Experimental and finite element studies of a large arch dam

Forced vibration field tests and finite element studies have been conducted on Morrow Point (arch) Dam in order to investigate dynamic dam-water interaction and water compressibility. Design of the data acquisition system incorporates several special features to retrieve both amplitude and phase of the response in a low signal to noise environment. These features contributed to the success of the experimental program which, for the first time, produced field evidence of water compressibility; this effect seems to play a significant role only in the symmetric response of Morrow Point Dam in the frequency range examined. In the accompanying analysis, frequency response curves for measured accelerations and water pressures as well as their resonating shapes are compared to predictions from the current state-of-the-art finite element model for which water compressibility is both included and neglected. Calibration of the numerical model employs the antisymmetric response data since they are only slightly affected by water compressibility, and, after calibration, good agreement to the data is obtained whether or not water compressibility is included. In the effort to reproduce the symmetric response data, on which water compressibility has a significant influence, the calibrated model shows better correlation when water compressibility is included, but the agreement is still inadequate. Similar results occur using data obtained previously by others at a low water level. A successful isolation of the fundamental water resonance from the experimental data shows significantly different features from those of the numerical water model, indicating possible inaccuracy in the assumed geometry and/or boundary conditions for the reservoir. However, the investigation does suggest possible directions in which the numerical model can be improved.

Nonexistence of looping trajectories in hydromagnetic waves of finite amplitude. Breaking of waves in a cold collision-free plasma in a magnetic field. On stabilities of periodic waves in a cold collision-free plasma in a magnetic field.

This dissertation consists of three parts. In Part I, it is shown that looping trajectories cannot exist in finite amplitude stationary hydromagnetic waves propagating across a magnetic field in a quasi-neutral cold collision-free plasma. In Part II, time-dependent solutions in series expansion are presented for the magnetic piston problem, which describes waves propagating into a quasi-neutral cold collision-free plasma, ensuing from magnetic disturbances on the boundary of the plasma. The expansion is equivalent to Picard's successive approximations. It is then shown that orbit crossings of plasma particles occur on the boundary for strong disturbances and inside the plasma for weak disturbances. In Part III, the existence of periodic waves propagating at an arbitrary angle to the magnetic field in a plasma is demonstrated by Stokes expansions in amplitude. Then stability analysis is made for such periodic waves with respect to side-band frequency disturbances. It is shown that waves of slow mode are unstable whereas waves of fast mode are stable if the frequency is below the cutoff frequency. The cutoff frequency depends on the propagation angle. For longitudinal propagation the cutoff frequency is equal to one-fourth of the electron's gyrofrequency. For transverse propagation the cutoff frequency is so high that waves of all frequencies are stable.

A mathematical study of finite-amplitude rock-folding

The problem of the finite-amplitude folding of an isolated, linearly viscous layer under compression and imbedded in a medium of lower viscosity is treated theoretically by using a variational method to derive finite difference equations which are solved on a digital computer. The problem depends on a single physical parameter, the ratio of the fold wavelength, L, to the "dominant wavelength" of the infinitesimal-amplitude treatment, L_d. Therefore, the natural range of physical parameters is covered by the computation of three folds, with L/L_d = 0, 1, and 4.6, up to a maximum dip of 90°.

Significant differences in fold shape are found among the three folds; folds with higher L/L_d have sharper crests. Folds with L/L_d = 0 and L/L_d = 1 become fan folds at high amplitude. A description of the shape in terms of a harmonic analysis of inclination as a function of arc length shows this systematic variation with L/L_d and is relatively insensitive to the initial shape of the layer. This method of shape description is proposed as a convenient way of measuring the shape of natural folds.

The infinitesimal-amplitude treatment does not predict fold-shape development satisfactorily beyond a limb-dip of 5°. A proposed extension of the treatment continues the wavelength-selection mechanism of the infinitesimal treatment up to a limb-dip of 15°; after this stage the wavelength-selection mechanism no longer operates and fold shape is mainly determined by L/L_d and limb-dip.

Strain-rates and finite strains in the medium are calculated f or all stages of the L/L_d = 1 and L/L_d = 4.6 folds. At limb-dips greater than 45° the planes of maximum flattening and maximum flattening rat e show the characteristic orientation and fanning of axial-plane cleavage.

