The abundances of ultraheavy elements in the cosmic radiation

Analysis of the data from the Heavy Nuclei Experiment on the HEAO-3 spacecraft has yielded the cosmic ray abundances of odd-even element pairs with atomic number, Z, in the range 33 ≤ Z ≤60, and the abundances of broad element groups in the range 62 ≤ Z ≤83, relative to iron. These data show that the cosmic ray source composition in this charge range is quite similar to that of the solar system provided an allowance is made for a source fractionation based on first ionization potential. The observations are inconsistent with a source composition which is dominated by either r-process or s-process material, whether or not an allowance is made for first ionization potential. Although the observations do not exclude a source containing the same mixture of r- and s-process material as in the solar system. the data are best fit by a source having an r- to s-process ratio of 1.22^(+0.25)_(0.21), relative to the solar system The abundances of secondary elements are consistent with the leaky box model of galactic propagation, implying a pathlength distribution similar to that which explains the abundances of nuclei with Z<29.

The energy spectra of the even elements in the range 38 ≤ Z ≤ 60 are found to have a deficiency of particles in the range ~1.5 to 3 GeV/amu, compared to iron. This deficiency may result from ionization energy loss in the interstellar medium, and is not predicted by propagation models which ignore such losses. ln addition, the energy spectra of secondary elements are found to be different to those of the primary elements. Such effects are consistent with observations of lighter nuclei, and are in qualitative agreement with galactic propagation models using a rigidity dependent escape length. The energy spectra of secondaries arising from the platinum group are found to be much steeper than those of lower Z. This effect may result from energy dependent fragmentation cross sections.

Equilibration of a liquid droplet-vapor-gas mixture downstream of a shock wave

The equations of motion for the flow of a mixture of liquid droplets, their vapor, and an inert gas through a normal shock wave are derived. A set of equations is obtained which is solved numerically for the equilibrium conditions far downstream of the shock. The equations describing the process of reaching equilibrium are also obtained. This is a set of first-order nonlinear differential equations and must also be solved numerically. The detailed equilibration process is obtained for several cases and the results are discussed.

I. The attenuation and dispersion of sound in a condensing medium. II. The flow of a gas-particle mixture downstream of a normal shock in a nozzle

I. The attenuation of sound due to particles suspended in a gas was first calculated by Sewell and later by Epstein in their classical works on the propagation of sound in a two-phase medium. In their work, and in more recent works which include calculations of sound dispersion, the calculations were made for systems in which there was no mass transfer between the two phases. In the present work, mass transfer between phases is included in the calculations.

The attenuation and dispersion of sound in a two-phase condensing medium are calculated as functions of frequency. The medium in which the sound propagates consists of a gaseous phase, a mixture of inert gas and condensable vapor, which contains condensable liquid droplets. The droplets, which interact with the gaseous phase through the interchange of momentum, energy, and mass (through evaporation and condensation), are treated from the continuum viewpoint. Limiting cases, for flow either frozen or in equilibrium with respect to the various exchange processes, help demonstrate the effects of mass transfer between phases. Included in the calculation is the effect of thermal relaxation within droplets. Pressure relaxation between the two phases is examined, but is not included as a contributing factor because it is of interest only at much higher frequencies than the other relaxation processes. The results for a system typical of sodium droplets in sodium vapor are compared to calculations in which there is no mass exchange between phases. It is found that the maximum attenuation is about 25 per cent greater and occurs at about one-half the frequency for the case which includes mass transfer, and that the dispersion at low frequencies is about 35 per cent greater. Results for different values of latent heat are compared.

II. In the flow of a gas-particle mixture through a nozzle, a normal shock may exist in the diverging section of the nozzle. In Marble’s calculation for a shock in a constant area duct, the shock was described as a usual gas-dynamic shock followed by a relaxation zone in which the gas and particles return to equilibrium. The thickness of this zone, which is the total shock thickness in the gas-particle mixture, is of the order of the relaxation distance for a particle in the gas. In a nozzle, the area may change significantly over this relaxation zone so that the solution for a constant area duct is no longer adequate to describe the flow. In the present work, an asymptotic solution, which accounts for the area change, is obtained for the flow of a gas-particle mixture downstream of the shock in a nozzle, under the assumption of small slip between the particles and gas. This amounts to the assumption that the shock thickness is small compared with the length of the nozzle. The shock solution, valid in the region near the shock, is matched to the well known small-slip solution, which is valid in the flow downstream of the shock, to obtain a composite solution valid for the entire flow region. The solution is applied to a conical nozzle. A discussion of methods of finding the location of a shock in a nozzle is included.

