Horizontal Bloch line motion in magnetic bubble materials

The purpose of this work is to extend experimental and theoretical understanding of horizontal Bloch line (HBL) motion in magnetic bubble materials. The present theory of HBL motion is reviewed, and then extended to include transient effects in which the internal domain wall structure changes with time. This is accomplished by numerically solving the equations of motion for the internal azimuthal angle ɸ and the wall position q as functions of z, the coordinate perpendicular to the thin-film material, and time. The effects of HBL's on domain wall motion are investigated by comparing results from wall oscillation experiments with those from the theory. In these experiments, a bias field pulse is used to make a step change in equilibrium position of either bubble or stripe domain walls, and the wall response is measured by using transient photography. During the initial response, the dynamic wall structure closely resembles the initial static structure. The wall accelerates to a relatively high velocity (≈20 m/sec), resulting in a short (≈22 nsec ) section of initial rapid motion. An HBL gradually forms near one of the film surfaces as a result of local dynamic properties, and moves along the wall surface toward the film center. The presence of this structure produces low-frequency, triangular-shaped oscillations in which the experimental wall velocity is nearly constant, v_s≈ 5-8 m/sec. If the HBL reaches the opposite surface, i.e., if the average internal angle reaches an integer multiple of π, the momentum stored in the HBL is lost, and the wall chirality is reversed. This results in abrupt transitions to overdamped motion and changes in wall chirality, which are observed as a function of bias pulse amplitude. The pulse amplitude at which the n^th punch- through occurs just as the wall reaches equilibrium is given within 0.2 0e by H_n = (2v_sH'/γ)^1/2 • (nπ)^1/2 + H_sv), where H' is the effective field gradient from the surrounding domains, and H_sv is a small (less than 0.03 0e), effective drag field. Observations of wall oscillation in the presence of in-plane fields parallel to the wall show that HBL formation is suppressed by fields greater than about 40 0e (≈2πM_s), resulting in the high-frequency, sinusoidal oscillations associated with a simple internal wall structure.

Teleseismic array analysis of upper mantle compressional velocity structure

Large quantities of teleseismic short-period seismograms recorded at SCARLET provide travel time, apparent velocity and waveform data for study of upper mantle compressional velocity structure. Relative array analysis of arrival times from distant (30° < Δ < 95°) earthquakes at all azimuths constrains lateral velocity variations beneath southern California. We compare dT/dΔ back azimuth and averaged arrival time estimates from the entire network for 154 events to the same parameters derived from small subsets of SCARLET. Patterns of mislocation vectors for over 100 overlapping subarrays delimit the spatial extent of an east-west striking, high-velocity anomaly beneath the Transverse Ranges. Thin lens analysis of the averaged arrival time differences, called 'net delay' data, requires the mean depth of the corresponding lens to be more than 100 km. Our results are consistent with the PKP-delay times of Hadley and Kanamori (1977), who first proposed the high-velocity feature, but we place the anomalous material at substantially greater depths than their 40-100 km estimate.

Detailed analysis of travel time, ray parameter and waveform data from 29 events occurring in the distance range 9° to 40° reveals the upper mantle structure beneath an oceanic ridge to depths of over 900 km. More than 1400 digital seismograms from earthquakes in Mexico and Central America yield 1753 travel times and 58 dT/dΔ measurements as well as high-quality, stable waveforms for investigation of the deep structure of the Gulf of California. The result of a travel time inversion with the tau method (Bessonova et al., 1976) is adjusted to fit the p(Δ) data, then further refined by incorporation of relative amplitude information through synthetic seismogram modeling. The application of a modified wave field continuation method (Clayton and McMechan, 1981) to the data with the final model confirms that GCA is consistent with the entire data set and also provides an estimate of the data resolution in velocity-depth space. We discover that the upper mantle under this spreading center has anomalously slow velocities to depths of 350 km, and place new constraints on the shape of the 660 km discontinuity.