On reconstruction theorems in noncommutative Riemannian geometry

We present a novel account of the theory of commutative spectral triples and their two closest noncommutative generalisations, almost-commutative spectral triples and toric noncommutative manifolds, with a focus on reconstruction theorems, viz, abstract, functional-analytic characterisations of global-analytically defined classes of spectral triples. We begin by reinterpreting Connes's reconstruction theorem for commutative spectral triples as a complete noncommutative-geometric characterisation of Dirac-type operators on compact oriented Riemannian manifolds, and in the process clarify folklore concerning stability of properties of spectral triples under suitable perturbation of the Dirac operator. Next, we apply this reinterpretation of the commutative reconstruction theorem to obtain a reconstruction theorem for almost-commutative spectral triples. In particular, we propose a revised, manifestly global-analytic definition of almost-commutative spectral triple, and, as an application of this global-analytic perspective, obtain a general result relating the spectral action on the total space of a finite normal compact oriented Riemannian cover to that on the base space. Throughout, we discuss the relevant refinements of these definitions and results to the case of real commutative and almost-commutative spectral triples. Finally, we outline progess towards a reconstruction theorem for toric noncommutative manifolds.

The intramolecular Buchner reaction of α-diazo-β-ketonitriles : development and application to the total synthesis of (+)-Salvileucalin B

Since its discovery in 1896, the Buchner reaction has fascinated chemists for more than a century. The highly reactive nature of the carbene intermediates allows for facile dearomatization of stable aromatic rings, and provides access to a diverse array of cyclopropane and seven-membered ring architectures. The power inherent in this transformation has been exploited in the context of a natural product total synthesis and methodology studies.

The total synthesis work details efforts employed in the enantioselective total synthesis of (+)-salvileucalin B. The fully-substituted cyclopropane within the core of the molecule arises from an unprecedented intramolecular Buchner reaction involving a highly functionalized arene and an α-diazo-β-ketonitrile. An unusual retro-Claisen rearrangement of a complex late-stage intermediate was discovered on route to the natural product.

The unique reactivity of α-diazo-β-ketonitriles toward arene cyclopropanation was then investigated in a broader methodological study. This specific di-substituted diazo moiety possesses hitherto unreported selectivity in intramolecular Buchner reactions. This technology was enables the preparation of highly functionalized norcaradienes and cyclopropanes, which themselves undergo various ring opening transformations to afford complex polycyclic structures.

Finally, an enantioselective variant of the intramolecular Buchner reaction is described. Various chiral copper and dirhodium catalysts afforded moderate stereoinduction in the cyclization event.

Palladium-catalyzed asymmetric allylic alkylation: insights, application toward cyclopentanoid and cycloheptanoid molecules, and the total synthesis of several daucane sesquiterpenes

The asymmetric construction of quaternary stereocenters is a topic of great interest in the organic chemistry community given their prevalence in natural products and biologically active molecules. Over the last decade, the Stoltz group has pursued the synthesis of this challenging motif via a palladium-catalyzed allylic alkylation using chiral phosphinooxazoline (PHOX) ligands. Recent results indicate that the alkylation of lactams and imides consistently proceeds with enantioselectivities substantially higher than any other substrate class previously examined in this system. This observation prompted exploration of the characteristics that distinguish these molecules as superior alkylation substrates, resulting in newfound insights and marked improvements in the allylic alkylation of carbocyclic compounds.

General routes to cyclopentanoid and cycloheptanoid core structures have been developed that incorporate the palladium-catalyzed allylic alkylation as a key transformation. The unique reactivity of α-quaternary vinylogous esters upon addition of hydride or organometallic reagents enables divergent access to γ-quaternary acylcyclopentenes or cycloheptenones through respective ring contraction or carbonyl transposition pathways. Derivatization of the resulting molecules provides a series of mono-, bi-, and tricyclic systems that can serve as valuable intermediates for the total synthesis of complex natural products.

The allylic alkylation and ring contraction methodology has been employed to prepare variably functionalized bicyclo[5.3.0]decane molecules and enables the enantioselective total syntheses of daucene, daucenal, epoxydaucenal B, and 14-p-anisoyloxydauc-4,8-diene. This route overcomes the challenge of accessing β-substituted acylcyclopentenes by employing a siloxyenone to effect the Grignard addition and ring opening in a single step. Subsequent ring-closing metathesis and aldol reactions form the hydroazulene core of these targets. Derivatization of a key enone intermediate allows access to either the daucane sesquiterpene or sphenobolane diterpene carbon skeletons, as well as other oxygenated scaffolds.

