I. Non-linear effects in a self-consistent calculation of SU_3 symmetry breaking in strong interaction coupling constants. II. Direct-channel reggeization of strong interaction scattering amplitudes

The thesis is divided into two parts. Part I generalizes a self-consistent calculation of residue shifts from SU₃ symmetry, originally performed by Dashen, Dothan, Frautschi, and Sharp, to include the effects of non-linear terms. Residue factorizability is used to transform an overdetermined set of equations into a variational problem, which is designed to take advantage of the redundancy of the mathematical system. The solution of this problem automatically satisfies the requirement of factorizability and comes close to satisfying all the original equations.

Part II investigates some consequences of direct channel Regge poles and treats the problem of relating Reggeized partial wave expansions made in different reaction channels. An analytic method is introduced which can be used to determine the crossed-channel discontinuity for a large class of direct-channel Regge representations, and this method is applied to some specific representations.

It is demonstrated that the multi-sheeted analytic structure of the Regge trajectory function can be used to resolve apparent difficulties arising from infinitely rising Regge trajectories. Also discussed are the implications of large collections of "daughter trajectories."

Two things are of particular interest: first, the threshold behavior in direct and crossed channels; second, the potentialities of Reggeized representations for us in self-consistent calculations. A new representation is introduced which surpasses previous formulations in these two areas, automatically satisfying direct-channel threshold constraints while being capable of reproducing a reasonable crossed channel discontinuity. A scalar model is investigated for low energies, and a relation is obtained between the mass of the lowest bound state and the slope of the Regge trajectory.

Part 1: Longitudinal static and dynamic effects in semiconductor lasers. Part II: Spectral characteristics of passively mode-locked quantum well lasers

In the first part of this thesis a study of the effect of the longitudinal distribution of optical intensity and electron density on the static and dynamic behavior of semiconductor lasers is performed. A static model for above threshold operation of a single mode laser, consisting of multiple active and passive sections, is developed by calculating the longitudinal optical intensity distribution and electron density distribution in a self-consistent manner. Feedback from an index and gain Bragg grating is included, as well as feedback from discrete reflections at interfaces and facets. Longitudinal spatial holeburning is analyzed by including the dependence of the gain and the refractive index on the electron density. The mechanisms of spatial holeburning in quarter wave shifted DFB lasers are analyzed. A new laser structure with a uniform optical intensity distribution is introduced and an implementation is simulated, resulting in a large reduction of the longitudinal spatial holeburning effect.

A dynamic small-signal model is then developed by including the optical intensity and electron density distribution, as well as the dependence of the grating coupling coefficients on the electron density. Expressions are derived for the intensity and frequency noise spectrum, the spontaneous emission rate into the lasing mode, the linewidth enhancement factor, and the AM and FM modulation response. Different chirp components are identified in the FM response, and a new adiabatic chirp component is discovered. This new adiabatic chirp component is caused by the nonuniform longitudinal distributions, and is found to dominate at low frequencies. Distributed feedback lasers with partial gain coupling are analyzed, and it is shown how the dependence of the grating coupling coefficients on the electron density can result in an enhancement of the differential gain with an associated enhancement in modulation bandwidth and a reduction in chirp.

In the second part, spectral characteristics of passively mode-locked two-section multiple quantum well laser coupled to an external cavity are studied. Broad-band wavelength tuning using an external grating is demonstrated for the first time in passively mode-locked semiconductor lasers. A record tuning range of 26 nm is measured, with pulse widths of typically a few picosecond and time-bandwidth products of more than 10 times the transform limit. It is then demonstrated that these large time-bandwidth products are due to a strong linear upchirp, by performing pulse compression by a factor of 15 to a record pulse widths as low 320 fs.

A model for pulse propagation through a saturable medium with self-phase-modulation, due to the a-parameter, is developed for quantum well material, including the frequency dependence of the gain medium. This model is used to simulate two-section devices coupled to an external cavity. When no self-phase-modulation is present, it is found that the pulses are asymmetric with a sharper rising edge, that the pulse tails have an exponential behavior, and that the transform limit is 0.3. Inclusion of self-phase-modulation results in a linear upchirp imprinted on the pulse after each round-trip. This linear upchirp is due to a combination of self-phase-modulation in a gain section and absorption of the leading edge of the pulse in the saturable absorber.

Theory of ozone isotopic effects and various electron transfer reactions

Three separate topics, each stimulated by experiments, are treated theoretically in this dessertation: isotopic effects of ozone, electron transfer at interfaces, and intramolecular directional electron transfer in a supramolecular system.