Optimization and Control of Power Flow in Distribution Networks

Climate change is arguably the most critical issue facing our generation and the next. As we move towards a sustainable future, the grid is rapidly evolving with the integration of more and more renewable energy resources and the emergence of electric vehicles. In particular, large scale adoption of residential and commercial solar photovoltaics (PV) plants is completely changing the traditional slowly-varying unidirectional power flow nature of distribution systems. High share of intermittent renewables pose several technical challenges, including voltage and frequency control. But along with these challenges, renewable generators also bring with them millions of new DC-AC inverter controllers each year. These fast power electronic devices can provide an unprecedented opportunity to increase energy efficiency and improve power quality, if combined with well-designed inverter control algorithms. The main goal of this dissertation is to develop scalable power flow optimization and control methods that achieve system-wide efficiency, reliability, and robustness for power distribution networks of future with high penetration of distributed inverter-based renewable generators.

Proposed solutions to power flow control problems in the literature range from fully centralized to fully local ones. In this thesis, we will focus on the two ends of this spectrum. In the first half of this thesis (chapters 2 and 3), we seek optimal solutions to voltage control problems provided a centralized architecture with complete information. These solutions are particularly important for better understanding the overall system behavior and can serve as a benchmark to compare the performance of other control methods against. To this end, we first propose a branch flow model (BFM) for the analysis and optimization of radial and meshed networks. This model leads to a new approach to solve optimal power flow (OPF) problems using a two step relaxation procedure, which has proven to be both reliable and computationally efficient in dealing with the non-convexity of power flow equations in radial and weakly-meshed distribution networks. We will then apply the results to fast time- scale inverter var control problem and evaluate the performance on real-world circuits in Southern California Edison’s service territory.

The second half (chapters 4 and 5), however, is dedicated to study local control approaches, as they are the only options available for immediate implementation on today’s distribution networks that lack sufficient monitoring and communication infrastructure. In particular, we will follow a reverse and forward engineering approach to study the recently proposed piecewise linear volt/var control curves. It is the aim of this dissertation to tackle some key problems in these two areas and contribute by providing rigorous theoretical basis for future work.

Part I. Coenzyme B12 as a hydroformylation-type catalyst. Part II. Mechanisms of hydrogen transfer in the methylmalonyl coenzyme a mutase reaction

Part I

The mechanism of the hydroformylation reaction was studied. Using cobalt deuterotetracarbonyl and 1-pentene as substrates, the first step in the reaction, addition of cobalt tetracarbonyl to an olefin, was shown to be reversible.

Part II

The role of coenzyme B₁₂ in the isomerization of methylmalonyl coenzyme A to succinyl coenzyme A by methylmalonyl coenzyme A mutase was studied. The reaction was allowed to proceed to partial completion using a mixture of methylmalonyl coenzyme A and 4, 4, 4-tri-²H-methylmalonyl coenzyme A as substrate. The deuterium distribution in the product, succinyl coenzyme A, was shown to best fit a model in which hydrogen is transferred from C-4 of methylmalonyl coenzyme A to C-5’ of the adenosyl moiety of coenzyme B₁₂ in the rate determining step. The three hydrogens at the 5’-adenosyl position of the coenzyme B₁₂ intermediate are then able to become enzymatically equivalent before hydrogen is transferred from the coenzyme B₁₂ intermediate to form succinyl coenzyme A.

The organometallic chemistry of the Ru(001) surface

The organometallic chemistry of the hexagonally close-packed Ru(001) surface has been studied using electron energy loss spectroscopy and thermal desorption mass spectrometry. The molecules that have been studied are acetylene, formamide and ammonia. The chemistry of acetylene and formamide has also been investigated in the presence of coadsorbed hydrogen and oxygen adatoms.

Acetylene is adsorbed molecularly on Ru(001) below approximately 230 K, with rehybridization of the molecule to nearly sp^3 occurring. The principal decomposition products at higher temperatures are ethylidyne (CCH_3) and acetylide (CCH) between 230 and 350 K, and methylidyne (CH) and surface carbon at higher temperatures. Some methylidyne is stable to approximately 700 K. The preadsorption of hydrogen does not alter the decomposition products of acetylene, but reduces the saturation coverage and also leads to the formation of a small amount of ethylene (via an η^2-CHCH_2 species) which desorbs molecularly near 175 K. Preadsorbed oxygen also reduces the saturation coverage of acetylene but has virtually no effect on the nature of the molecularly chemisorbed acetylene. It does, however, lead to the formation of an sp^2-hybridized vinylidene (CCH_2) species in the decomposition of acetylene, in addition to the decomposition products that are formed on the clean surface. There is no molecular desorption of chemisorbed acetylene from clean Ru(001), hydrogen-presaturated Ru(001), or oxygen-presaturated Ru(001).

