Studies in vortex motion

This thesis covers four different problems in the understanding of vortex sheets, and these are presented in four chapters.

In Chapter 1, free streamline theory is used to determine the steady solutions of an array of identical, hollow or stagnant core vortices in an inviscid, incompressible fluid. Assuming the array is symmetric to rotation through π radians about an axis through any vortex centre, there are two solutions or no solutions depending on whether A^(1/2)/L is less than or greater than 0.38 where A is the area of the vortex and L is the separation distance. Stability analysis shows that the more deformed shape is unstable to infinitesimal symmetric disturbances which leave the centres of the vortices undisplaced.

Chapter 2 is concerned with the roll-up of vortex sheets in homogeneous fluid. The flow over conventional and ring wings is used to test the method of Fink and Soh (1974). Despite modifications which improve the accuracy of the method, unphysical results occur. A possible explanation for this is that small scales are important and an alternate method based on "Cloud-in-Cell" techniques is introduced. The results show small scale growth and amalgamation into larger structures.

The motion of a buoyant pair of line vortices of opposite circulation is considered in Chapter 3. The density difference between the fluid carried by the vortices and the fluid outside is considered small, so that the Boussinesq approximation may be used. A macroscopic model is developed which shows the formation of a detrainment filament and this is included as a modification to the model. The results agree well with the numerical solution as developed by Hill (1975b) and show that after an initial slowdown, the vortices begin to accelerate downwards.

Chapter 4 reproduces completely a paper that has already been published (Baker, Barker, Bofah and Saffman (1974)) on the effect of "vortex wandering" on the measurement of velocity profiles of the trailing vortices behind a wing.

Nucleon structure functions from ν_µ-Fe interactions and a study of the valence quark distribution

Data were taken in 1979-80 by the CCFRR high energy neutrino experiment at Fermilab. A total of 150,000 neutrino and 23,000 antineutrino charged current events in the approximate energy range 25 < E_v < 250GeV are measured and analyzed. The structure functions F2 and xF_3 are extracted for three assumptions about σ_L/σ_T:R=0., R=0.1 and R= a QCD based expression. Systematic errors are estimated and their significance is discussed. Comparisons or the X and Q^2 behaviour or the structure functions with results from other experiments are made.

We find that statistical errors currently dominate our knowledge of the valence quark distribution, which is studied in this thesis. xF_3 from different experiments has, within errors and apart from level differences, the same dependence on x and Q^2, except for the HPWF results. The CDHS F_2 shows a clear fall-off at low-x from the CCFRR and EMC results, again apart from level differences which are calculable from cross-sections.

The result for the the GLS rule is found to be 2.83±.15±.09±.10 where the first error is statistical, the second is an overall level error and the third covers the rest of the systematic errors. QCD studies of xF_3 to leading and second order have been done. The QCD evolution of xF_3, which is independent of R and the strange sea, does not depend on the gluon distribution and fits yield

ʌ_(LO) = 88^(+163)_(-78) ^(+113)_(-70) MeV

The systematic errors are smaller than the statistical errors. Second order fits give somewhat different values of ʌ, although α_s (at Q^2_0 = 12.6 GeV^2) is not so different.

A fit using the better determined F_2 in place of xF_3 for x > 0.4 i.e., assuming q = 0 in that region, gives

ʌ_(LO) = 266^(+114)_(-104) ^(+85)_(-79) MeV

Again, the statistical errors are larger than the systematic errors. An attempt to measure R was made and the measurements are described. Utilizing the inequality q(x)≥0 we find that in the region x > .4 R is less than 0.55 at the 90% confidence level.