Seismograms from 22 earthquakes along the northeast Pacific rim recorded in southern California form the data set for a comparative investigation of the upper mantle beneath the Cascade Ranges-Juan de Fuca region, an ocean-continent transit ion. These data consist of 853 seismograms (6° < Δ < 42°) which produce 1068 travel times and 40 ray parameter estimates. We use the spreading center model initially in synthetic seismogram modeling, and perturb GCA until the Cascade Ranges data are matched. Wave field continuation of both data sets with a common reference model confirms that real differences exist between the two suites of seismograms, implying lateral variation in the upper mantle. The ocean-continent transition model, CJF, features velocities from 200 and 350 km that are intermediate between GCA and T7 (Burdick and Helmberger, 1978), a model for the inland western United States. Models of continental shield regions (e.g., King and Calcagnile, 1976) have higher velocities in this depth range, but all four model types are similar below 400 km. This variation in rate of velocity increase with tectonic regime suggests an inverse relationship between velocity gradient and lithospheric age above 400 km depth.

Part I. A study of the velocity structure of the earth by the use of core phases. Part II. The 1971 San Fernando earthquake series focal mechanisms and tectonics

The initial objective of Part I was to determine the nature of upper mantle discontinuities, the average velocities through the mantle, and differences between mantle structure under continents and oceans by the use of P'dP', the seismic core phase P'P' (PKPPKP) that reflects at depth d in the mantle. In order to accomplish this, it was found necessary to also investigate core phases themselves and their inferences on core structure. P'dP' at both single stations and at the LASA array in Montana indicates that the following zones are candidates for discontinuities with varying degrees of confidence: 800-950 km, weak; 630-670 km, strongest; 500-600 km, strong but interpretation in doubt; 350-415 km, fair; 280-300 km, strong, varying in depth; 100-200 km, strong, varying in depth, may be the bottom of the low-velocity zone. It is estimated that a single station cannot easily discriminate between asymmetric P'P' and P'dP' for lead times of about 30 sec from the main P'P' phase, but the LASA array reduces this uncertainty range to less than 10 sec. The problems of scatter of P'P' main-phase times, mainly due to asymmetric P'P', incorrect identification of the branch, and lack of the proper velocity structure at the velocity point, are avoided and the analysis shows that one-way travel of P waves through oceanic mantle is delayed by 0.65 to 0.95 sec relative to United States mid-continental mantle.

A new P-wave velocity core model is constructed from observed times, dt/dΔ's, and relative amplitudes of P'; the observed times of SKS, SKKS, and PKiKP; and a new mantle-velocity determination by Jordan and Anderson. The new core model is smooth except for a discontinuity at the inner-core boundary determined to be at a radius of 1215 km. Short-period amplitude data do not require the inner core Q to be significantly lower than that of the outer core. Several lines of evidence show that most, if not all, of the arrivals preceding the DF branch of P' at distances shorter than 143° are due to scattering as proposed by Haddon and not due to spherically symmetric discontinuities just above the inner core as previously believed. Calculation of the travel-time distribution of scattered phases and comparison with published data show that the strongest scattering takes place at or near the core-mantle boundary close to the seismic station.

In Part II, the largest events in the San Fernando earthquake series, initiated by the main shock at 14 00 41.8 GMT on February 9, 1971, were chosen for analysis from the first three months of activity, 87 events in all. The initial rupture location coincides with the lower, northernmost edge of the main north-dipping thrust fault and the aftershock distribution. The best focal mechanism fit to the main shock P-wave first motions constrains the fault plane parameters to: strike, N 67° (± 6°) W; dip, 52° (± 3°) NE; rake, 72° (67°-95°) left lateral. Focal mechanisms of the aftershocks clearly outline a downstep of the western edge of the main thrust fault surface along a northeast-trending flexure. Faulting on this downstep is left-lateral strike-slip and dominates the strain release of the aftershock series, which indicates that the downstep limited the main event rupture on the west. The main thrust fault surface dips at about 35° to the northeast at shallow depths and probably steepens to 50° below a depth of 8 km. This steep dip at depth is a characteristic of other thrust faults in the Transverse Ranges and indicates the presence at depth of laterally-varying vertical forces that are probably due to buckling or overriding that causes some upward redirection of a dominant north-south horizontal compression. Two sets of events exhibit normal dip-slip motion with shallow hypocenters and correlate with areas of ground subsidence deduced from gravity data. Several lines of evidence indicate that a horizontal compressional stress in a north or north-northwest direction was added to the stresses in the aftershock area 12 days after the main shock. After this change, events were contained in bursts along the downstep and sequencing within the bursts provides evidence for an earthquake-triggering phenomenon that propagates with speeds of 5 to 15 km/day. Seismicity before the San Fernando series and the mapped structure of the area suggest that the downstep of the main fault surface is not a localized discontinuity but is part of a zone of weakness extending from Point Dume, near Malibu, to Palmdale on the San Andreas fault. This zone is interpreted as a decoupling boundary between crustal blocks that permits them to deform separately in the prevalent crustal-shortening mode of the Transverse Ranges region.

