The statistical bootstrap model

A review is presented of the statistical bootstrap model of Hagedorn and Frautschi. This model is an attempt to apply the methods of statistical mechanics in high-energy physics, while treating all hadron states (stable or unstable) on an equal footing. A statistical calculation of the resonance spectrum on this basis leads to an exponentially rising level density ρ(m) ~ cm^-3 e^βom at high masses.

In the present work, explicit formulae are given for the asymptotic dependence of the level density on quantum numbers, in various cases. Hamer and Frautschi's model for a realistic hadron spectrum is described.

A statistical model for hadron reactions is then put forward, analogous to the Bohr compound nucleus model in nuclear physics, which makes use of this level density. Some general features of resonance decay are predicted. The model is applied to the process of NN annihilation at rest with overall success, and explains the high final state pion multiplicity, together with the low individual branching ratios into two-body final states, which are characteristic of the process. For more general reactions, the model needs modification to take account of correlation effects. Nevertheless it is capable of explaining the phenomenon of limited transverse momenta, and the exponential decrease in the production frequency of heavy particles with their mass, as shown by Hagedorn. Frautschi's results on "Ericson fluctuations" in hadron physics are outlined briefly. The value of β_o required in all these applications is consistently around [120 MeV]^-1 corresponding to a "resonance volume" whose radius is very close to ƛ_π. The construction of a "multiperipheral cluster model" for high-energy collisions is advocated.

Techniques for strength measurement at high pressures and strain-rates using transverse waves

The study of the strength of a material is relevant to a variety of applications including automobile collisions, armor penetration and inertial confinement fusion. Although dynamic behavior of materials at high pressures and strain-rates has been studied extensively using plate impact experiments, the results provide measurements in one direction only. Material behavior that is dependent on strength is unaccounted for. The research in this study proposes two novel configurations to mitigate this problem.

The first configuration introduced is the oblique wedge experiment, which is comprised of a driver material, an angled target of interest and a backing material used to measure in-situ velocities. Upon impact, a shock wave is generated in the driver material. As the shock encounters the angled target, it is reflected back into the driver and transmitted into the target. Due to the angle of obliquity of the incident wave, a transverse wave is generated that allows the target to be subjected to shear while being compressed by the initial longitudinal shock such that the material does not slip. Using numerical simulations, this study shows that a variety of oblique wedge configurations can be used to study the shear response of materials and this can be extended to strength measurement as well. Experiments were performed on an oblique wedge setup with a copper impactor, polymethylmethacrylate driver, aluminum 6061-t6 target, and a lithium fluoride window. Particle velocities were measured using laser interferometry and results agree well with the simulations.

The second novel configuration is the y-cut quartz sandwich design, which uses the anisotropic properties of y-cut quartz to generate a shear wave that is transmitted into a thin sample. By using an anvil material to back the thin sample, particle velocities measured at the rear surface of the backing plate can be implemented to calculate the shear stress in the material and subsequently the strength. Numerical simulations were conducted to show that this configuration has the ability to measure the strength for a variety of materials.

Aperiodic structures in optics and integrated optics and the transverse Bragg reflector laser

The first part of this work describes the uses of aperiodic structures in optics and integrated optics. In particular, devices are designed, fabricated, tested and analyzed which make use of a chirped grating corrugation on the surface of a dielectric waveguide. These structures can be used as input-output couplers, multiplexers and demultiplexers, and broad band filters.

Next, a theoretical analysis is made of the effects of a random statistical variation in the thicknesses of layers in a dielectric mirror on its reflectivity properties. Unlike the intentional aperiodicity introduced in the chirped gratings, the aperiodicity in the Bragg reflector mirrors is unintentional and is present to some extent in all devices made. The analysis involved in studying these problems relies heavily on the coupled mode formalism. The results are compared with computer experiments, as well as tests of actual mirrors.

The second part of this work describes a novel method for confining light in the transverse direction in an injection laser. These so-called transverse Bragg reflector lasers confine light normal to the junction plane in the active region, through reflection from an adjacent layered medium. Thus, in principle, it is possible to guide light in a dielectric layer whose index is lower than that of the surrounding material. The design, theory and testing of these diode lasers are discussed.