The strange mass-independent isotope effect for the enrichment of ozone, which has been a puzzle in the literature for some 20 years, and the equally puzzling unconventional strong mass-dependent effect of individual reaction rate constants are studied as different aspects of a symmetry-driven behavior. A statistical (RRKM-based) theory with a hindered-rotor transition state is used. The individual rate constant ratios of recombination reactions at low pressures are calculated using the theory involving (1) small deviation from the statistical density of states for symmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. The weak collision and partitioning among exit channels play major roles in producing the large unconventional isotope effect in "unscrambled" systems. The enrichment studies reflect instead the non-statistical effect in "scrambled" systems. The theoretical results of low-pressure ozone enrichments and individual rate constant ratios obtained from these calculations are consistent with the corresponding experimental results. The isotopic exchange rate constant for the reaction ^(16)O + ^(18)O ^(18)O→+ ^(16)O ^(18)O + ^(18)O provides information on the nature of a variationally determined hindered-rotor transition state using experimental data at 130 K and 300 K. Pressure effects on the recombination rate constant, on the individual rate constant ratios and on the enrichments are also investigated. The theoretical results are consistent with the experimental data. The temperature dependence of the enrichment and rate constant ratios is also discussed, and experimental tests are suggested. The desirability of a more accurate potential energy surface for ozone in the transition state region is also noted.

Electron transfer reactions at semiconductor /liquid interfaces are studied using a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the tight-binding electronic structures of semiconductors having surfaces. The maximum electron transfer rate constants at Si/viologen^(2-/+) and InP /Me_(2)Fc^(+/O) interfaces are computed using the tight-binding type calculations for the solid and the extended-Huckel for the coupling to the redox agent at the interface. These electron transfer reactions are also studied using a free electron model for the semiconductor and the redox molecule, where Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states. The calculated results for maximum rate constant of the electron transfer from the semiconductor bulk states are compared with the experimentally measured values of Lewis and coworkers, and are in reasonable agreement, without adjusting parameters. In the case of InP /liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states.

Photoinduced electron transfer reactions in small supramolecular systems, such as 4-aminonaphthalimide compounds, are interesting in that there are, in principle, two alternative pathways (directions) for the electron transfer. The electron transfer, however, is unidirectional, as deduced from pH-dependent fluorescence quenching studies on different compounds. The role of electronic coupling matrix element and the charges in protonation are considered to explain the directionality of the electron transfer and other various results. A related mechanism is proposed to interpret the fluorescence behavior of similar molecules as fluorescent sensors of metal ions.

Boundary-layer transition on a slender cone in hypervelocity flow with real gas effects

The laminar to turbulent transition process in boundary layer flows in thermochemical nonequilibrium at high enthalpy is measured and characterized. Experiments are performed in the T5 Hypervelocity Reflected Shock Tunnel at Caltech, using a 1 m length 5-degree half angle axisymmetric cone instrumented with 80 fast-response annular thermocouples, complemented by boundary layer stability computations using the STABL software suite. A new mixing tank is added to the shock tube fill apparatus for premixed freestream gas experiments, and a new cleaning procedure results in more consistent transition measurements. Transition location is nondimensionalized using a scaling with the boundary layer thickness, which is correlated with the acoustic properties of the boundary layer, and compared with parabolized stability equation (PSE) analysis. In these nondimensionalized terms, transition delay with increasing CO₂ concentration is observed: tests in 100% and 50% CO₂, by mass, transition up to 25% and 15% later, respectively, than air experiments. These results are consistent with previous work indicating that CO₂ molecules at elevated temperatures absorb acoustic instabilities in the MHz range, which is the expected frequency of the Mack second-mode instability at these conditions, and also consistent with predictions from PSE analysis. A strong unit Reynolds number effect is observed, which is believed to arise from tunnel noise. N_Tr for air from 5.4 to 13.2 is computed, substantially higher than previously reported for noisy facilities. Time- and spatially-resolved heat transfer traces are used to track the propagation of turbulent spots, and convection rates at 90%, 76%, and 63% of the boundary layer edge velocity, respectively, are observed for the leading edge, centroid, and trailing edge of the spots. A model constructed with these spot propagation parameters is used to infer spot generation rates from measured transition onset to completion distance. Finally, a novel method to control transition location with boundary layer gas injection is investigated. An appropriate porous-metal injector section for the cone is designed and fabricated, and the efficacy of injected CO₂ for delaying transition is gauged at various mass flow rates, and compared with both no injection and chemically inert argon injection cases. While CO₂ injection seems to delay transition, and argon injection seems to promote it, the experimental results are inconclusive and matching computations do not predict a reduction in N factor from any CO₂ injection condition computed.