Digested sludge: delineation and modeling for ocean disposal

Experimental work was performed to delineate the system of digested sludge particles and associated trace metals and also to measure the interactions of sludge with seawater. Particle-size and particle number distributions were measured with a Coulter Counter. Number counts in excess of 10¹² particles per liter were found in both the City of Los Angeles Hyperion mesophilic digested sludge and the Los Angeles County Sanitation Districts (LACSD) digested primary sludge. More than 90 percent of the particles had diameters less than 10 microns.

Total and dissolved trace metals (Ag, Cd, Cr, Cu, Fe, Mn, Ni, Pb, and Zn) were measured in LACSD sludge. Manganese was the only metal whose dissolved fraction exceeded one percent of the total metal. Sedimentation experiments for several dilutions of LACSD sludge in seawater showed that the sedimentation velocities of the sludge particles decreased as the dilution factor increased. A tenfold increase in dilution shifted the sedimentation velocity distribution by an order of magnitude. Chromium, Cu, Fe, Ni, Pb, and Zn were also followed during sedimentation. To a first approximation these metals behaved like the particles.

Solids and selected trace metals (Cr, Cu, Fe, Ni, Pb, and Zn) were monitored in oxic mixtures of both Hyperion and LACSD sludges for periods of 10 to 28 days. Less than 10 percent of the filterable solids dissolved or were oxidized. Only Ni was mobilized away from the particles. The majority of the mobilization was complete in less than one day.

The experimental data of this work were combined with oceanographic, biological, and geochemical information to propose and model the discharge of digested sludge to the San Pedro and Santa Monica Basins. A hydraulic computer simulation for a round buoyant jet in a density stratified medium showed that discharges of sludge effluent mixture at depths of 730 m would rise no more than 120 m. Initial jet mixing provided dilution estimates of 450 to 2600. Sedimentation analyses indicated that the solids would reach the sediments within 10 km of the point discharge.

Mass balances on the oxidizable chemical constituents in sludge indicated that the nearly anoxic waters of the basins would become wholly anoxic as a result of proposed discharges. From chemical-equilibrium computer modeling of the sludge digester and dilutions of sludge in anoxic seawater, it was predicted that the chemistry of all trace metals except Cr and Mn will be controlled by the precipitation of metal sulfide solids. This metal speciation held for dilutions up to 3000.

The net environmental impacts of this scheme should be salutary. The trace metals in the sludge should be immobilized in the anaerobic bottom sediments of the basins. Apparently no lifeforms higher than bacteria are there to be disrupted. The proposed deep-water discharges would remove the need for potentially expensive and energy-intensive land disposal alternatives and would end the discharge to the highly productive water near the ocean surface.

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.

Velocity resolved - scalar modeled simulations of high Schmidt number turbulent transport