Inelastic K+p reactions at incident momenta from 1.37 GeV/c to 2.17 GeV/c

A number of recent experiments have suggested the possibility of a highly inelastic resonance in K⁺p scattering. To study the inelastic K⁺p reactions, a 400 K exposure has been taken at the L.R.L. 25 inch bubble chamber. The data are spread over seven K⁺ momenta between 1.37 and 2.17 GeV/c.

Cross-sections have been measured for the reaction K⁺p → pK°π+ which is dominated by the quasi-two body channels K∆ and K*N. Both these channels are strongly peripheral, as at other momenta. The decay of the ∆ is in good agreement with the predictions of the rho-photon analogy of Stodolsky and Sakurai. The data on the K*p channel show evidence of both pseudo scalar and vector exchange.

Cross-sections for the final state pK⁺π+π- shows a strong contribution from the quasi-two body channel K*∆. This reaction is also very peripheral even at threshold. The decay angular distributions indicate the reaction is dominated as at higher momenta by a pion exchange mechanism. The data are also in good agreement with the quark model predictions of Bialas and Zalewski for the K* and ∆ decay.

Invariants, Lie-Bäcklund operators and Bäcklund transformations

This thesis is mainly concerned with the application of groups of transformations to differential equations and in particular with the connection between the group structure of a given equation and the existence of exact solutions and conservation laws. In this respect the Lie-Bäcklund groups of tangent transformations, particular cases of which are the Lie tangent and the Lie point groups, are extensively used.

In Chapter I we first review the classical results of Lie, Bäcklund and Bianchi as well as the more recent ones due mainly to Ovsjannikov. We then concentrate on the Lie-Bäcklund groups (or more precisely on the corresponding Lie-Bäcklund operators), as introduced by Ibragimov and Anderson, and prove some lemmas about them which are useful for the following chapters. Finally we introduce the concept of a conditionally admissible operator (as opposed to an admissible one) and show how this can be used to generate exact solutions.

In Chapter II we establish the group nature of all separable solutions and conserved quantities in classical mechanics by analyzing the group structure of the Hamilton-Jacobi equation. It is shown that consideration of only Lie point groups is insufficient. For this purpose a special type of Lie-Bäcklund groups, those equivalent to Lie tangent groups, is used. It is also shown how these generalized groups induce Lie point groups on Hamilton's equations. The generalization of the above results to any first order equation, where the dependent variable does not appear explicitly, is obvious. In the second part of this chapter we investigate admissible operators (or equivalently constants of motion) of the Hamilton-Jacobi equation with polynornial dependence on the momenta. The form of the most general constant of motion linear, quadratic and cubic in the momenta is explicitly found. Emphasis is given to the quadratic case, where the particular case of a fixed (say zero) energy state is also considered; it is shown that in the latter case additional symmetries may appear. Finally, some potentials of physical interest admitting higher symmetries are considered. These include potentials due to two centers and limiting cases thereof. The most general two-center potential admitting a quadratic constant of motion is obtained, as well as the corresponding invariant. Also some new cubic invariants are found.

In Chapter III we first establish the group nature of all separable solutions of any linear, homogeneous equation. We then concentrate on the Schrodinger equation and look for an algorithm which generates a quantum invariant from a classical one. The problem of an isomorphism between functions in classical observables and quantum observables is studied concretely and constructively. For functions at most quadratic in the momenta an isomorphism is possible which agrees with Weyl' s transform and which takes invariants into invariants. It is not possible to extend the isomorphism indefinitely. The requirement that an invariant goes into an invariant may necessitate variants of Weyl' s transform. This is illustrated for the case of cubic invariants. Finally, the case of a specific value of energy is considered; in this case Weyl's transform does not yield an isomorphism even for the quadratic case. However, for this case a correspondence mapping a classical invariant to a quantum orie is explicitly found.

Chapters IV and V are concerned with the general group structure of evolution equations. In Chapter IV we establish a one to one correspondence between admissible Lie-Bäcklund operators of evolution equations (derivable from a variational principle) and conservation laws of these equations. This correspondence takes the form of a simple algorithm.

In Chapter V we first establish the group nature of all Bäcklund transformations (BT) by proving that any solution generated by a BT is invariant under the action of some conditionally admissible operator. We then use an algorithm based on invariance criteria to rederive many known BT and to derive some new ones. Finally, we propose a generalization of BT which, among other advantages, clarifies the connection between the wave-train solution and a BT in the sense that, a BT may be thought of as a variation of parameters of some. special case of the wave-train solution (usually the solitary wave one). Some open problems are indicated.