The adsorption and decomposition of formamide has been studied on clean Ru(001), hydrogen-presaturated Ru(001), and Ru(001)-p(1x2)-O (oxygen adatom coverage = 0.5). On clean Ru(001), the adsorption of low coverages of formamide at 80 K results in CH bond cleavage and rehybridization of the carbonyl double bond to produce an η^2 (C,O)-NH_2CO species. This species is stable to approximately 250 K at which point it decomposes to yield a mixture of coadsorbed carbon monoxide, ammonia, an NH species and hydrogen adatoms. The decomposition of NH to hydrogen and nitrogen adatoms occurs between 350 and 400 K, and the thermal desorption products are NH_3 (-315 K), H_2 (-420 K), CO (-480 K) and N_2 (-770 K). At higher formamide coverages, some formamide is adsorbed molecularly at 80 K, leading both to molecular desorption and to the formation of a new surface intermediate between 300 and 375 K that is identified tentatively as η^1(N)-NCHO. On Ru(001)- p(1x2)-O and hydrogen-presaturated Ru(001), formamide adsorbs molecularly at 80 K in an η^1(O)- NH_2CHO configuration. On the oxygen-precovered surface, the molecularly adsorbed formamide undergoes competing desorption and decomposition, resulting in the formation of an η^2(N,O)-NHCHO species (analogous to a bidentate formate) at approximately 265 K. This species decomposes near 420 K with the evolution of CO and H_2 into the gas phase. On the hydrogen precovered surface, the Η^1(O)-NH_2CHO converts below 200 K to η^2(C,O)-NH_2CHO and η^2(C,O)-NH^2CO, with some molecular desorption occurring also at high coverage. The η^2(C,O)-bonded species decompose in a manner similar to the decomposition of η^2(C,O)-NH_2CO on the clean surface, although the formation of ammonia is not detected.

Ammonia adsorbs reversibly on Ru(001) at 80 K, with negligible dissociation occurring as the surface is annealed The EEL spectra of ammonia on Ru(001) are very similar to those of ammonia on other metal surfaces. Off-specular EEL spectra of chemisorbed ammonia allow the v(Ru-NH_3) and ρ(NH_3) vibrational loss features to be resolved near 340 and 625 cm^(-1), respectively. The intense δ_g (NH_3) loss feature shifts downward in frequency with increasing ammonia coverage, from approximately 1160 cm^(-1) in the low coverage limit to 1070 cm^(-1) at saturation. In coordination compounds of ammonia, the frequency of this mode shifts downward with decreasing charge on the metal atom, and its downshift on Ru(001) can be correlated with the large work function decrease that the surface has previously been shown to undergo when ammonia is adsorbed. The EELS data are consistent with ammonia adsorption in on-top sites. Second-layer and multilayer ammonia on Ru(001) have also been characterized vibrationally, and the results are similar to those obtained for other metal surfaces.

2,4-dimethylene-1,3-cyclobutanediyl and 2,4-dimethylenebicyclobutane. Synthesis, spectroscopy, and reactivity of a triplet biradical and its covalent isomer

The preparation and direct observation of triplet 2,4-dimethylene-1,3- cyclobutanediyl (1), the non-Kekule isomer of benzene, is described. The biradical was generated by photolysis of 5,6-dimethylene-2,3- diazabicyclo[2.1.1]hex-2-ene (2) (which was synthesized in several steps from benzvalene) under cryogenic, matrix-isolation conditions. Biradical 1 was characterized by EPR spectroscopy (‌‌‌‌‌│D/hc│ =0.0204 cm^(-1), │E/hc│ =0.0028 cm^(-1)) and found to have a triplet ground state. The Δm_s= 2 transition displays hyperfine splitting attributed to a 7.3-G coupling to the ring methine and a 5.9-G coupling to the exocyclic methylene protons. Several experiments, including application of the magnetophotoselection (mps) technique in the generation of biradical 1, have allowed a determination of the zero-field triplet sublevels as x = -0.0040, y = +0.0136, and z = -0.0096 cm^(-1), where x and y are respectively the long and short in-plane axes and z the out-of-plane axis of 1.