The objective of this thesis is to develop a framework to conduct velocity resolved - scalar modeled (VR-SM) simulations, which will enable accurate simulations at higher Reynolds and Schmidt (Sc) numbers than are currently feasible. The framework established will serve as a first step to enable future simulation studies for practical applications. To achieve this goal, in-depth analyses of the physical, numerical, and modeling aspects related to Sc>>1 are presented, specifically when modeling in the viscous-convective subrange. Transport characteristics are scrutinized by examining scalar-velocity Fourier mode interactions in Direct Numerical Simulation (DNS) datasets and suggest that scalar modes in the viscous-convective subrange do not directly affect large-scale transport for high Sc. Further observations confirm that discretization errors inherent in numerical schemes can be sufficiently large to wipe out any meaningful contribution from subfilter models. This provides strong incentive to develop more effective numerical schemes to support high Sc simulations. To lower numerical dissipation while maintaining physically and mathematically appropriate scalar bounds during the convection step, a novel method of enforcing bounds is formulated, specifically for use with cubic Hermite polynomials. Boundedness of the scalar being transported is effected by applying derivative limiting techniques, and physically plausible single sub-cell extrema are allowed to exist to help minimize numerical dissipation. The proposed bounding algorithm results in significant performance gain in DNS of turbulent mixing layers and of homogeneous isotropic turbulence. Next, the combined physical/mathematical behavior of the subfilter scalar-flux vector is analyzed in homogeneous isotropic turbulence, by examining vector orientation in the strain-rate eigenframe. The results indicate no discernible dependence on the modeled scalar field, and lead to the identification of the tensor-diffusivity model as a good representation of the subfilter flux. Velocity resolved - scalar modeled simulations of homogeneous isotropic turbulence are conducted to confirm the behavior theorized in these a priori analyses, and suggest that the tensor-diffusivity model is ideal for use in the viscous-convective subrange. Simulations of a turbulent mixing layer are also discussed, with the partial objective of analyzing Schmidt number dependence of a variety of scalar statistics. Large-scale statistics are confirmed to be relatively independent of the Schmidt number for Sc>>1, which is explained by the dominance of subfilter dissipation over resolved molecular dissipation in the simulations. Overall, the VR-SM framework presented is quite effective in predicting large-scale transport characteristics of high Schmidt number scalars, however, it is determined that prediction of subfilter quantities would entail additional modeling intended specifically for this purpose. The VR-SM simulations presented in this thesis provide us with the opportunity to overlap with experimental studies, while at the same time creating an assortment of baseline datasets for future validation of LES models, thereby satisfying the objectives outlined for this work.

The influence of freestream turbulence, freestream nuclei populations and a drag-reducing polymer on cavitation inception on two axisymmetric bodies

The influence upon the basic viscous flow about two axisymmetric bodies of (i) freestream turbulence level and (ii) the injection of small amounts of a drag-reducing polymer (Polyox WSR 301) into the test model boundary layer was investigated by the schlieren flow visualization technique. The changes in the type and occurrence of cavitation inception caused by the subsequent modifications in the viscous flow were studied. A nuclei counter using the holographic technique was built to monitor freestream nuclei populations and a few preliminary tests investigating the consequences of different populations on cavitation inception were carried out.

Both test models were observed to have a laminar separation over their respective test Reynolds number ranges. The separation on one test model was found to be insensitive to freestream turbulence levels of up to 3.75 percent. The second model was found to be very susceptible having its critical velocity reduced from 30 feet per second at a 0.04 percent turbulence level to 10 feet per second at a 3.75 percent turbulence level. Cavitation tests on both models at the lowest turbulence level showed the value of the incipient cavitation number and the type of cavitation were controlled by the presence of the laminar separation. Cavitation tests on the second model at 0.65 percent turbulence level showed no change in the inception index, but the appearance of the developed cavitation was altered.

The presence of Polyox in the boundary layer resulted in a cavitation suppression comparable to that found by other investigators. The elimination of the normally occurring laminar separation on these bodies by a polymer-induced instability in the laminar boundary layer was found to be responsible for the suppression of inception.

Freestream nuclei populations at test conditions were measured and it was found that if there were many freestream gas bubbles the normally present laminar separation was elminated and travelling bubble type cavitation occurred - the value of the inception index then depended upon the nuclei population. In cases where the laminar separation was present it was found that the value of the inception index was insensitive to the free stream nuclei populations.

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.