Growth and characterization of novel, III-V semiconductor heterostructures

The material presented in this thesis concerns the growth and characterization of III-V semiconductor heterostructures. Studies of the interactions between bound states in coupled quantum wells and between well and barrier bound states in AlAs/GaAs heterostructures are presented. We also demonstrate the broad array of novel tunnel structures realizable in the InAs/GaSb/AlSb material system. Because of the unique broken-gap band alignment of InAs/GaSb these structures involve transport between the conduction- and valence-bands of adjacent layers. These devices possess a wide range of electrical properties and are fundamentally different from conventional AlAs/GaAs tunnel devices. We report on the fabrication of a novel tunnel transistor with the largest reported room temperature current gains. We also present time-resolved studies of the growth fronts of InAs/GainSb strained layer superlattices and investigations of surface anion exchange reactions.

Chapter 2 covers tunneling studies of conventional AlAs/GaAs RTD's. The results of two studies are presented: (i) A test of coherent vs. sequential tunneling in triple barrier heterostructures, (ii) An optical measurement of the effect of barrier X-point states on Γ-point well states. In the first it was found if two quantum wells are separated by a sufficiently thin barrier, then the eigenstates of the system extend coherently across both wells and the central barriers. For thicker barriers between the wells, the electrons become localized in the individual wells and transport is best described by the electrons hopping between the wells. In the second, it was found that Γ-point well states and X-point barrier states interact strongly. The barrier X-point states modify the energies of the well states and increase the escape rate for carriers in the quantum well.

The results of several experimental studies of a novel class of tunnel devices realized in the InAs/GaSb/AlSb material system are presented in Chapter 3. These interband tunnel structures involve transport between conduction- and valence-band states in adjacent material layers. These devices are compared and contrasted with the conventional AlAs/GaAs structures discussed in Chapter 2 and experimental results are presented for both resonant and nonresonant devices. These results are compared with theoretical simulations and necessary extensions to the theoretical models are discussed.

In chapter 4 experimental results from a novel tunnel transistor are reported. The measured current gains in this transistor exceed 100 at room temperature. This is the highest reported gain at room temperature for any tunnel transistor. The device is analyzed and the current conduction and gain mechanisms are discussed.

Chapters 5 and 6 are studies of the growth of structures involving layers with different anions. Chapter 5 covers the growth of InAs/GainSb superlattices for far infrared detectors and time resolved, in-situ studies of their growth fronts. It was found that the bandgap of superlattices with identical layer thicknesses and compositions varied by as much as 40 meV depending on how their internal interfaces are formed. The absorption lengths in superlattices with identical bandgaps but whose interfaces were formed in different ways varied by as much as a factor of two. First the superlattice is discussed including an explanation of the device and the complications involved in its growth. The experimental technique of reflection high energy electron diffraction (RHEED) is reviewed, and the results of RHEED studies of the growth of these complicated structures are presented. The development of a time resolved, in-situ characterization of the internal interfaces of these superlattices is described. Chapter 6 describes the result of a detailed study of some of the phenomena described in chapter 5. X-ray photoelectron spectroscopy (XPS) studies of anion exchange reactions on the growth fronts of these superlattices are reported. Concurrent RHEED studies of the same physical systems studied with XPS are presented. Using the RHEED and XPS results, a real-time, indirect measurement of surface exchange reactions was developed.

Geometric quantization and foliation reduction

A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether “quantization commutes with reduction.” Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact Kähler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-Kähler manifolds. For realistic physical examples, however, it is desirable to have a proof which also applies to non-compact symplectic manifolds.

In this thesis we give a proof of the quantization-reduction problem for general symplectic manifolds. This is accomplished by working in a particular wavefunction representation, associated with a polarization that is in some sense compatible with reduction. While the polarized sections described by Guillemin and Sternberg are nonzero on a dense subset of the Kähler manifold, the ones considered here are distributional, having support only on regions of the phase space associated with certain quantized, or “admissible”, values of momentum.

We first propose a reduction procedure for the prequantum geometric structures that “covers” symplectic reduction, and demonstrate how both symplectic and prequantum reduction can be viewed as examples of foliation reduction. Consistency of prequantum reduction imposes the above-mentioned admissibility conditions on the quantized momenta, which can be seen as analogues of the Bohr-Wilson-Sommerfeld conditions for completely integrable systems.