Most of the material of Chapters II and III is contained in [I], [II], [III] and [IV] and the first part of Chapter V in [V].

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

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

Nuclear Hartree-Fock calculations on parallel computers

Hartree-Fock (HF) calculations have had remarkable success in describing large nuclei at high spin, temperature and deformation. To allow full range of possible deformations, the Skyrme HF equations can be discretized on a three-dimensional mesh. However, such calculations are currently limited by the computational resources provided by traditional supercomputers. To take advantage of recent developments in massively parallel computing technology, we have implemented the LLNL Skyrme-force static and rotational HF codes on Intel's DELTA and GAMMA systems at Caltech.

We decomposed the HF code by assigning a portion of the mesh to each node, with nearest neighbor meshes assigned to nodes connected by communication· channels. This kind of decomposition is well-suited for the DELTA and the GAMMA architecture because the only non-local operations are wave function orthogonalization and the boundary conditions of the Poisson equation for the Coulomb field.

Our first application of the HF code on parallel computers has been the study of identical superdeformed (SD) rotational bands in the Hg region. In the last ten years, many SD rotational bands have been found experimentally. One very surprising feature found in these SD rotational bands is that many pairs of bands in nuclei that differ by one or two mass units have nearly identical deexcitation gamma-ray energies. Our calculations of the five rotational bands in ^(192)Hg and ^(194)Pb show that the filling of specific orbitals can lead to bands with deexcitation gamma-ray energies differing by at most 2 keV in nuclei differing by two mass units and over a range of angular momenta comparable to that observed experimentally. Our calculations of SD rotational bands in the Dy region also show that twinning can be achieved by filling or emptying some specific orbitals.

The interpretation of future precise experiments on atomic parity nonconservation (PNC) in terms of parameters of the Standard Model could be hampered by uncertainties in the atomic and nuclear structure. As a further application of the massively parallel HF calculations, we calculated the proton and neutron densities of the Cesium isotopes from A = 125 to A = 139. Based on our good agreement with experimental charge radii, binding energies, and ground state spins, we conclude that the uncertainties in the ratios of weak charges are less than 10^(-3), comfortably smaller than the anticipated experimental error.

Searches for new symmetries in pp collisions with the razor kinematic variables at √s = 7 TeV

The construction and LHC phenomenology of the razor variables M_R, an event-by-event indicator of the heavy particle mass scale, and R, a dimensionless variable related to the transverse momentum imbalance of events and missing transverse energy, are presented.  The variables are used  in the analysis of the first proton-proton collisions dataset at CMS  (35 pb^-1) in a search for superpartners of the quarks and gluons, targeting indirect hints of dark matter candidates in the context of supersymmetric theoretical frameworks. The analysis produced the highest sensitivity results for SUSY to date and extended the LHC reach far beyond the previous Tevatron results.  A generalized inclusive search is subsequently presented for new heavy particle pairs produced in √s = 7 TeV proton-proton collisions at the LHC using 4.7±0.1 fb^-1 of integrated luminosity from the second LHC run of 2011.  The selected events are analyzed in the 2D razor-space of M_R and R and the analysis is performed in 12 tiers of all-hadronic, single and double leptons final states in the presence and absence of b-quarks, probing the third generation sector using the event heavy-flavor content.   The search is sensitive to generic supersymmetry models with minimal assumptions about the superpartner decay chains. No excess is observed in the number or shape of event yields relative to Standard Model predictions. Exclusion limits are derived in the CMSSM framework with  gluino masses up to 800 GeV and squark masses up to 1.35 TeV excluded at 95% confidence level, depending on the model parameters. The results are also interpreted for a collection of simplified models, in which gluinos are excluded with masses as large as 1.1 TeV, for small neutralino masses, and the first-two generation squarks, stops and sbottoms are excluded for masses up to about 800, 425 and 400 GeV, respectively.