Simulation of shock-induced bubble collapse with application to vascular injury in shockwave lithotripsy

Shockwave lithotripsy is a noninvasive medical procedure wherein shockwaves are repeatedly focused at the location of kidney stones in order to pulverize them. Stone comminution is thought to be the product of two mechanisms: the propagation of stress waves within the stone and cavitation erosion. However, the latter mechanism has also been implicated in vascular injury. In the present work, shock-induced bubble collapse is studied in order to understand the role that it might play in inducing vascular injury. A high-order accurate, shock- and interface-capturing numerical scheme is developed to simulate the three-dimensional collapse of the bubble in both the free-field and inside a vessel phantom. The primary contributions of the numerical study are the characterization of the shock-bubble and shock-bubble-vessel interactions across a large parameter space that includes clinical shockwave lithotripsy pressure amplitudes, problem geometry and tissue viscoelasticity, and the subsequent correlation of these interactions to vascular injury. Specifically, measurements of the vessel wall pressures and displacements, as well as the finite strains in the fluid surrounding the bubble, are utilized with available experiments in tissue to evaluate damage potential. Estimates are made of the smallest injurious bubbles in the microvasculature during both the collapse and jetting phases of the bubble's life cycle. The present results suggest that bubbles larger than 1 μm in diameter could rupture blood vessels under clinical SWL conditions.

I. The Superstition Hills, California, earthquakes of 24 November 1987. II. Three-dimensional velocity structure of southern California.

Part 1 of this thesis is about the 24 November, 1987, Superstition Hills earthquakes. The Superstition Hills earthquakes occurred in the western Imperial Valley in southern California. The earthquakes took place on a conjugate fault system consisting of the northwest-striking right-lateral Superstition Hills fault and a previously unknown Elmore Ranch fault, a northeast-striking left-lateral structure defined by surface rupture and a lineation of hypocenters. The earthquake sequence consisted of foreshocks, the M_s 6.2 first main shock, and aftershocks on the Elmore Ranch fault followed by the M_s 6.6 second main shock and aftershocks on the Superstition Hills fault. There was dramatic surface rupture along the Superstition Hills fault in three segments: the northern segment, the southern segment, and the Wienert fault.

In Chapter 2, M_L≥4.0 earthquakes from 1945 to 1971 that have Caltech catalog locations near the 1987 sequence are relocated. It is found that none of the relocated earthquakes occur on the southern segment of the Superstition Hills fault and many occur at the intersection of the Superstition Hills and Elmore Ranch faults. Also, some other northeast-striking faults may have been active during that time.

Chapter 3 discusses the Superstition Hills earthquake sequence using data from the Caltech-U.S.G.S. southern California seismic array. The earthquakes are relocated and their distribution correlated to the type and arrangement of the basement rocks. The larger earthquakes occur only where continental crystalline basement rocks are present. The northern segment of the Superstition Hills fault has more aftershocks than the southern segment.

An inversion of long period teleseismic data of the second mainshock of the 1987 sequence, along the Superstition Hills fault, is done in Chapter 4. Most of the long period seismic energy seen teleseismically is radiated from the southern segment of the Superstition Hills fault. The fault dip is near vertical along the northern segment of the fault and steeply southwest dipping along the southern segment of the fault.

Chapter 5 is a field study of slip and afterslip measurements made along the Superstition Hills fault following the second mainshock. Slip and afterslip measurements were started only two hours after the earthquake. In some locations, afterslip more than doubled the coseismic slip. The northern and southern segments of the Superstition Hills fault differ in the proportion of coseismic and postseismic slip to the total slip.

The northern segment of the Superstition Hills fault had more aftershocks, more historic earthquakes, released less teleseismic energy, and had a smaller proportion of afterslip to total slip than the southern segment. The boundary between the two segments lies at a step in the basement that separates a deeper metasedimentary basement to the south from a shallower crystalline basement to the north.

Part 2 of the thesis deals with the three-dimensional velocity structure of southern California. In Chapter 7, an a priori three-dimensional crustal velocity model is constructed by partitioning southern California into geologic provinces, with each province having a consistent one-dimensional velocity structure. The one-dimensional velocity structures of each region were then assembled into a three-dimensional model. The three-dimension model was calibrated by forward modeling of explosion travel times.

In Chapter 8, the three-dimensional velocity model is used to locate earthquakes. For about 1000 earthquakes relocated in the Los Angeles basin, the three-dimensional model has a variance of the the travel time residuals 47 per cent less than the catalog locations found using a standard one-dimensional velocity model. Other than the 1987 Whittier earthquake sequence, little correspondence is seen between these earthquake locations and elements of a recent structural cross section of the Los Angeles basin. The Whittier sequence involved rupture of a north dipping thrust fault bounded on at least one side by a strike-slip fault. The 1988 Pasadena earthquake was deep left-lateral event on the Raymond fault. The 1989 Montebello earthquake was a thrust event on a structure similar to that on which the Whittier earthquake occurred. The 1989 Malibu earthquake was a thrust or oblique slip event adjacent to the 1979 Malibu earthquake.