We then describe our reduction-compatible polarization, and demonstrate a one-to-one correspondence between polarized sections on the unreduced and reduced spaces.

Finally, we describe a factorization of the reduced prequantum bundle, suggested by the structure of the underlying reduced symplectic manifold. This in turn induces a factorization of the space of polarized sections that agrees with its usual decomposition by irreducible representations, and so proves that quantization and reduction do indeed commute in this context.

A significant omission from the proof is the construction of an inner product on the space of polarized sections, and a discussion of its behavior under reduction. In the concluding chapter of the thesis, we suggest some ideas for future work in this direction.

Tools for the study of dynamical spacetimes

This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program.

We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi_4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction.

Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6.

For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various properties of these modes to wave packets traveling on unstable photon orbits around the black hole. In Chapter 8, we study a bifurcation in the QNM spectrum as the spin of the black hole a approaches extremality.

I. Geology of the Southwest quarter of the Elsinore Quadrangle. II. Geochemical properties of the waters of the Elsinore Quadrangle [= Geology of the Lake Elsinore Quadrangle, California. Mineral deposits of Lake Elsinore Quadrangle, California]

The Lake Elsinore quadrangle covers about 250 square miles and includes parts of the southwest margin of the Perris Block, the Elsinore trough, the southeastern end of the Santa Ana Mountains, and the Elsinore Mountains.

The oldest rocks consist of an assemblage of metamorphics of igneous effusive and sedimentary origin, probably, for the most part, of Triassic age. They are intruded by diorite and various hypabyssal rocks, then in turn by granitic rocks, which occupy over 40 percent of the area. Following this last igneous activity of probable Lower Cretaceous age, an extended period of sedimentation started with the deposition of the marine Upper Cretaceous Chico formation and continued during the Paloecene under alternating marine and continental conditions on the margins of the blocks. A marine regression towards the north, during the Neocene, accounts for the younger Tertiary strata in the region under consideration.

Outpouring of basalts to the southeast indicates that igneous activity was resumed toward the close of the Tertiary. The fault zone, which characterizes the Elsinor trough, marks one of the major tectonic lines of southem California. It separates the upthrown and tilted block of the Santa Ana Mountains to the south from the Perris Block to the north.

Most of the faults are normal in type and nearly parallel to the general trend of the trough, or intersect each other at an acute angle. Vertical displacements generally exceed the horizontal ones and several periods of activity are recognized.

Tilting of Tertiary and older Quaternary sediments in the trough have produced broad synclinal structures which have been modified by subsequent faulting.

Five old surfaces of erosion are exposed on the highlands.

The mineral resources of the region are mainly high-grade clay deposits and mineral waters.

Structure, chemistry, and energetics of organic and inorganic adsorbates on Ga-rich GaAs and GaP(001) surfaces

The work described in this dissertation includes fundamental investigations into three surface processes, namely inorganic film growth, water-induced oxidation, and organic functionalization/passivation, on the GaP and GaAs(001) surfaces. The techniques used to carry out this work include scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), and density functional theory (DFT) calculations. Atomic structure, electronic structure, reaction mechanisms, and energetics related to these surface processes are discussed at atomic or molecular levels.

First, we investigate epitaxial Zn₃P₂ films grown on the Ga-rich GaAs(001)(6×6) surface. The film growth mechanism, electronic properties, and atomic structure of the Zn₃P₂/GaAs(001) system are discussed based on experimental and theoretical observations. We discover that a P-rich amorphous layer covers the crystalline Zn3P2 film during and after growth. We also propose more accurate picture of the GaP interfacial layer between Zn₃P₂ and GaAs, based on the atomic structure, chemical bonding, band diagram, and P-replacement energetics, than was previously anticipated.