Progress towards the total synthesis of a spermine-conjugated dynemicin analog

Progress towards the synthesis of the spermine-conjugated Dynemicin analog 4 is described. The synthetic route starts with the Michael addition of menthyl acetoacetate to trans-ethyl crotonate followed by a Dieckman condensation to form the cyclohexanedione 14 which, through a series of chemical reactions, is transformed into the quinone imine 6. Key features in the route include the Suzuki coupling reaction of the aryl boronic acid 11 and the enol triflate 12, thermal deprotection/internal amidation of the biaryl 19, cis addition of the (Z)-enediyne 33 to the quinoline 25, intramolecular acetylide addition to a carbonyl within the ketone 29, and an addition/elimination of the cyanophthalide to the quinone imine 6 to form the anthraquinone 36 utilizing the Kraus and Sugimoto methodology.

New strategies for the total synthesis of aza-propellane natural products

The propellane alkaloids comprise a large class of natural products that possess varying degrees of structural complexity and biological activity. The earliest of these to be isolated was acutumine, a chlorinated alkaloid that has been shown to exhibit selective T-cell cytotoxicity and antiamnesic properties. Alternatively, the hasubanan family of natural products has garnered considerable attention from the synthetic community in part due to its structural similarities to morphine. While these alkaloids have been the subject of numerous synthetic studies over the last forty years, very few enantioselective total syntheses have been reported to date.

As part of a research program directed towards the synthesis of various alkaloid natural products, we have developed a unified strategy for the preparation of the hasubanan and acutumine alkaloids. Specifically, a highly diastereoselective 1,2-addition of organometallic reagents to benzoquinone-derived tert-butanesulfinimines was established, which provides access to enantioenriched 4-aminocyclohexadienone products. This methodology enabled the enantioselective construction of functionalized dihydroindolones, which were found to undergo intramolecular Friedel-Crafts conjugate additions to furnish the propellane cores of several hasubanan alkaloids. As a result of these studies, the first enantioselective total syntheses of 8-demethoxyrunanine and cepharatines A, C, and D were accomplished in 9-11 steps from commercially available starting materials.

More recent efforts have focused on applying the sulfinimine methodology to the synthesis of a more structurally complex propellane alkaloid, acutumine. Extensive studies have determined that a properly functionalized dihydroindolone undergoes a photochemical [2+2] cycloaddition followed by a lactone fragmentation/Dieckmann cyclization to establish the carbocyclic framework of the natural product. The preparation of more appropriately oxidized propellane intermediates is currently under investigation, and is anticipated to facilitate our synthetic endeavors toward acutumine.

A unified strategy to ent-kauranoid natural products : total syntheses of (–)-maoecrystal Z, (–)-trichorabdal A, and (–)-longikaurin E

The diterpenoid constituents of the Isodon plants have attracted reasearchers interested in both their chemical structures and biological properties for more than a half-century. In recent years, the isolations of new members displaying previously unprecedented ring systems and highly selective biological properties have piqued interest from the synthetic community in this class of natural products.

Reported herein is the first total synthesis of such a recently isolated diterpenoid, (–)-maoecrystal Z. The principal transformations implemented in this synthesis include two highly diastereoselective radical cyclization reactions: a Sm^(II)-mediated reductive cascade cyclization, which forms two rings and establishes four new stereocenters in a single step, and a Ti^(III)-mediated reductive epoxide-acrylate coupling that yields a functionalized spirolactone product, which forms a core bicycle of maoecrystal Z.

The preparation of two additional ent-kauranoid natural products, (–)-trichorabdal A and (–)-longikaurin E, is also described from a derivative of this key spirolactone. These syntheses are additionally enabled by the palladium-mediated oxidative cyclization reaction of a silyl ketene acetal precursor that is used to install the bridgehead all-carbon quaternary stereocenter and bicyclo[3.2.1]octane present in each natural product. These studies have established a synthetic relationship among three architecturally distinct ent-kaurane diterpenoids and have forged a path for the preparation of interesting unnatural ent-kauranoid structural analogs for more thorough biological study.

The development of an asymmetric palladium-catalyzed conjugate addition and its application toward the total syntheses of taiwaniaquinoid natural products

The asymmetric synthesis of quaternary stereocenters remains a challenging problem in organic synthesis. Past work from the Stoltz laboratory has resulted in methodology to install quaternary stereocenters α- or γ- to carbonyl compounds. Thus, the asymmetric synthesis of β-quaternary stereocenters was a desirable objective, and was accomplished by engineering the palladium-catalyzed addition of arylmetal organometallic reagents to α,β-unsaturated conjugate acceptors.