With the discovery of a new boson by the CMS and ATLAS experiments in the γ-γ and 4 lepton final states, the identity of the putative Higgs candidate must be established through the measurements of its properties. The spin and quantum numbers are of particular importance, and we describe a method for measuring the J^PC of this particle using the observed signal events in the H to ZZ^* to 4 lepton channel developed before the discovery. Adaptations of the razor kinematic variables are introduced for the H to WW^* to 2 lepton/2 neutrino channel, improving the resonance mass resolution and increasing the discovery significance. The prospects for incorporating this channel in an examination of the new boson J^PC is discussed, with indications that this it could provide complementary information to the H to ZZ^* to 4 lepton final state, particularly for measuring CP-violation in these decays.

Trapped ion magnetic resonance: concepts and designs

A novel spectroscopy of trapped ions is proposed which will bring single-ion detection sensitivity to the observation of magnetic resonance spectra. The approaches developed here are aimed at resolving one of the fundamental problems of molecular spectroscopy, the apparent incompatibility in existing techniques between high information content (and therefore good species discrimination) and high sensitivity. Methods for studying both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) are designed. They assume established methods for trapping ions in high magnetic field and observing the trapping frequencies with high resolution (<1 Hz) and sensitivity (single ion) by electrical means. The introduction of a magnetic bottle field gradient couples the spin and spatial motions together and leads to a small spin-dependent force on the ion, which has been exploited by Dehmelt to observe directly the perturbation of the ground-state electron's axial frequency by its spin magnetic moment.

A series of fundamental innovations is described m order to extend magnetic resonance to the higher masses of molecular ions (100 amu = 2x 10^5 electron masses) and smaller magnetic moments (nuclear moments = 10^(-3) of the electron moment). First, it is demonstrated how time-domain trapping frequency observations before and after magnetic resonance can be used to make cooling of the particle to its ground state unnecessary. Second, adiabatic cycling of the magnetic bottle off between detection periods is shown to be practical and to allow high-resolution magnetic resonance to be encoded pointwise as the presence or absence of trapping frequency shifts. Third, methods of inducing spindependent work on the ion orbits with magnetic field gradients and Larmor frequency irradiation are proposed which greatly amplify the attainable shifts in trapping frequency.

The dissertation explores the basic concepts behind ion trapping, adopting a variety of classical, semiclassical, numerical, and quantum mechanical approaches to derive spin-dependent effects, design experimental sequences, and corroborate results from one approach with those from another. The first proposal presented builds on Dehmelt's experiment by combining a "before and after" detection sequence with novel signal processing to reveal ESR spectra. A more powerful technique for ESR is then designed which uses axially synchronized spin transitions to perform spin-dependent work in the presence of a magnetic bottle, which also converts axial amplitude changes into cyclotron frequency shifts. A third use of the magnetic bottle is to selectively trap ions with small initial kinetic energy. A dechirping algorithm corrects for undesired frequency shifts associated with damping by the measurement process.

The most general approach presented is spin-locked internally resonant ion cyclotron excitation, a true continuous Stern-Gerlach effect. A magnetic field gradient modulated at both the Larmor and cyclotron frequencies is devised which leads to cyclotron acceleration proportional to the transverse magnetic moment of a coherent state of the particle and radiation field. A preferred method of using this to observe NMR as an axial frequency shift is described in detail. In the course of this derivation, a new quantum mechanical description of ion cyclotron resonance is presented which is easily combined with spin degrees of freedom to provide a full description of the proposals.

Practical, technical, and experimental issues surrounding the feasibility of the proposals are addressed throughout the dissertation. Numerical ion trajectory simulations and analytical models are used to predict the effectiveness of the new designs as well as their sensitivity and resolution. These checks on the methods proposed provide convincing evidence of their promise in extending the wealth of magnetic resonance information to the study of collisionless ions via single-ion spectroscopy.

Studies of Zγ production and constraints on anomalous triple gauge couplings in pp collisions at √s = 7 TeV

In this thesis, we test the electroweak sector of the Standard Model of particle physics through the measurements of the cross section of the simultaneous production of the neutral weak boson Z and photon γ, and the limits on the anomalous Zγγ and ZZγ triple gauge couplings h3 and h4 with the Z decaying to leptons (electrons and muons). We analyze events collected in proton-proton collisions at center of mass energy of sqrt(s) = 7 TeV corresponding to an integrated luminosity of 5.0 inverse femtobarn. The analyzed events were recorded by the Compact Muon Solenoid detector at the Large Hadron Collider in 2011.

