Applications of nuclear magnetic resonance spectroscopy to the study of medium-sized rings. I. Conformational properties of cycloheptane. II. Conformational properties of cycloöctane

Conformational equilibrium in medium-sized rings has been investigated by the temperature variation of the fluorine-19 n.m.r. spectra of 1, 1-difluorocycloalkanes and various substituted derivatives of them. Inversion has been found to be fast on the n.m.r. time scale at -180˚ for 1, 1-difluorocycloheptane, but slow for 1, 1-difluoro-4, 4-dimethylcycloheptane at -150˚. At low temperature, the latter compound affords a single AB pattern with a chemical-shift difference of 841 cps. which has been interpreted in terms of the twist-chair conformation with the methyl groups on the axis position and the fluorine atoms in the 4-position. At room temperature, the n.m.r. spectrum of 1, 1-difluoro-4-t-butylcycloheptane affords an AB pattern with a chemical-shift difference of 185 cps. The presence of distinct trans and gauche couplings from the adjacent hydrogens has been interpreted to suggest the existence of a single predominant form, the twist chair with the fluorine atoms on the axis position.

Investigation of 1, 1-difluorocycloöctane and 1, 1, 4, 4-tetrafluorocycloöctane has led to the detection of two kinetic processes both having activation energies of 8-10 kcal./mole but quite different A values. In light of these results eleven different conformations of cycloöctane along with a detailed description of the ways in which they may be interconverted are discussed. An interpretation involving the twist-boat conformation rapidly equilibrating through the saddle and the parallel-boat forms at room temperature is compatible with the results.

Wave propagation in an inhomogeneous medium

This paper is in two parts. In the first part we give a qualitative study of wave propagation in an inhomogeneous medium principally by geometrical optics and ray theory. The inhomogeneity is represented by a sound-speed profile which is dependent upon one coordinate, namely the depth; and we discuss the general characteristics of wave propagation which result from a source placed on the sound channel axis. We show that our mathematical model of the sound- speed in the ocean actually predicts some of the behavior of the observed physical phenomena in the underwater sound channel. Using ray theoretic techniques we investigate the implications of our profile on the following characteristics of SOFAR propagation: (i) the sound energy traveling further away from the axis takes less time to travel from source to receiver than sound energy traveling closer to the axis, (ii) the focusing of sound energy in the sound channel at certain ranges, (iii) the overall ray picture in the sound channel.

In the second part a more penetrating quantitative study is done by means of analytical techniques on the governing equations. We study the transient problem for the Epstein profile by employing a double transform to formally derive an integral representation for the acoustic pressure amplitude, and from this representation we obtain several alternative representations. We study the case where both source and receiver are on the channel axis and greatly separated. In particular we verify some of the earlier results derived by ray theory and obtain asymptotic results for the acoustic pressure in the far-field.

Application of the Schwinger multichannel method to multichannel studies of electronically inelastic electron-molecule collisions

We have applied the Schwinger Multichannel Method(SMC) to the study of electronically inelastic, low energy electron-molecule collisions. The focus of these studies has been the assessment of the importance of multichannel coupling to the dynamics of these excitation processes. It has transpired that the promising quality of results realized in early SMC work on such inelastic scattering processes has been far more difficult to obtain in these more sophisticated studies.

We have attempted to understand the sources of instability of the SMC method which are evident in these multichannel studies. Particular instances of such instability have been considered in detail, which indicate that linear dependence, failure of the separable potential approximation, and difficulties in converging matrix elements involving recorrelation or Q-space terms all conspire to complicate application of the SMC method to these studies. A method involving singular value decomposition(SVD) has been developed to, if not resolve these problems, at least mitigate their deleterious effects on the computation of electronically inelastic cross sections.