Effects of self energy of the ions on the double layer structure and properties at the dielectric interface

Although numerous theoretical efforts have been put forth, a systematic, unified and predictive theoretical framework that is able to capture all the essential physics of the interfacial behaviors of ions, such as the Hofmeister series effect, Jones-Ray effect and the salt effect on the bubble coalescence remain an outstanding challenge. The most common approach to treating electrostatic interactions in the presence of salt ions is the Poisson-Boltzmann (PB) theory. However, there are many systems for which the PB theory fails to offer even a qualitative explanation of the behavior, especially for ions distributed in the vicinity of an interface with dielectric contrast between the two media (like the water-vapor/oil interface). A key factor missing in the PB theory is the self energy of the ion.

In this thesis, we develop a self-consistent theory that treats the electrostatic self energy (including both the short-range Born solvation energy and the long-range image charge interactions), the nonelectrostatic contribution of the self energy, the ion-ion correlation and the screening effect systematically in a single framework. By assuming a finite charge spread of the ion instead of using the point-charge model, the self energy obtained by our theory is free of the divergence problems and gives a continuous self energy across the interface. This continuous feature allows ions on the water side and the vapor/oil side of the interface to be treated in a unified framework. The theory involves a minimum set of parameters of the ion, such as the valency, radius, polarizability of the ions, and the dielectric constants of the medium, that are both intrinsic and readily available. The general theory is first applied to study the thermodynamic property of the bulk electrolyte solution, which shows good agreement with the experiment result for predicting the activity coefficient and osmotic coefficient.

Next, we address the effect of local Born solvation energy on the bulk thermodynamics and interfacial properties of electrolyte solution mixtures. We show that difference in the solvation energy between the cations and anions naturally gives rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The miscibility of the mixture can either increases or decreases depending on the competition between the solvation energy and translation entropy of the ions. The interfacial tension shows a non-monotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations, and decreases approximately as the square root of the salt concentration for dilute solutions, which is in agreement with the Jones-Ray effect observed in experiment.

Next, we investigate the image effects on the double layer structure and interfacial properties near a single charged plate. We show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. The image charge effect is then studied for electrolyte solutions between two plates. For two neutral plates, we show that depletion of the salt ions by the image charge repulsion results in short-range attractive and long-range repulsive forces. If cations and anions are of different valency, the asymmetric depletion leads to the formation of an induced electrical double layer. For two charged plates, the competition between the surface charge and the image charge effect can give rise to like- charge attraction.

Then, we study the inhomogeneous screening effect near the dielectric interface due to the anisotropic and nonuniform ion distribution. We show that the double layer structure and interfacial properties is drastically affected by the inhomogeneous screening if the bulk Debye screening length is comparable or smaller than the Bjerrum length. The width of the depletion layer is characterized by the Bjerrum length, independent of the salt concentration. We predict that the negative adsorption of ions at the interface increases linearly with the salt concentration, which cannot be captured by either the bulk screening approximation or the WKB approximation. For asymmetric salt, the inhomogeneous screening enhances the charge separation in the induced double layer and significantly increases the value of the surface potential.

Finally, to account for the ion specificity, we study the self energy of a single ion across the dielectric interface. The ion is considered to be polarizable: its charge distribution can be self-adjusted to the local dielectric environment to minimize the self energy. Using intrinsic parameters of the ions, such as the valency, radius, and polarizability, we predict the specific ion effect on the interfacial affinity of halogen anions at the water/air interface, and the strong adsorption of hydrophobic ions at the water/oil interface, in agreement with experiments and atomistic simulations.

The theory developed in this work represents the most systematic theoretical technique for weak-coupling electrolytes. We expect the theory to be more useful for studying a wide range of structural and dynamic properties in physicochemical, colloidal, soft-matter and biophysical systems.

