position of the thiophene via an alkene linkage. In addition, monomers were constructed using porphyrin condensation methods to afford alpha-thiophene meso-substituted porphryins. Another set of monomers was also prepared via porphyrin condensation routes, but instead utilising beta-formylthiophenes. By utilising different formyloligothiophenes we were able to generate a series of monomers that can be used to control the loading of the porphyrin in the polythiophene matrix.     

Comparison of simulations and data from a seismo-acoustic tank experiment

A tank experiment was carried out to investigate underwater sound propagation over an elastic bottom in flat and sloping configurations. The purpose of the experiment was to evaluate range-dependent propagation models with high-quality experimental data. The sea floor was modeled as an elastic medium by a polyvinyl chloride slab. The relatively high rigidity of the slab requires accounting for shear waves in this environment. Acoustic measurements were obtained along virtual arrays in the water column using a robotic apparatus. Elastic parabolic equation solutions are in excellent agreement with data.     

Generation of (nonafluoro-tert-butoxy)methyl ponytails for enhanced fluorous partition of aromatics and heterocycles

The reaction of sodium perfluoro-tert-butoxide with benzylic carbon-bromide bond(s) leads to the formation of (nonafluoro-tert-butoxy)methyl ponytail(s), which can enhance the fluorous solubility and partition of aromatics and heterocycles.     

Atom-Transfer Cyclization with CuSO(4)/KBH(4): A Formal "Activators Generated by Electron Transfer" Process Also Applicable to Atom-Transfer Polymerization

The 4-exo and 5-exo-trig atom-transfer cyclizations of 1, 8a-e, 9, 12, and 13 can be mediated with as little as 0.05 mol % of Cu(TPMA)SO(4)·5H(2)O in the presence of 2.5 mol % of borohydride salts in 10 min at room temperature in air. This formal "activators generated by electron transfer" (AGET) procedure utilizes a cheap and oxidatively stable copper source (CuSO(4)·5H(2)O) and can be carried out in environmentally benign solvents (EtOH). It is possible to alter the product distribution in the 5-endo radical-polar crossover reactions of 10a,b and 11 by tailoring the amount of borohydride. Cyclization onto alkynes 14 and 15 is also possible in only 20 min. Controlled radical polymerization of styrene, with increased rates over conventional atom-transfer radical polymerization (ATRP), can be carried out in a controlled fashion (Mn, PDI) using either CuBr or CuSO(4)·5H(2)O and Bu(4)NBH(4).     

A modular procedure for the synthesis of functionalised β-substituted terthiophene monomers for conducting polymer applications

An efficient modular strategy has been developed for the synthesis of β-functionalised terthiophene monomers using Suzuki-Miyaura and Wittig/Horner-Emmons chemistries. This paper discusses the problems encountered with converting the β-terthiophene aldehyde building block to the β-terthiophene phosphonium salt and the use of this material in a Wittig condensation. An improved strategy using the β-terthiophene phosphonate building block constructed via Suzuki-Miyaura coupling protocols was developed. We have synthesised and characterised a broad range of functionalised terthiophene materials that have been designed for specific end-use applications. The availability of these building blocks has dramatically increased access to a range of key monomers.