Triplet 1 is yellow-orange and displays highly structured absorption (λ_(max)= 506 nm) and fluorescence (λ_(max) = 510 nm) spectra, with vibronic spacings of 1520 and 620 cm^(-1) for absorption and 1570 and 620 cm^(-1) for emission. The spectra were unequivocally assigned to triplet 1 by the use of a novel technique that takes advantage of the biradical's photolability. The absorption є = 7200 M^(-1) cm^(-1) and f = 0.022, establishing that the transition is spin-allowed. Further use of the mps technique has demonstrated that the transition is x-polarized, and the excited state 1s therefore of B_(1g) symmetry, in accord with theoretical predictions.

Thermolysis or direct photolysis of diazene 2 in fluid solution produces 2,4- dimethylenebicyclo[l.l.0]butane (3), whose ^(l)H NMR spectrum (-80°C, CD_(2)Cl_(2)) consists of singlets at δ 4.22 and 3.18 in a 2:1 ratio. Compound 3 is thermally unstable and dimerizes with second-order kinetics between -80 and -25°C (∆H^(‡) = 6.8 kcal mol^(-1), (∆s^(‡) = -28 eu) by a mechanism involving direct combination of two molecules of 3 in the rate-determining step. This singlet-manifold reaction ultimately produces a mixture of two dimers, 3,8,9- trimethylenetricyclo[5.1.1.0^(2,5)]non-4-ene (75) and trans-3,10-dimethylenetricyclo[6.2.0.0^(2,5)]deca-4,8-diene (76t), with the former predominating. In contrast, triplet-sensitized photolysis of 2, which leads to triplet 1, provides, in addition to 75 and 76t, a substantial amount of trans-5,10- dimethylenetricyclo[6.2.0.0^(3,6)]deca-3,8-diene (77t) and small amounts of two unidentified dimers.

In addition, triplet biradical 1 ring-closes to 3 in rigid media both thermally (77-140 K) and photochemically. In solution 3 forms triplet 1 upon energy transfer from sensitizers having relatively low triplet energies. The implications of the thermal chemistry for the energy surfaces of the system are discussed.

Synthetic, structural and mechanistic studies of interactions of carbon, nitrogen, and oxygen nucleophiles with bis-pentamethylcyclopentadienyl zirconium and hafnium derivatives

The reactivity of permethylzirconocene and permethylhafnocene complexes with various nucleophiles has been investigated. Permethylzirconocene reacts with sterically hindered ketenes and allenes to afford metallacycle products. Reaction of these cummulenes with permethylzirconocene hydride complexes affords enolate and σ-allyl species, respectively. Reactions which afford enolate products are nonstereospecific, whereas reactions which afford allyl products initially give a cis-σ-allyl complex which rearranges to its trans isomer. The mechanism of these reactions is proposed to occur either by a Lewis Acid-Lewis Base interaction (ketenes) or by formation of a π-olefin intermediate (allenes).

Permethylzirconocene haloacyl complexes react with strong bases such as lithium diisopropylamide or methylene trimethylphosphorane to afford ketene compounds. Depending on the size of the alkyl ketene substituent, the hydrogenation of these compounds affords enolate-hydride products with varying degrees of stereoselectivity. The larger the substituent, the greater is the selectivity for cis hydrogenation products.

The reaction of permethylzirconocene dihydride and permethylhafnocene dihydride with methylene trimethylphosphorane affords methyl-hydride and dimethyl derivatives. Under appropriate conditions, the metallated-ylide complex 1, (η^5-C_5(CH_3)_5)_2 Zr(H)CH_2PMe_2CH_2, is also obtained and has been structurally characterized by X-ray diffraction techniques. Reaction of 1 with CO affords (η^5-C_5(CH_3)_5)_2 Zr(C,O-η^2 -(PMe_3)HC=CO)H which exists in solution as an equilibrium mixture of isomers. In one isomer (2), the η^2-acyl oxygen atom occupies a lateral equatorial coordination position about zirconium, whereas in the other isomer (3), the η-acyl oxygen atom occupies the central equatorial position. The equilibrium kinetics of the 2→3 isomerization have been studied and the structures of both complexes confirmed by X-ray diffraction methods. These studies suggest a mechanism for CO insertion into metal-carbon bonds of the early transition metals.