The production cross section has been measured for hard photons with transverse momentum greater than 15 GeV that are separated from the the final state leptons in the eta-phi plane by Delta R greater than 0.7, whose sum of the transverse energy of hadrons over the transverse energy of the photon in a cone around the photon with Delta R less than 0.3 is less than 0.5, and with the invariant mass of the dilepton system greater than 50 GeV. The measured cross section value is 5.33 +/- 0.08 (stat.) +/- 0.25 (syst.) +/- 0.12 (lumi.) picobarn. This is compatible with the Standard Model prediction that includes next-to-leading-order QCD contributions: 5.45 +/- 0.27 picobarn.

The measured 95 % confidence-level upper limits on the absolute values of the anomalous couplings h3 and h4 are 0.01 and 8.8E-5 for the Zγγ interactions, and, 8.6E-3 and 8.0E-5 for the ZZγ interactions. These values are also compatible with the Standard Model where they vanish in the tree-level approximation. They extend the sensitivity of the 2012 results from the ATLAS collaboration based on 1.02 inverse femtobarn of data by a factor of 2.4 to 3.1.

The optoelectronic swept-frequency laser and its applications in ranging, three-dimensional imaging, and coherent beam combining of chirped-seed amplifiers

This thesis explores the design, construction, and applications of the optoelectronic swept-frequency laser (SFL). The optoelectronic SFL is a feedback loop designed around a swept-frequency (chirped) semiconductor laser (SCL) to control its instantaneous optical frequency, such that the chirp characteristics are determined solely by a reference electronic oscillator. The resultant system generates precisely controlled optical frequency sweeps. In particular, we focus on linear chirps because of their numerous applications. We demonstrate optoelectronic SFLs based on vertical-cavity surface-emitting lasers (VCSELs) and distributed-feedback lasers (DFBs) at wavelengths of 1550 nm and 1060 nm. We develop an iterative bias current predistortion procedure that enables SFL operation at very high chirp rates, up to 10^16 Hz/sec. We describe commercialization efforts and implementation of the predistortion algorithm in a stand-alone embedded environment, undertaken as part of our collaboration with Telaris, Inc. We demonstrate frequency-modulated continuous-wave (FMCW) ranging and three-dimensional (3-D) imaging using a 1550 nm optoelectronic SFL.

We develop the technique of multiple source FMCW (MS-FMCW) reflectometry, in which the frequency sweeps of multiple SFLs are "stitched" together in order to increase the optical bandwidth, and hence improve the axial resolution, of an FMCW ranging measurement. We demonstrate computer-aided stitching of DFB and VCSEL sweeps at 1550 nm. We also develop and demonstrate hardware stitching, which enables MS-FMCW ranging without additional signal processing. The culmination of this work is the hardware stitching of four VCSELs at 1550 nm for a total optical bandwidth of 2 THz, and a free-space axial resolution of 75 microns.

We describe our work on the tomographic imaging camera (TomICam), a 3-D imaging system based on FMCW ranging that features non-mechanical acquisition of transverse pixels. Our approach uses a combination of electronically tuned optical sources and low-cost full-field detector arrays, completely eliminating the need for moving parts traditionally employed in 3-D imaging. We describe the basic TomICam principle, and demonstrate single-pixel TomICam ranging in a proof-of-concept experiment. We also discuss the application of compressive sensing (CS) to the TomICam platform, and perform a series of numerical simulations. These simulations show that tenfold compression is feasible in CS TomICam, which effectively improves the volume acquisition speed by a factor ten.

We develop chirped-wave phase-locking techniques, and apply them to coherent beam combining (CBC) of chirped-seed amplifiers (CSAs) in a master oscillator power amplifier configuration. The precise chirp linearity of the optoelectronic SFL enables non-mechanical compensation of optical delays using acousto-optic frequency shifters, and its high chirp rate simultaneously increases the stimulated Brillouin scattering (SBS) threshold of the active fiber. We characterize a 1550 nm chirped-seed amplifier coherent-combining system. We use a chirp rate of 5*10^14 Hz/sec to increase the amplifier SBS threshold threefold, when compared to a single-frequency seed. We demonstrate efficient phase-locking and electronic beam steering of two 3 W erbium-doped fiber amplifier channels, achieving temporal phase noise levels corresponding to interferometric fringe visibilities exceeding 98%.

