Velocity resolved - scalar modeled simulations of high Schmidt number turbulent transport

The objective of this thesis is to develop a framework to conduct velocity resolved - scalar modeled (VR-SM) simulations, which will enable accurate simulations at higher Reynolds and Schmidt (Sc) numbers than are currently feasible. The framework established will serve as a first step to enable future simulation studies for practical applications. To achieve this goal, in-depth analyses of the physical, numerical, and modeling aspects related to Sc>>1 are presented, specifically when modeling in the viscous-convective subrange. Transport characteristics are scrutinized by examining scalar-velocity Fourier mode interactions in Direct Numerical Simulation (DNS) datasets and suggest that scalar modes in the viscous-convective subrange do not directly affect large-scale transport for high Sc. Further observations confirm that discretization errors inherent in numerical schemes can be sufficiently large to wipe out any meaningful contribution from subfilter models. This provides strong incentive to develop more effective numerical schemes to support high Sc simulations. To lower numerical dissipation while maintaining physically and mathematically appropriate scalar bounds during the convection step, a novel method of enforcing bounds is formulated, specifically for use with cubic Hermite polynomials. Boundedness of the scalar being transported is effected by applying derivative limiting techniques, and physically plausible single sub-cell extrema are allowed to exist to help minimize numerical dissipation. The proposed bounding algorithm results in significant performance gain in DNS of turbulent mixing layers and of homogeneous isotropic turbulence. Next, the combined physical/mathematical behavior of the subfilter scalar-flux vector is analyzed in homogeneous isotropic turbulence, by examining vector orientation in the strain-rate eigenframe. The results indicate no discernible dependence on the modeled scalar field, and lead to the identification of the tensor-diffusivity model as a good representation of the subfilter flux. Velocity resolved - scalar modeled simulations of homogeneous isotropic turbulence are conducted to confirm the behavior theorized in these a priori analyses, and suggest that the tensor-diffusivity model is ideal for use in the viscous-convective subrange. Simulations of a turbulent mixing layer are also discussed, with the partial objective of analyzing Schmidt number dependence of a variety of scalar statistics. Large-scale statistics are confirmed to be relatively independent of the Schmidt number for Sc>>1, which is explained by the dominance of subfilter dissipation over resolved molecular dissipation in the simulations. Overall, the VR-SM framework presented is quite effective in predicting large-scale transport characteristics of high Schmidt number scalars, however, it is determined that prediction of subfilter quantities would entail additional modeling intended specifically for this purpose. The VR-SM simulations presented in this thesis provide us with the opportunity to overlap with experimental studies, while at the same time creating an assortment of baseline datasets for future validation of LES models, thereby satisfying the objectives outlined for this work.

Part I. Efforts directed towards the total synthesis of shionone. Part II. Conversion of estrone to androst-4-EN-3-ONE: a new method for activating the C-9 and C-10 positions of estrogenic steroids for substitution

Part I: An approach to the total synthesis of the triterpene shionone is described, which proceeds through the tetracyclic ketone i. The shionone side chain has been attached to this key intermediate in 5 steps, affording the olefin 2 in 29% yield. A method for the stereo-specific introduction of the angular methyl group at C-5 of shionone has been developed on a model system. The attempted utilization of this method to convert olefin 2 into shionone is described.

Part II: A method has been developed for activating the C-9 and C-10 positions of estrogenic steroids for substitution. Estrone has been converted to 4β,5β-epoxy-10β-hydroxyestr-3-one; cleavage of this epoxyketone using an Eschenmoser procedure, and subsequent modification of the product afforded 4-seco-9-estren-3,5-dione 3-ethylene acetal. This versatile intermediate, suitable for substitution at the 9 and/or 10 position, was converted to androst-4-ene-3-one by known procedures.

Trimethylsilyl anions: stereospecific deoxygenation of epoxides and trimethylsilyldehalogenation of aryl halides

I. Trimethylsilylpotassium reacts with epoxides to give olefins with inversion of stereochemistry. The reaction appears to proceed via the potassium β-silyl alkoxide (2) formed from the S_N2 attack of the silyl anion on the epoxide. Subsequent stereospecific synelimination of 2 affords the olefin of inverted stereo-chemistry. The reaction is convenient and preparatively useful.

The byproduct of the reaction, potassium trimethylsilanolate (17), effectively cleaves hexamethyldisilane to yield trimethylsilylpotassium. Since the latter reagent is generated and reacted in situ with epoxides, the overall reaction can be carried out with less than one equivalent of potassium methoxide.

II. The reaction of aryl halides with trimethylsilyl anions in HMPT provides good yields of aryltrimethylsilanes, useful synthetic intermediates. The choice of metal cation is unimportant. Chlorides and bromides give high yields of silylated products, while iodides give lower yields, with correspondingly increased amounts of reduced products. Arylammonium and arylphosphonium salts also undergo the reaction.