In conjunction with this SVD procedure, the SMC method has been applied to the study of the H_2 , H_2O, and N_2 molecules. Rydberg excitations of the first two molecules were found to be most sensitive to multichannel coupling near threshold. The (3σ_g → 1π_g ) and (1π_u → 1π_g) valence excitations of the N_2 molecule were found to be strongly influenced by the choice of channel coupling scheme at all collision energies considered in these studies.

On-chip integrated label-free optical biosensing

This thesis investigates the design and implementation of a label-free optical biosensing system utilizing a robust on-chip integrated platform. The goal has been to transition optical micro-resonator based label-free biosensing from a laborious and delicate laboratory demonstration to a tool for the analytical life scientist. This has been pursued along four avenues: (1) the design and fabrication of high-$Q$ integrated planar microdisk optical resonators in silicon nitride on silica, (2) the demonstration of a high speed optoelectronic swept frequency laser source, (3) the development and integration of a microfluidic analyte delivery system, and (4) the introduction of a novel differential measurement technique for the reduction of environmental noise.

The optical part of this system combines the results of two major recent developments in the field of optical and laser physics: the high-$Q$ optical resonator and the phase-locked electronically controlled swept-frequency semiconductor laser. The laser operates at a wavelength relevant for aqueous sensing, and replaces expensive and fragile mechanically-tuned laser sources whose frequency sweeps have limited speed, accuracy and reliability. The high-$Q$ optical resonator is part of a monolithic unit with an integrated optical waveguide, and is fabricated using standard semiconductor lithography methods. Monolithic integration makes the system significantly more robust and flexible compared to current, fragile embodiments that rely on the precarious coupling of fragile optical fibers to resonators. The silicon nitride on silica material system allows for future manifestations at shorter wavelengths. The sensor also includes an integrated microfluidic flow cell for precise and low volume delivery of analytes to the resonator surface. We demonstrate the refractive index sensing action of the system as well as the specific and nonspecific adsorption of proteins onto the resonator surface with high sensitivity. Measurement challenges due to environmental noise that hamper system performance are discussed and a differential sensing measurement is proposed, implemented, and demonstrated resulting in the restoration of a high performance sensing measurement.

The instrument developed in this work represents an adaptable and cost-effective platform capable of various sensitive, label-free measurements relevant to the study of biophysics, biomolecular interactions, cell signaling, and a wide range of other life science fields. Further development is necessary for it to be capable of binding assays, or thermodynamic and kinetics measurements; however, this work has laid the foundation for the demonstration of these applications.

Logarithmic Potential Theory on Riemann Surfaces

We develop a logarithmic potential theory on Riemann surfaces which generalizes logarithmic potential theory on the complex plane. We show the existence of an equilibrium measure and examine its structure. This leads to a formula for the structure of the equilibrium measure which is new even in the plane. We then use our results to study quadrature domains, Laplacian growth, and Coulomb gas ensembles on Riemann surfaces. We prove that the complement of the support of the equilibrium measure satisfies a quadrature identity. Furthermore, our setup allows us to naturally realize weak solutions of Laplacian growth (for a general time-dependent source) as an evolution of the support of equilibrium measures. When applied to the Riemann sphere this approach unifies the known methods for generating interior and exterior Laplacian growth. We later narrow our focus to a special class of quadrature domains which we call Algebraic Quadrature Domains. We show that many of the properties of quadrature domains generalize to this setting. In particular, the boundary of an Algebraic Quadrature Domain is the inverse image of a planar algebraic curve under a meromorphic function. This makes the study of the topology of Algebraic Quadrature Domains an interesting problem. We briefly investigate this problem and then narrow our focus to the study of the topology of classical quadrature domains. We extend the results of Lee and Makarov and prove (for n ≥ 3) c ≤ 5n-5, where c and n denote the connectivity and degree of a (classical) quadrature domain. At the same time we obtain a new upper bound on the number of isolated points of the algebraic curve corresponding to the boundary and thus a new upper bound on the number of special points. In the final chapter we study Coulomb gas ensembles on Riemann surfaces.