Second, DFT calculations are carried out in order to understand water-induced oxidation mechanisms on the Ga-rich GaP(001)(2×4) surface. Structural and energetic information of every step in the gaseous water-induced GaP oxidation reactions are elucidated at the atomic level in great detail. We explore all reasonable ground states involved in most of the possible adsorption and decomposition pathways. We also investigate structures and energies of the transition states in the first hydrogen dissociation of a water molecule on the (2×4) surface.

Finally, adsorption structures and thermal decomposition reactions of 1-propanethiol on the Ga-rich GaP(001)(2×4) surface are investigated using high resolution STM, XPS, and DFT simulations. We elucidate adsorption locations and their associated atomic structures of a single 1-propanethiol molecule on the (2×4) surface as a function of annealing temperature. DFT calculations are carried out to optimize ground state structures and search transition states. XPS is used to investigate variations of the chemical bonding nature and coverage of the adsorbate species.

A new ground motion intensity measure, peak filtered acceleration (PFA), to estimate collapse vulnerability of buildings in earthquakes

In this thesis, we develop an efficient collapse prediction model, the PFA (Peak Filtered Acceleration) model, for buildings subjected to different types of ground motions.

For the structural system, the PFA model covers modern steel and reinforced concrete moment-resisting frame buildings (potentially reinforced concrete shear wall buildings). For ground motions, the PFA model covers ramp-pulse-like ground motions, long-period ground motions, and short-period ground motions.

To predict whether a building will collapse in response to a given ground motion, we first extract long-period components from the ground motion using a Butterworth low-pass filter with suggested order and cutoff frequency. The order depends on the type of ground motion, and the cutoff frequency depends on the building’s natural frequency and ductility. We then compare the filtered acceleration time history with the capacity of the building. The capacity of the building is a constant for 2-dimentional buildings and a limit domain for 3-dimentional buildings. If the filtered acceleration exceeds the building’s capacity, the building is predicted to collapse. Otherwise, it is expected to survive the ground motion.

The parameters used in PFA model, which include fundamental period, global ductility and lateral capacity, can be obtained either from numerical analysis or interpolation based on the reference building system proposed in this thesis.

The PFA collapse prediction model greatly reduces computational complexity while archiving good accuracy. It is verified by FEM simulations of 13 frame building models and 150 ground motion records.

Based on the developed collapse prediction model, we propose to use PFA (Peak Filtered Acceleration) as a new ground motion intensity measure for collapse prediction. We compare PFA with traditional intensity measures PGA, PGV, PGD, and Sa in collapse prediction and find that PFA has the best performance among all the intensity measures.

We also provide a close form in term of a vector intensity measure (PGV, PGD) of the PFA collapse prediction model for practical collapse risk assessment.

Bimetallic olefin polymerization catalysis : mechanisms and applications of proximal effects

This dissertation covers progress with bimetallic polymerization catalysts. The complexes we have designed were aimed at expanding the capabilities of homogeneous polymerization catalysts by taking advantage of multimetallic effects. Such effects were examined in group 4 and group 10 bimetallic complexes; proximity and steric repulsion were determined to be major factors in the effects observed.

Chapters 2 and 3 introduce the rigid p-terphenyl dinucleating framework utilized in most of this thesis. The permethylation of the central arene allows for the separation of syn and anti atropisomers of the terphenyl compounds. Kinetic studies were carried out to examine the isomerization of the dinucleating bis(salicylaldimine) ligand precursors. Metallation of the syn and anti bis(salicylaldimine)s using Ni(Me)2(tmeda) and excess pyridine afforded dinickel bisphenoxyiminato complexes with a methyl and a pyridyl ligand on each nickel. The syn and anti atropisomers of the dinickel complexes were structurally characterized and utilized in ethylene and ethylene/α-olefin polymerizations. Monometallic analogues were also synthesized and tested for polymerization activity. Ethylene polymerizations were performed in the presence of primary, secondary, and tertiary amines – additives that generally deactivate nickel polymerization catalysts. Inhibition of this deactivation was observed with the syn atropisomer of the bimetallic species, but not with the anti or monometallic analogues. A mechanism was proposed wherein steric repulsion of the substituents on proximal nickel centers disfavors simultaneous ligation of base to both of the metal centers. The bimetallic effect has been explored with respect to size and binding ability of the added base.