We have permissive evidence for the reaction proceeding via both aryl radical and aryl anion intermediates.

III. Trimethylsilyl and trimethylstannyl methoxycarbene complexes of chromium and tungsten have been prepared. One of these, (CO)_5WC(OMe)SnMe_3, reacts with norbornene at 80° to afford a new olefin polymer. Efforts to effect the alpha-elimination of the nonmetallic carbene ligands have not yet been successful. Reactions of these carbene complexes with acetone have been investigated.

The structure specificity of alpha-chymotrypsin. I. Polypeptides as substrates. II. N-acylated peptide esters as substrates. III. Some reactive esters of N-acylated amino acids as substrates

The structural specificity of α-chymotrypsin for polypeptides and denatured proteins has been examined. The primary specificity of the enzyme for these natural substrates is shown to closely correspond to that observed for model substrates. A pattern of secondary specificity is proposed.

A series of N-acetylated peptide esters of varying length have been evaluated as substrates of α-chymotrypsin. The results are interpreted in terms of proposed specificity theories.

The α-chymotrypsin-catalyzed hydrolyses of a number of N-acetylated dipeptide methyl esters were studied. The results are interpreted in terms of the available specificity theories and are compared with results obtained in the study of polypeptide substrates. The importance of non-productive binding in determining the kinetic parameters of these substrates is discussed. A partial model of the locus of the active site which interacts with the R’₁CONH- group of a substrate of the form R’₁CONHCHR₂COR’₃ is proposed.

Finally, some reactive esters of N-acetylated amino acids have been evaluated as substrates of α-chymotrypsin. Their reactivity and stereo-chemical behavior are discussed in terms of the specificity theories available. The importance of a binding interaction between the carboxyl function of the substrate and the enzyme is suggested by the results obtained.

Photoproduction of charged pion pairs from hydrogen at energies up to 1500 MeV

Charged pion pair photoproduction has been investigated up to a gamma energy of 1500 MeV, using the Caltech 12-inch heavy liquid bubble chamber with a small diameter, high intensity photon beam passing through a central beam tube gaseous hydrogen target surrounded by the sensitive Freon. Scanning, analysis, and data reduction techniques have been developed to deal with the problems of two-vie stereo, hidden event origins, absence of magnetic field, and the range-energy and multiple scattering relationships that occur in the heavy materials. Roughly 5700 pictures have been scanned and analyzed, yielding 754 acceptable events. Cross section and parameter distributions are generally consistent with the results of previous experiments. A statistically insignificant “bump” was observed in the dipion mass spectrum in the region of 500 MeV, the disputed σ meson mass. This region was investigated as carefully as the limited statistics would allow; dipion angular distributions are consistent with isotropy, and there is indication that some of the events in this region might come from decay of an intermediate N*₁₁ (1425) into a proton and dipion.

Photographic materials on pp. 18, 20, 22, and 24 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

The structure elucidation of a proposed intermediate in the stereoselective synthesis of dl-desoxypodocarpic acid

The hydroxyketone C-3, an intermediate in the stereo-selective total synthesis of dl-Desoxypodocarpic acid (ii), has been shown by both degradative and synthetic pathways to rearrange in the presence of base to diosphenol E-1 (5-isoabietic acid series). The exact spatial arrangements of the systems represented by formulas C-3 and E-1 have been investigated (as the p-bromobenzoates) by single-crystal X-ray diffraction analyses. The hydroxyketone F-1, the proposed intermediate in the rearrangement, has been synthesized. Its conversion to diosphenol E-1 has been studied, and a single-crystal analysis of the p-bromobenzoate derivative has been performed. The initially desired diosphenol C-6 has been prepared, and has been shown to be stable to the potassium t-butoxide rearrangement conditions. Oxidative cleavage of diosphenol E-1 and subsequent cyclization with the aid of polyphosphoric acid has been shown to lead to keto acid I-2 (benzobicyclo [3.3.1] nonane series) rather than keto acid H-2 (5-isoabietic acid series).

The interaction of color and luminance in stereoscopic vision

Experiments are described using the random dot stereo patterns devised by Julesz, but substituting various colors and luminances for the usual black and white random squares. The ability to perceive the patterns in depth depends on a luminance difference between the colors used. If two colors are the same luminance, then depth is not perceived although each of the individual squares which make up the patterns is easily seen due to the color difference. This is true for any combination of different colors. If different colors are used for corresponding random squares between the left and right eye patterns, stereopsis is possible for all combinations of binocular rivalry in color, provided the luminance difference is large enough. Rivalry in luminance always precludes stereopsis, regardless of the colors involved.