Herein, we described the rational design of a palladium-catalyzed conjugate addition reactions utilizing a catalyst derived from palladium(II) trifluoroacetate and pyridinooxazole ligands. This reaction is highly tolerant of protic solvents and oxygen atmosphere, making it a practical and operationally simple reaction. The mild conditions facilitate a remarkably high functional group tolerance, including carbonyls, halogens, and fluorinated functional groups. Furthermore, the reaction catalyzed conjugate additions with high enantioselectivity with conjugate acceptors of 5-, 6-, and 7-membered ring sizes. Extension of the methodology toward the asymmetric synthesis of flavanone products is presented, as well.

A computational and experimental investigation into the reaction mechanism provided a stereochemical model for enantioinduction, whereby the α-methylene protons adjacent the enone carbonyl clashes with the tert-butyl groups of the chiral ligand. Additionally, it was found that the addition of water and ammonium hexafluorophosphate significantly increases the reaction rate without sacrificing enantioselectivity. The synergistic effects of these additives allowed for the reaction to proceed at a lower temperature, and thus facilitated expansion of the substrate scope to sensitive functional groups such as protic amides and aryl bromides. Investigations into a scale-up synthesis of the chiral ligand (S)-tert-butylPyOx are also presented. This three-step synthetic route allowed for synthesis of the target compound of greater than 10 g scale.

Finally, the application of the newly developed conjugate addition reaction toward the synthesis of the taiwaniaquinoid class of terpenoid natural products is discussed. The conjugate addition reaction formed the key benzylic quaternary stereocenter in high enantioselectivity, joining together the majority of the carbons in the taiwaniaquinoid scaffold. Efforts toward the synthesis of the B-ring are presented.

Studies of phonon anharmonicity in solids

Today our understanding of the vibrational thermodynamics of materials at low temperatures is emerging nicely, based on the harmonic model in which phonons are independent. At high temperatures, however, this understanding must accommodate how phonons interact with other phonons or with other excitations. We shall see that the phonon-phonon interactions give rise to interesting coupling problems, and essentially modify the equilibrium and non-equilibrium properties of materials, e.g., thermodynamic stability, heat capacity, optical properties and thermal transport of materials. Despite its great importance, to date the anharmonic lattice dynamics is poorly understood and most studies on lattice dynamics still rely on the harmonic or quasiharmonic models. There have been very few studies on the pure phonon anharmonicity and phonon-phonon interactions. The work presented in this thesis is devoted to the development of experimental and computational methods on this subject.

Modern inelastic scattering techniques with neutrons or photons are ideal for sorting out the anharmonic contribution. Analysis of the experimental data can generate vibrational spectra of the materials, i.e., their phonon densities of states or phonon dispersion relations. We obtained high quality data from laser Raman spectrometer, Fourier transform infrared spectrometer and inelastic neutron spectrometer. With accurate phonon spectra data, we obtained the energy shifts and lifetime broadenings of the interacting phonons, and the vibrational entropies of different materials. The understanding of them then relies on the development of the fundamental theories and the computational methods.

We developed an efficient post-processor for analyzing the anharmonic vibrations from the molecular dynamics (MD) calculations. Currently, most first principles methods are not capable of dealing with strong anharmonicity, because the interactions of phonons are ignored at finite temperatures. Our method adopts the Fourier transformed velocity autocorrelation method to handle the big data of time-dependent atomic velocities from MD calculations, and efficiently reconstructs the phonon DOS and phonon dispersion relations. Our calculations can reproduce the phonon frequency shifts and lifetime broadenings very well at various temperatures.

To understand non-harmonic interactions in a microscopic way, we have developed a numerical fitting method to analyze the decay channels of phonon-phonon interactions. Based on the quantum perturbation theory of many-body interactions, this method is used to calculate the three-phonon and four-phonon kinematics subject to the conservation of energy and momentum, taking into account the weight of phonon couplings. We can assess the strengths of phonon-phonon interactions of different channels and anharmonic orders with the calculated two-phonon DOS. This method, with high computational efficiency, is a promising direction to advance our understandings of non-harmonic lattice dynamics and thermal transport properties.

These experimental techniques and theoretical methods have been successfully performed in the study of anharmonic behaviors of metal oxides, including rutile and cuprite stuctures, and will be discussed in detail in Chapters 4 to 6. For example, for rutile titanium dioxide (TiO₂), we found that the anomalous anharmonic behavior of the B_1g mode can be explained by the volume effects on quasiharmonic force constants, and by the explicit cubic and quartic anharmonicity. For rutile tin dioxide (SnO₂), the broadening of the B_2g mode with temperature showed an unusual concave downwards curvature. This curvature was caused by a change with temperature in the number of down-conversion decay channels, originating with the wide band gap in the phonon dispersions. For silver oxide (Ag₂O), strong anharmonic effects were found for both phonons and for the negative thermal expansion.