Chapter 4 presents the optimization of the bisphenoxyimine ligand synthesis and synthesis of syn and anti m-terphenyl analogues. Metallation with NiClMe(PMe₃)₂ yielded phosphine-ligated dinickel complexes, which have been structurally characterized. Ethylene/1-hexene copolymerizations in the presence of amines using Ni(COD)₂ as a phosphine scavenger showed significantly improved activity relative to the pyridine-ligated analogues. Incorporation of amino olefins in copolymerizations with ethylene was accomplished, and a mechanism was proposed based on proximal effects. Copolymerization trials with a variety of amino olefins and ethylene/1-hexene/amino olefin terpolymerizations were completed.

Early transition metal complexes based on the rigid p-terphenyl framework were designed with a variety of donor sets (Chapter 5 and Appendix B). Chapter 5 details the use of syn dizirconium di[amine bis(phenolate)] complexes for isoselective 1-hexene and propylene homopolymerizations. Ligand variation and monometallic complexes were studied to determine the origin of tacticity control. A mechanistic proposal was presented based on the symmetry at zirconium and the steric effects of the proximal metal center. Appendix B covers additional studies of bimetallic early transition metal complexes based on the p-terphenyl. Dititanium, dizirconium, and asymmetric complexes with bisphenoxyiminato ligands and derivatives thereof were targeted. Progress toward the synthesis of these complexes is described along with preliminary polymerization data. 1-hexene/diene copolymerizations and attempted polymerizations in the presence of ethers and esters with the syn dizirconium di[amine bis(phenolate)] complexes demonstrate the potential for further applications of this system in catalysis.

Appendix A includes work toward palladium catalysts for insertion polymerization of polar monomers. These complexes were based on dioxime and diimine frameworks with the intent of binding Lewis acidic metals at the oxime oxygens, at pendant phenolic donors, or at pendant aminediol moieties. The synthesis and structural characterization of a number of palladium and Lewis acid complexes is presented. Due to the instability of the desired species, efforts toward isolation of the desired complexes proved unsuccessful, though preliminary ethylene/methyl acrylate copolymerizations using in situ activation of the palladium species were attempted.

Studies of the serotonin type 3A receptor and the chemical preparation of tRNA

This thesis describes studies surrounding a ligand-gated ion channel (LGIC): the serotonin type 3A receptor (5-HT₃AR). Structure-function experiments using unnatural amino acid mutagenesis are described, as well as experiments on the methodology of unnatural amino acid mutagenesis. Chapter 1 introduces LGICs, experimental methods, and an overview of the unnatural amino acid mutagenesis.

In Chapter 2, the binding orientation of the clinically available drugs ondansetron and granisetron within 5-HT₃A is determined through a combination of unnatural amino acid mutagenesis and an inhibition based assay. A cation-π interaction is found for both ondansetron and granisetron with a specific tryptophan residue (Trp183, TrpB) of the mouse 5-HT₃AR, which establishes a binding orientation for these drugs.

In Chapter 3, further studies were performed with ondansetron and granisetron with 5-HT₃A. The primary determinant of binding for these drugs was determined to not include interactions with a specific tyrosine residue (Tyr234, TyrC2). In completing these studies, evidence supporting a cation-π interaction of a synthetic agonist, meta-chlorophenylbiguanide, was found with TyrC2.

In Chapter 4, a direct chemical acylation strategy was implemented to prepare full-length suppressor tRNA mediated by lanthanum(III) and amino acid phosphate esters. The derived aminoacyl-tRNA is shown to be translationally competent in Xenopus oocytes.