Permethylhafnocene dihydride and permethylzirconocene hydride complexes react with diazoalkanes to afford η^2-N, N' -hydrazonido species in which the terminal nitrogen atom of the diazoalkane molecule has inserted into a metal-hydride or metal-carbon bond. The structure of one of these compounds, Cp*_2Zr(NMeNCTol_2)OH, has been determined by X-ray diffraction techniques. Under appropriate conditions, the hydrazonido-hydride complexes react with a second equivalent of diazoalkene to afford η' -N-hydrazonido-η^2-N, N' -hydrazonido species.

Latent variable models for neural data analysis

The brain is perhaps the most complex system to have ever been subjected to rigorous scientific investigation. The scale is staggering: over 10^11 neurons, each making an average of 10^3 synapses, with computation occurring on scales ranging from a single dendritic spine, to an entire cortical area. Slowly, we are beginning to acquire experimental tools that can gather the massive amounts of data needed to characterize this system. However, to understand and interpret these data will also require substantial strides in inferential and statistical techniques. This dissertation attempts to meet this need, extending and applying the modern tools of latent variable modeling to problems in neural data analysis.

It is divided into two parts. The first begins with an exposition of the general techniques of latent variable modeling. A new, extremely general, optimization algorithm is proposed - called Relaxation Expectation Maximization (REM) - that may be used to learn the optimal parameter values of arbitrary latent variable models. This algorithm appears to alleviate the common problem of convergence to local, sub-optimal, likelihood maxima. REM leads to a natural framework for model size selection; in combination with standard model selection techniques the quality of fits may be further improved, while the appropriate model size is automatically and efficiently determined. Next, a new latent variable model, the mixture of sparse hidden Markov models, is introduced, and approximate inference and learning algorithms are derived for it. This model is applied in the second part of the thesis.

The second part brings the technology of part I to bear on two important problems in experimental neuroscience. The first is known as spike sorting; this is the problem of separating the spikes from different neurons embedded within an extracellular recording. The dissertation offers the first thorough statistical analysis of this problem, which then yields the first powerful probabilistic solution. The second problem addressed is that of characterizing the distribution of spike trains recorded from the same neuron under identical experimental conditions. A latent variable model is proposed. Inference and learning in this model leads to new principled algorithms for smoothing and clustering of spike data.

Liquid silicate equation of state : using shock waves to understand the properties of the deep Earth

The equations of state (EOS) of several geologically important silicate liquids have been constrained via preheated shock wave techniques. Results on molten Fe₂SiO₄ (fayalite), Mg₂SiO₄ (forsterite), CaFeSi₂O₆ (hedenbergite), an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆ (anorthite-hedenbergite), and an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆-CaMgSi₂O₆(anorthite-hedenbergite-diopside) are presented. This work represents the first ever direct EOS measurements of an iron-bearing liquid or of a forsterite liquid at pressures relevant to the deep Earth (> 135 GPa). Additionally, revised EOS for molten CaMgSi₂O₆ (diopside), CaAl₂Si₂O₈ (anorthite), and MgSiO₃ (enstatite), which were previously determined by shock wave methods, are also presented.

The liquid EOS are incorporated into a model, which employs linear mixing of volumes to determine the density of compositionally intermediate liquids in the CaO-MgO-Al₂O₃-SiO₂-FeO major element space. Liquid volumes are calculated for temperature and pressure conditions that are currently present at the core-mantle boundary or that may have occurred during differentiation of a fully molten mantle magma ocean.

The most significant implications of our results include: (1) a magma ocean of either chondrite or peridotite composition is less dense than its first crystallizing solid, which is not conducive to the formation of a basal mantle magma ocean, (2) the ambient mantle cannot produce a partial melt and an equilibrium residue sufficiently dense to form an ultralow velocity zone mush, and (3) due to the compositional dependence of Fe2+ coordination, there is a threshold of Fe concentration (molar X_Fe ≤ 0.06) permitted in a liquid for which its density can still be approximated by linear mixing of end-member volumes.