Experimental study on inertial effects in liquid-solid flows

This thesis presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Reynolds (defined by the shear rate and particle diameter) and Stokes numbers, ranging from 3 ≤ Re ≤ 1.6 × 10³ and 0.4 ≤ St ≤ 195. The experiments use a specifically designed Couette cylindrical rheometer that allows for probing the transition from transporting a pure liquid to transporting a dense suspension of particles. Measurements of the shear stress are presented for a wide range of particle concentration (10 to 60% in volume) and for particle to fluid density ratio between 1 and 1.05. The effective relative viscosity exhibits a strong dependence on the solid fraction for all density ratios tested. For density ratio of 1 the effective viscosity increases with Stokes number (St) for volume fractions (φ) lower than 40% and becomes constant for higher φ. When the particles are denser than the liquid, the effective viscosity shows a stronger dependance on St. An analysis of the particle resuspension for the case with a density ratio of 1.05 is presented and used to predict the local volume fraction where the shear stress measurements take place. When the local volume fraction is considered, the effective viscosity for settling and no settling particles is consistent, indicating that the effective viscosity is independent of differences in density between the solid and liquid phase. Shear stress measurements of pure fluids (no particles) were performed using the same rheometer, and a deviation from laminar behavior is observed for gap Reynolds numbers above 4× 10³, indicating the presence of hydrodynamic instabilities associated with the rotation of the outer cylinder. The increase on the effective viscosity with Stokes numbers observed for mixtures with φ ≤ 30% appears to be affected by such hydrodynamic instabilities. The effective viscosity for the current experiments is considerably higher than the one reported in non-inertial suspensions.

Magnetic field and pressure effects in a saturated gas laser amplifier

Theoretical and experimental studies of a gas laser amplifier are presented, assuming the amplifier is operating with a saturating optical frequency signal. The analysis is primarily concerned with the effects of the gas pressure and the presence of an axial magnetic field on the characteristics of the amplifying medium. Semiclassical radiation theory is used, along with a density matrix description of the atomic medium which relates the motion of single atoms to the macroscopic observables. A two-level description of the atom, using phenomenological source rates and decay rates, forms the basis of our analysis of the gas laser medium. Pressure effects are taken into account to a large extent through suitable choices of decay rate parameters.

Two methods for calculating the induced polarization of the atomic medium are used. The first method utilizes a perturbation expansion which is valid for signal intensities which barely reach saturation strength, and it is quite general in applicability. The second method is valid for arbitrarily strong signals, but it yields tractable solutions only for zero magnetic field or for axial magnetic fields large enough such that the Zeeman splitting is much larger than the power broadened homogeneous linewidth of the laser transition. The effects of pressure broadening of the homogeneous spectral linewidth are included in both the weak-signal and strong-signal theories; however the effects of Zeeman sublevel-mixing collisions are taken into account only in the weak-signal theory.

The behavior of a He-Ne gas laser amplifier in the presence of an axial magnetic field has been studied experimentally by measuring gain and Faraday rotation of linearly polarized resonant laser signals for various values of input signal intensity, and by measuring nonlinearity - induced anisotropy for elliptically polarized resonant laser signals of various input intensities. Two high-gain transitions in the 3.39-μ region were used for study: a J = 1 to J = 2 (3s₂ → 3p₄) transition and a J = 1 to J = 1 (3s₂ → 3p₂) transition. The input signals were tuned to the centers of their respective resonant gain lines.

The experimental results agree quite well with corresponding theoretical expressions which have been developed to include the nonlinear effects of saturation strength signals. The experimental results clearly show saturation of Faraday rotation, and for the J = 1 t o J = 1 transition a Faraday rotation reversal and a traveling wave gain dip are seen for small values of axial magnetic field. The nonlinearity induced anisotropy shows a marked dependence on the gas pressure in the amplifier tube for the J = 1 to J = 2 transition; this dependence agrees with the predictions of the general perturbational or weak signal theory when allowances are made for the effects of Zeeman sublevel-mixing collisions. The results provide a method for measuring the upper (neon 3s₂) level quadrupole moment decay rate, the dipole moment decay rates for the 3s₂ → 3p₄ and 3s₂ → 3p₂ transitions, and the effects of various types of collision processes on these decay rates.

A theory of strong and weak scintillations with applications to astrophysics

The propagation of waves in an extended, irregular medium is studied under the "quasi-optics" and the "Markov random process" approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of the moment equations with different transverse coordinates and different wavenumbers is then obtained from the characteristic functional. The derivation does not require Gaussian statistics of the random medium and the result can be applied to the time-dependent problem. We then solve the moment equations for the phase correlation function, angular broadening, temporal pulse smearing, intensity correlation function, and the probability distribution of the random waves. The necessary and sufficient conditions for strong scintillation are also given.

We also consider the problem of diffraction of waves by a random, phase-changing screen. The intensity correlation function is solved in the whole Fresnel diffraction region and the temporal pulse broadening function is derived rigorously from the wave equation.