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.

Crustal structure in Southern California from array data

Crustal structure in Southern California is investigated using travel times from over 200 stations and thousands of local earthquakes. The data are divided into two sets of first arrivals representing a two-layer crust. The Pg arrivals have paths that refract at depths near 10 km and the Pn arrivals refract along the Moho discontinuity. These data are used to find lateral and azimuthal refractor velocity variations and to determine refractor topography.

In Chapter 2 the Pn raypaths are modeled using linear inverse theory. This enables statistical verification that static delays, lateral slowness variations and anisotropy are all significant parameters. However, because of the inherent size limitations of inverse theory, the full array data set could not be processed and the possible resolution was limited. The tomographic backprojection algorithm developed for Chapters 3 and 4 avoids these size problems. This algorithm allows us to process the data sequentially and to iteratively refine the solution. The variance and resolution for tomography are determined empirically using synthetic structures.

The Pg results spectacularly image the San Andreas Fault, the Garlock Fault and the San Jacinto Fault. The Mojave has slower velocities near 6.0 km/s while the Peninsular Ranges have higher velocities of over 6.5 km/s. The San Jacinto block has velocities only slightly above the Mojave velocities. It may have overthrust Mojave rocks. Surprisingly, the Transverse Ranges are not apparent at Pg depths. The batholiths in these mountains are possibly only surficial.

Pn velocities are fast in the Mojave, slow in Southern California Peninsular Ranges and slow north of the Garlock Fault. Pn anisotropy of 2% with a NWW fast direction exists in Southern California. A region of thin crust (22 km) centers around the Colorado River where the crust bas undergone basin and range type extension. Station delays see the Ventura and Los Angeles Basins but not the Salton Trough, where high velocity rocks underlie the sediments. The Transverse Ranges have a root in their eastern half but not in their western half. The Southern Coast Ranges also have a thickened crust but the Peninsular Ranges have no major root.

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.

Singularities and horizons in the collisions of gravitational waves

This thesis presents a study of the dynamical, nonlinear interaction of colliding gravitational waves, as described by classical general relativity. It is focused mainly on two fundamental questions: First, what is the general structure of the singularities and Killing-Cauchy horizons produced in the collisions of exactly plane-symmetric gravitational waves? Second, under what conditions will the collisions of almost-plane gravitational waves (waves with large but finite transverse sizes) produce singularities?

In the work on the collisions of exactly-plane waves, it is shown that Killing horizons in any plane-symmetric spacetime are unstable against small plane-symmetric perturbations. It is thus concluded that the Killing-Cauchy horizons produced by the collisions of some exactly plane gravitational waves are nongeneric, and that generic initial data for the colliding plane waves always produce "pure" spacetime singularities without such horizons. This conclusion is later proved rigorously (using the full nonlinear theory rather than perturbation theory), in connection with an analysis of the asymptotic singularity structure of a general colliding plane-wave spacetime. This analysis also proves that asymptotically the singularities created by colliding plane waves are of inhomogeneous-Kasner type; the asymptotic Kasner axes and exponents of these singularities in general depend on the spatial coordinate that runs tangentially to the singularity in the non-plane-symmetric direction.

In the work on collisions of almost-plane gravitational waves, first some general properties of single almost-plane gravitational-wave spacetimes are explored. It is shown that, by contrast with an exact plane wave, an almost-plane gravitational wave cannot have a propagation direction that is Killing; i.e., it must diffract and disperse as it propagates. It is also shown that an almost-plane wave cannot be precisely sandwiched between two null wavefronts; i.e., it must leave behind tails in the spacetime region through which it passes. Next, the occurrence of spacetime singularities in the collisions of almost-plane waves is investigated. It is proved that if two colliding, almost-plane gravitational waves are initially exactly plane-symmetric across a central region of sufficiently large but finite transverse dimensions, then their collision produces a spacetime singularity with the same local structure as in the exact-plane-wave collision. Finally, it is shown that a singularity still forms when the central regions are only approximately plane-symmetric initially. Stated more precisely, it is proved that if the colliding almost-plane waves are initially sufficiently close to being exactly plane-symmetric across a bounded central region of sufficiently large transverse dimensions, then their collision necessarily produces spacetime singularities. In this case, nothing is now known about the local and global structures of the singularities.