Studies toward the total synthesis of ritterazine B : the investigation of alkynylation reactions for use in the synthesis of the western fragment

The ritterazine and cephalostatin natural products have biological activities and structures that are interesting to synthetic organic chemists. These products have been found to exhibit significant cytotoxicity against P388 murine leukemia cells, and therefore have the potential to be used as anticancer drugs. The ritterazines and cephalostatins are steroidal dimers joined by a central pyrazine ring. Given that the steroid halves are unsymmetrical and highly oxygenated, there are several challenges in synthesizing these compounds in an organic laboratory.

Ritterazine B is the most potent derivative in the ritterazine family. Its biological activity is comparable to drugs that are being used to treat cancer today. For this reason, and the fact that there are no reported syntheses of ritterazine B to date, our lab set out to synthesize this natural product.

Herein, efforts toward the synthesis of the western fragment of ritterazine B are described. Two different routes are explored to access a common intermediate. An alkyne conjugate addition reaction was initially investigated due to the success of this key reaction in the synthesis of the eastern fragment. However, it has been found that a propargylation reaction has greater reactivity and yields, and has the potential to reduce the step count of the synthesis of the western fragment of ritterazine B.

High-strain composites and dual-matrix composite structures

Most space applications require deployable structures due to the limiting size of current launch vehicles. Specifically, payloads in nanosatellites such as CubeSats require very high compaction ratios due to the very limited space available in this typo of platform. Strain-energy-storing deployable structures can be suitable for these applications, but the curvature to which these structures can be folded is limited to the elastic range. Thanks to fiber microbuckling, high-strain composite materials can be folded into much higher curvatures without showing significant damage, which makes them suitable for very high compaction deployable structure applications. However, in applications that require carrying loads in compression, fiber microbuckling also dominates the strength of the material. A good understanding of the strength in compression of high-strain composites is then needed to determine how suitable they are for this type of application.

The goal of this thesis is to investigate, experimentally and numerically, the microbuckling in compression of high-strain composites. Particularly, the behavior in compression of unidirectional carbon fiber reinforced silicone rods (CFRS) is studied. Experimental testing of the compression failure of CFRS rods showed a higher strength in compression than the strength estimated by analytical models, which is unusual in standard polymer composites. This effect, first discovered in the present research, was attributed to the variation in random carbon fiber angles respect to the nominal direction. This is an important effect, as it implies that microbuckling strength might be increased by controlling the fiber angles. With a higher microbuckling strength, high-strain materials could carry loads in compression without reaching microbuckling and therefore be suitable for several space applications.

A finite element model was developed to predict the homogenized stiffness of the CFRS, and the homogenization results were used in another finite element model that simulated a homogenized rod under axial compression. A statistical representation of the fiber angles was implemented in the model. The presence of fiber angles increased the longitudinal shear stiffness of the material, resulting in a higher strength in compression. The simulations showed a large increase of the strength in compression for lower values of the standard deviation of the fiber angle, and a slight decrease of strength in compression for lower values of the mean fiber angle. The strength observed in the experiments was achieved with the minimum local angle standard deviation observed in the CFRS rods, whereas the shear stiffness measured in torsion tests was achieved with the overall fiber angle distribution observed in the CFRS rods.

High strain composites exhibit good bending capabilities, but they tend to be soft out-of-plane. To achieve a higher out-of-plane stiffness, the concept of dual-matrix composites is introduced. Dual-matrix composites are foldable composites which are soft in the crease regions and stiff elsewhere. Previous attempts to fabricate continuous dual-matrix fiber composite shells had limited performance due to excessive resin flow and matrix mixing. An alternative method, presented in this thesis uses UV-cure silicone and fiberglass to avoid these problems. Preliminary experiments on the effect of folding on the out-of-plane stiffness are presented. An application to a conical log-periodic antenna for CubeSats is proposed, using origami-inspired stowing schemes, that allow a conical dual-matrix composite shell to reach very high compaction ratios.

Integral finite surgeries on knots in S^3

Using the correction terms in Heegaard Floer homology, we prove that if a knot in S³ admits a positive integral T-, O-, or I-type surgery, it must have the same knot Floer homology as one of the knots given in our complete list, and the resulting manifold is orientation-preservingly homeomorphic to the p-surgery on the corresponding knot.

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.