The electrocatalytic and stoichiometric oxidation chemistry of binuclear ruthenium complexes incorporating the anionic tripod ligand {(η5-C5H5)Co[P(OCH3)2(=O)]3}-

The anionic tripod ligand NaLoMe (L_(oMe) - = [(η^5-C_5H_5)Co{P(O)(OCH_3)_2}_3]^-) reacts with RuO_4 in a biphasic reaction mixture of 1% H_2SO_4 and CCI_4 to afford [(L_(oMe) (HO)Ru^(IV) (µ-O)_2Ru ^(IV)(OH)(L_(oMe)] (1), which is treated with aqueous CF_3S0_3H to generate [(L_(oMe)(H_2O)Ru^(IV) (µ-O)_2R^(IV) (OH_2)(L_(oMe)][CF_3SO_3]_2 ([H_21][CF_3SO_3]_2). Addition of iodosobenzene to an acetonitrile solution of this salt yields [(L_(oMe)(O)Ru^v(µ-0)2Ru^v-(O)(_(LoMe)] (2). The dimer 1 can be reduced chemically or electrochemically to the Ru^(III)- Ru^(III) dimers [(L_(oMe)(H_20)Ru^(III) (µ-OH)_2Ru^(III) (OH_2)(L_(oMe)) ]^2+ and [(L_(oMe)) ^(III) (µ-0Hh(µ-0H2)Ru^(III) (L_(oMe)]^2+ which interconvert in aqueous media. Two electron processes dominate both the bulk chemistry and the electrochemistry of 1. Among these processes are the quasi-reversible Ru^(IV) - Ru^(IV)/Ru^(III)- Ru^(III) and Ru^(III)- Ru^(III)/ Ru^(II)- Ru^(II) reductions and a largely irreversible Ru^(V) - Ru^(V)/ Ru^(IV) - Ru^(IV)/oxidation. The dioxo dimer 2 oxidizes alcohols and aldehydes in organic media to afford 1 and the corresponding aldehydes and acids. Analogously, the Ru^(V) - Ru^(V)/ Ru^(IV)- Ru^(IV) redox wave mediates the electrooxidation of alcohols and aldehydes in aqueous buffer. In this system, substrates can be oxidized completely to CO_2. The kinetic behavior of these oxidations was examined by UV-vis and chronoamperometry, respectively, and the chemistry is typical of metal-oxo complexes, indicating that electronic coupling between two metal centers does not dramatically affect the metal-oxo chemistry. Dimer [H_21]^(2+) also reacts with alcohols, aldehydes, and triphenylphosphine in CH_3CN to afford Ru^(III)- Ru^(III) products including [(L_(oMe))CH_3CN) Ru^(III) (µ-OH)_2 Ru^(III) (NCCH_3)( L_(oMe))][CF_3SO_3]2 (characterized by X-ray crystallography) and the corresponding organic products. Reaction of 1 with formaldehyde in aqueous buffer quantitatively affords the triply bridged dimer [(L_(oMe)Ru^(III) (µ-OH)2- (µ-HCOO) Ru^(III) (L_(oMe)][CF_3SO_3] (characterized by X-ray crystallography). This reaction evidently proceeds by two parallel inner-sphere pathways, one of which is autocatalytic. Neither pathway exhibits a primary isotope effect suggesting the rate determining process could be the formation of an intermediate, perhaps a Ru^(IV) - Ru^(IV) formate adduct. The Ru^(III)- Ru^(III)formate adduct is easily oxidized to the Ru^(IV) - Ru^(IV) analog [(L_(oMe)Ru^(IV)(µ-OH)_2-(µ-HCOO) Ru^(IV) (L_(oMe)][CF_3SO_3], which, after isolation, reacts slowly with aqueous formaldehyde to generate free formate and the Ru^(III)- Ru^(III) formate adduct. These dimers function as catalysts for the electrooxidation of formaldehyde at low anodic potentials (+0.0 V versus SCE in aqueous buffer, pH 8.5) and enhance the activity of Nafion treated palladium/carbon heterogeneous fuel cell catalysts.

The design and synthesis of a true, heterogeneous, asymmetric catalyst

This work describes the design and synthesis of a true, heterogeneous, asymmetric catalyst. The catalyst consists of a thin film that resides on a high-surface- area hydrophilic solid and is composed of a chiral, hydrophilic organometallic complex dissolved in ethylene glycol. Reactions of prochiral organic reactants take place predominantly at the ethylene glycol-bulk organic interface.