Appendix A.1 gives details of a pharmacological method for determining the equilibrium dissociation constant, K_B, of a competitive antagonist with a receptor, known as Schild analysis. Appendix A.2 describes an examination of the inhibitory activity of new chemical analogs of the 5-HT₃A antagonist ondansetron. Appendix A.3 reports an organic synthesis of an intermediate for a new unnatural amino acid. Appendix A.4 covers an additional methodological examination for the preparation of amino-acyl tRNA.

Design of antenna-coupled lumped-element titanium nitride KIDs for long-wavelength multi-band continuum imaging

Many applications in cosmology and astrophysics at millimeter wavelengths including CMB polarization, studies of galaxy clusters using the Sunyaev-Zeldovich effect (SZE), and studies of star formation at high redshift and in our local universe and our galaxy, require large-format arrays of millimeter-wave detectors. Feedhorn and phased-array antenna architectures for receiving mm-wave light present numerous advantages for control of systematics, for simultaneous coverage of both polarizations and/or multiple spectral bands, and for preserving the coherent nature of the incoming light. This enables the application of many traditional "RF" structures such as hybrids, switches, and lumped-element or microstrip band-defining filters.

Simultaneously, kinetic inductance detectors (KIDs) using high-resistivity materials like titanium nitride are an attractive sensor option for large-format arrays because they are highly multiplexable and because they can have sensitivities reaching the condition of background-limited detection. A KID is a LC resonator. Its inductance includes the geometric inductance and kinetic inductance of the inductor in the superconducting phase. A photon absorbed by the superconductor breaks a Cooper pair into normal-state electrons and perturbs its kinetic inductance, rendering it a detector of light. The responsivity of KID is given by the fractional frequency shift of the LC resonator per unit optical power.

However, coupling these types of optical reception elements to KIDs is a challenge because of the impedance mismatch between the microstrip transmission line exiting these architectures and the high resistivity of titanium nitride. Mitigating direct absorption of light through free space coupling to the inductor of KID is another challenge. We present a detailed titanium nitride KID design that addresses these challenges. The KID inductor is capacitively coupled to the microstrip in such a way as to form a lossy termination without creating an impedance mismatch. A parallel plate capacitor design mitigates direct absorption, uses hydrogenated amorphous silicon, and yields acceptable noise. We show that the optimized design can yield expected sensitivities very close to the fundamental limit for a long wavelength imager (LWCam) that covers six spectral bands from 90 to 400 GHz for SZE studies.

Excess phase (frequency) noise has been observed in KID and is very likely caused by two-level systems (TLS) in dielectric materials. The TLS hypothesis is supported by the measured dependence of the noise on resonator internal power and temperature. However, there is still a lack of a unified microscopic theory which can quantitatively model the properties of the TLS noise. In this thesis we derive the noise power spectral density due to the coupling of TLS with phonon bath based on an existing model and compare the theoretical predictions about power and temperature dependences with experimental data. We discuss the limitation of such a model and propose the direction for future study.

Varieties generated by modular lattices of width four

A variety (equational class) of lattices is said to be finitely based if there exists a finite set of identities defining the variety. Let M^∞_n denote the lattice variety generated by all modular lattices of width not exceeding n. M^∞₁ and M^∞₂ are both the class of all distributive lattices and consequently finitely based. B. Jónsson has shown that M^∞₃ is also finitely based. On the other hand, K. Baker has shown that M^∞_n is not finitely based for 5 ≤ n ˂ ω. This thesis settles the finite basis problem for M^∞₄. M^∞₄ is shown to be finitely based by proving the stronger result that there exist ten varieties which properly contain M^∞₄ and such that any variety which properly contains M^∞₄ contains one of these ten varieties.

The methods developed also yield a characterization of sub-directly irreducible width four modular lattices. From this characterization further results are derived. It is shown that the free M^∞₄ lattice with n generators is finite. A variety with exactly k covers is exhibited for all k ≥ 15. It is further shown that there are 2^Ӄo sub- varieties of M^∞₄.