At least two of the largest recent thrust earthquakes (San Fernando and Whittier) in the Los Angeles basin have had the extent of their thrust plane ruptures limited by strike-slip faults. This suggests that the buried thrust faults underlying the Los Angeles basin are segmented by strike-slip faults.

Earthquake and explosion travel times are inverted for the three-dimensional velocity structure of southern California in Chapter 9. The inversion reduced the variance of the travel time residuals by 47 per cent compared to the starting model, a reparameterized version of the forward model of Chapter 7. The Los Angeles basin is well resolved, with seismically slow sediments atop a crust of granitic velocities. Moho depth is between 26 and 32 km.

Relativistic velocity - potential hydrodynamics and stellar stability

The equations of relativistic, perfect-fluid hydrodynamics are cast in Eulerian form using six scalar "velocity-potential" fields, each of which has an equation of evolution. These equations determine the motion of the fluid through the equation

U_ʋ=µ^-1 (ø,_ʋ + αβ,_ʋ + ƟS,_ʋ).

Einstein's equations and the velocity-potential hydrodynamical equations follow from a variational principle whose action is

I = (R + 16π p) (-g)^1/2 d⁴x,

where R is the scalar curvature of spacetime and p is the pressure of the fluid. These equations are also cast into Hamiltonian form, with Hamiltonian density –T₀⁰ (-g^oo)^-1/2.

The second variation of the action is used as the Lagrangian governing the evolution of small perturbations of differentially rotating stellar models. In Newtonian gravity this leads to linear dynamical stability criteria already known. In general relativity it leads to a new sufficient condition for the stability of such models against arbitrary perturbations.

By introducing three scalar fields defined by

ρ ᵴ = ∇λ + ∇x(xi + ∇xɣi)

(where ᵴ is the vector displacement of the perturbed fluid element, ρ is the mass-density, and i, is an arbitrary vector), the Newtonian stability criteria are greatly simplified for the purpose of practical applications. The relativistic stability criterion is not yet in a form that permits practical calculations, but ways to place it in such a form are discussed.

Solar flare particle propagation--comparison of a new analytic solution with spacecraft measurements

A new analytic solution has been obtained to the complete Fokker-Planck equation for solar flare particle propagation including the effects of convection, energy-change, corotation, and diffusion with ĸ_r = constant and ĸ_Ɵ ∝ r². It is assumed that the particles are injected impulsively at a single point in space, and that a boundary exists beyond which the particles are free to escape. Several solar flare particle events have been observed with the Caltech Solar and Galactic Cosmic Ray Experiment aboard OGO-6. Detailed comparisons of the predictions of the new solution with these observations of 1-70 MeV protons show that the model adequately describes both the rise and decay times, indicating that ĸ_r = constant is a better description of conditions inside 1 AU than is ĸ_r ∝ r. With an outer boundary at 2.7 AU, a solar wind velocity of 400 km/sec, and a radial diffusion coefficient ĸ_r ≈ 2-8 x 10²⁰ cm²/sec, the model gives reasonable fits to the time-profile of 1-10 MeV protons from "classical" flare-associated events. It is not necessary to invoke a scatter-free region near the sun in order to reproduce the fast rise times observed for directly-connected events. The new solution also yields a time-evolution for the vector anisotropy which agrees well with previously reported observations.

In addition, the new solution predicts that, during the decay phase, a typical convex spectral feature initially at energy T_o will move to lower energies at an exponential rate given by T_KINK = T_oexp(-t/Ƭ_KINK). Assuming adiabatic deceleration and a boundary at 2.7 AU, the solution yields Ƭ_KINK ≈ 100h, which is faster than the measured ~200h time constant and slower than the adiabatic rate of ~78h at 1 AU. Two possible explanations are that the boundary is at ~5 AU or that some other energy-change process is operative.