The synthesis of this new heterogeneous catalyst is accomplished in a series of designed steps. A novel, water-soluble, tetrasulfonated 2,2'-bis (diphenylphosphino)-1,1'-binaphthyl (BINAP-4S0_3Na) is synthesized by direct sulfonation of 2,2'-bis(diphenylphosphino)-1,1'-binaphthyl (BINAP). The rhodium (I) complex of BINAP-4SO_3Na is prepared and is shown to be the first homogeneous catalyst to perform asymmetric reductions of prochiral 2-acetamidoacrylic acids in neat water with enantioselectivities as high as those obtained in non-aqueous solvents. The ruthenium (II) complex, [Ru(BINAP-4SO_3Na)(benzene)Cl]Cl is also synthesized and exhibits a broader substrate specificity as well as higher enantioselectivities for the homogeneous asymmetric reduction of prochiral 2-acylamino acid precursors in water. Aquation of the ruthenium-chloro bond in water is found to be detrimental to the enantioselectivity with some substrates. Replacement of water by ethylene glycol results in the same high e.e's as those found in neat methanol. The ruthenium complex is impregnated onto a controlled pore-size glass CPG-240 by the incipient wetness technique. Anhydrous ethylene glycol is used as the immobilizing agent in this heterogeneous catalyst, and a non-polar 1:1 mixture of chloroform and cyclohexane is employed as the organic phase.

Asymmetric reduction of 2-(6'-methoxy-2'-naphthyl)acrylic acid to the non-steroidal anti-inflammatory agent, naproxen, is accomplished with this heterogeneous catalyst at a third of the rate observed in homogeneous solution with an e.e. of 96% at a reaction temperature of 3°C and 1,400 psig of hydrogen. No leaching of the ruthenium complex into the bulk organic phase is found at a detection limit of 32 ppb. Recycling of the catalyst is possible without any loss in enantioselectivity. Long-term stability of this new heterogeneous catalyst is proven by a self-assembly test. That is, under the reaction conditions, the individual components of the present catalytic system self-assemble into the supported-catalyst configuration.

The strategies outlined here for the design and synthesis of this new heterogeneous catalyst are general, and can hopefully be applied to the development of other heterogeneous, asymmetric catalysts.

Characterizing distribution rules for cost sharing games

In noncooperative cost sharing games, individually strategic agents choose resources based on how the welfare (cost or revenue) generated at each resource (which depends on the set of agents that choose the resource) is distributed. The focus is on finding distribution rules that lead to stable allocations, which is formalized by the concept of Nash equilibrium, e.g., Shapley value (budget-balanced) and marginal contribution (not budget-balanced) rules.

Recent work that seeks to characterize the space of all such rules shows that the only budget-balanced distribution rules that guarantee equilibrium existence in all welfare sharing games are generalized weighted Shapley values (GWSVs), by exhibiting a specific 'worst-case' welfare function which requires that GWSV rules be used. Our work provides an exact characterization of the space of distribution rules (not necessarily budget-balanced) for any specific local welfare functions remains, for a general class of scalable and separable games with well-known applications, e.g., facility location, routing, network formation, and coverage games.

We show that all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to GWSV rules on some 'ground' welfare functions. Therefore, it is neither the existence of some worst-case welfare function, nor the restriction of budget-balance, which limits the design to GWSVs. Also, in order to guarantee equilibrium existence, it is necessary to work within the class of potential games, since GWSVs result in (weighted) potential games.

We also provide an alternative characterization—all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to generalized weighted marginal contribution (GWMC) rules on some 'ground' welfare functions. This result is due to a deeper fundamental connection between Shapley values and marginal contributions that our proofs expose—they are equivalent given a transformation connecting their ground welfare functions. (This connection leads to novel closed-form expressions for the GWSV potential function.) Since GWMCs are more tractable than GWSVs, a designer can tradeoff budget-balance with computational tractability in deciding which rule to implement.

Reactivity of titanocene methylidene with metal halides, alkene sulfides, and alkene oxides

Titanocene metallacyclobutanes show a wide variety of reactivites with organic and inorganic reagents. Their reactions include methylene transfer to organic carbonyls, formation of enolates, electron transfer from activated alkyl chlorides, olefin metathesis, ring opening polymerization. Recently, preparations of heterobinuclear µ-methylene complexes were reported. In this thesis, mechanistic, synthetic, and structural studies of the heterobinuclear µ-methylene complexes will be described. Also, the reaction of titanocene methylidene trimethylphosphine complex with alkene sulfide and styrene sulfide will be presented.