The method of smooth perturbations is applied to interplanetary scintillations. We formulate and calculate the effects of the solar-wind velocity fluctuations on the observed intensity power spectrum and on the ratio of the observed "pattern" velocity and the true velocity of the solar wind in the three-dimensional spherical model. The r.m.s. solar-wind velocity fluctuations are found to be ~200 km/sec in the region about 20 solar radii from the Sun.

We then interpret the observed interstellar scintillation data using the theories derived under the Markov approximation, which are also valid for the strong scintillation. We find that the Kolmogorov power-law spectrum with an outer scale of 10 to 100 pc fits the scintillation data and that the ambient averaged electron density in the interstellar medium is about 0.025 cm^-3. It is also found that there exists a region of strong electron density fluctuation with thickness ~10 pc and mean electron density ~7 cm^-3 between the PSR 0833-45 pulsar and the earth.

Investigation of strong earthquake ground motion

The pattern of energy release during the Imperial Valley, California, earthquake of 1940 is studied by analysing the El Centro strong motion seismograph record and records from the Tinemaha seismograph station, 546 km from the epicenter. The earthquake was a multiple event sequence with at least 4 events recorded at El Centro in the first 25 seconds, followed by 9 events recorded in the next 5 minutes. Clear P, S and surface waves were observed on the strong motion record. Although the main part of the earthquake energy was released during the first 15 seconds, some of the later events were as large as M = 5.8 and thus are important for earthquake engineering studies. The moment calculated using Fourier analysis of surface waves agrees with the moment estimated from field measurements of fault offset after the earthquake. The earthquake engineering significance of the complex pattern of energy release is discussed. It is concluded that a cumulative increase in amplitudes of building vibration resulting from the present sequence of shocks would be significant only for structures with relatively long natural period of vibration. However, progressive weakening effects may also lead to greater damage for multiple event earthquakes.

The model with surface Love waves propagating through a single layer as a surface wave guide is studied. It is expected that the derived properties for this simple model illustrate well several phenomena associated with strong earthquake ground motion. First, it is shown that a surface layer, or several layers, will cause the main part of the high frequency energy, radiated from the nearby earthquake, to be confined to the layer as a wave guide. The existence of the surface layer will thus increase the rate of the energy transfer into the man-made structures on or near the surface of the layer. Secondly, the surface amplitude of the guided SH waves will decrease if the energy of the wave is essentially confined to the layer and if the wave propagates towards an increasing layer thickness. It is also shown that the constructive interference of SH waves will cause the zeroes and the peaks in the Fourier amplitude spectrum of the surface ground motion to be continuously displaced towards the longer periods as the distance from the source of the energy release increases.

Classical and Quantum Effects in Plasmonic Metals

The field of plasmonics exploits the unique optical properties of metallic nanostructures to concentrate and manipulate light at subwavelength length scales. Metallic nanostructures get their unique properties from their ability to support surface plasmons– coherent wave-like oscillations of the free electrons at the interface between a conductive and dielectric medium. Recent advancements in the ability to fabricate metallic nanostructures with subwavelength length scales have created new possibilities in technology and research in a broad range of applications.

In the first part of this thesis, we present two investigations of the relationship between the charge state and optical state of plasmonic metal nanoparticles. Using experimental bias-dependent extinction measurements, we derive a potential- dependent dielectric function for Au nanoparticles that accounts for changes in the physical properties due to an applied bias that contribute to the optical extinction. We also present theory and experiment for the reverse effect– the manipulation of the carrier density of Au nanoparticles via controlled optical excitation. This plasmoelectric effect takes advantage of the strong resonant properties of plasmonic materials and the relationship between charge state and optical properties to eluci- date a new avenue for conversion of optical power to electrical potential.

The second topic of this thesis is the non-radiative decay of plasmons to a hot-carrier distribution, and the distribution’s subsequent relaxation. We present first-principles calculations that capture all of the significant microscopic mechanisms underlying surface plasmon decay and predict the initial excited carrier distributions so generated. We also preform ab initio calculations of the electron-temperature dependent heat capacities and electron-phonon coupling coefficients of plasmonic metals. We extend these first-principle methods to calculate the electron-temperature dependent dielectric response of hot electrons in plasmonic metals, including direct interband and phonon-assisted intraband transitions. Finally, we combine these first-principles calculations of carrier dynamics and optical response to produce a complete theoretical description of ultrafast pump-probe measurements, free of any fitting parameters that are typical in previous analyses.