Heterobinuclear µ-methylene-µ-methyl complexes C_(p2)Ti(µ-CH_2)( µ-CH_3)M(1,5-COD) have been prepared (M = Rh, Ir). X-ray crystallography showed that the methyl group of the complex was bonded to the rhodium and bridges to the titanium through an agostic bond. The ^(1)H,^(13)CNMR, IR spectra along with partial deuteration studies supported the structure in both solution and solid state. Activation of the agostic bond is demonstrated by the equilibration of the µ-CH_3 and µ-CH_2 groups. A nonlinear Arrhenius plot, an unusually large kinetic isotope effect (24(5)), and a large negative activation entropy (-64(3)eu) can be explained by the quantum-mechanical tunneling. Calculated rate constants with Bell-type barrier fitted well with the observed one. This equilibration was best explained by a 4e-4c mechanism (or σ bond metathesis) with the character of quantum-mechanical tunneling.

Heterobinuclear µ-methylene-µ-phenyl complexes were synthesized. Structural study of C_(p2)Ti(µ-CH_(2))(µ-p-Me_(2)NC_(6)H_(4))Rh(l,5-COD) showed that the two metal atoms are bridged by the methylene carbon and the ipso carbon of the p-N,N-dimethylarninophenyl group. The analogous structure of C_(p2))Ti(µ-CH_(2))(µ-o-MeOC_(6)H_(4))Rh(1,5-COD) has been verified by the differential NOE. The aromaticity of the phenyl group observed by ^(1)H NMR, was confirmed by the comparison of the C-C bond lengths in the crystallographic structure. The unusual downfield shifts of the ipso carbon in the ^(13)C NMR are assumed to be an indication of the interaction between the ipso carbon and electron-deficient titanium.

Titanium-platinum heterobinuclear µ-methylene complexes C_(p2)Ti(µ-CH_(2))(µ -X)Pt(Me)(PM_(2)Ph) have been prepared (X= Cl, Me). Structural studies indicate the following:(1) the Ti-CH2 bond possesses residual double bond character, (2) there is a dative Pt→Ti interaction which may be regarded as a π back donation from the platinum atom to the 'Ti=CH_(2)'' group, and (3) the µ-CH_3 group is bound to the titanium atom through a three-center, two-electron agostic bond.

Titanocene (η^(2)-thioformaldehyde)•PMe_3 was prepared from C_(p2)Ti=CH_(2)•PMe_3 and sulfur-containing organic compounds (e.g. alkene sulfide, triphenylphosphine sulfide) including elemental sulfur. Mechanistic studies utilizing trans-styrene sulfide-d_1 suggested the stepwise reaction to explain equimolar mixture of trans- and cis-styrene-d_1 as by-products. The product reacted with methyl iodide to produce cationic titanocene (η_(2)-thiomethoxymethyl) complex. Complexes having less coordinating anion like BF_4 or BPh_4 could be obtained through metathesis. Together with structural analyses, the further reactivities of the complexes have been explored.

The complex C_(p2)TiOCH_(2)CH(Ph)CH_2 was prepared from the compound C_(p2)Ti=CH_(2)-PMe_3 and styrene oxide. The product was characterized with ^(1)H-^(1)H correlated 2-dimensional NMR, selective decoupling of ^(1)H NMR, and differential NOE. Stereospecificity of deuterium in the product was lost when trans-styrene oxide-d_1 was allowed to react. Relative rates of the reaction were measured with varying substituents on the phenyl ring. Better linearity (r = -0.98, p^(+) = -0.79) was observed with σ_(p)^(+)than σ(r = -0.87, p = -1.26). The small magnitude of p^+ value and stereospecificity loss during the formation of product were best explained by the generation of biradicals, but partial generation of charge cannot be excluded. Carbonylation of the product followed by exposure to iodine yields the corresponding β-phenyl γ-lactone.

Probing the thermodynamic properties of mantle rocks in solid and liquid states

Our understanding of the structure and evolution of the deep Earth is strongly linked to knowledge of the thermodynamic properties of rocky materials at extreme temperatures and pressures. In this thesis, I present work that helps constrain the equation of state properties of iron-bearing Mg-silicate perovskite as well as oxide-silicate melts. I use a mixture of experimental, statistical, and theoretical techniques to obtain knowledge about these phases. These include laser-heated diamond anvil cell experiments, Bayesian statistical analysis of powder diffraction data, and the development of a new simplified model for understanding oxide and silicate melts at mantle conditions. By shedding light on the thermodynamic properties of such ubiquitous Earth-forming materials, I hope to aid our community’s progress toward understanding the large-scale processes operating in the Earth’s mantle, both in the modern day and early in Earth’s history.