Committee Feed
https://feeds.library.caltech.edu/people/Thorne-K-S/committee.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 02:02:50 +0000I. Application of multi-Regge theory to production processes. II. High energy model for proton-proton scattering
https://resolver.caltech.edu/CaltechTHESIS:02182014-114114913
Authors: {'items': [{'email': 'lipes@lipes.com', 'id': 'Lipes-R-G', 'name': {'family': 'Lipes', 'given': 'Richard Gwin'}, 'show_email': 'YES'}]}
Year: 1969
DOI: 10.7907/R5YJ-NJ84
<p>This dissertation consists of two parts. The first part presents
an explicit procedure for applying multi-Regge theory to
production processes. As an illustrative example, the case of three
body final states is developed in detail, both with respect to kinematics
and multi-Regge dynamics. Next, the experimental consistency
of the multi-Regge hypothesis is tested in a specific high
energy reaction; the hypothesis is shown to provide a good qualitative
fit to the data. In addition, the results demonstrate a severe suppression
of double Pomeranchon exchange, and show the coupling of
two "Reggeons" to an external particle to be strongly damped as the
particle's mass increases. Finally, with the use of two body Regge
parameters, order of magnitude estimates of the multi-Regge cross
section for various reactions are given.</p>
<p>The second part presents a diffraction model for high energy
proton-proton scattering. This model developed by Chou and Yang
assumes high energy elastic scattering results from absorption of
the incident wave into the many available inelastic channels, with
the absorption proportional to the amount of interpenetrating hadronic
matter. The assumption that the hadronic matter distribution is
proportional to the charge distribution relates the scattering amplitude
for pp scattering to the proton form factor. The Chou-Yang
model with the empirical proton form factor as input is then applied
to calculate a high energy, fixed momentum transfer limit for the
scattering cross section, This limiting cross section exhibits the
same "dip" or "break" structure indicated in present experiments,
but falls significantly below them in magnitude. Finally, possible spin
dependence is introduced through a weak spin-orbit type term which
gives rather good agreement with pp polarization data.</p>https://thesis.library.caltech.edu/id/eprint/8079Nuclear Weak Interaction Rates During Stellar Evolution and Collapse
https://resolver.caltech.edu/CaltechTHESIS:06052013-092608399
Authors: {'items': [{'email': 'gfuller@ucsd.edu', 'id': 'Fuller-George-Michael', 'name': {'family': 'Fuller', 'given': 'George Michael'}, 'show_email': 'YES'}]}
Year: 1981
DOI: 10.7907/Y2W8-MB57
<p>Nuclear weak interaction rates, including electron and positron emission rates, and continuum electron and positron capture rates, as well as the associated ν and ⊽ energy loss rates are calculated on a detailed grid of temperature and density for the free nucleons and 226 nuclei with masses between A = 21 and 60. Gamow-Teller and Fermi discrete-state transition matrix element systematics and the Gamow-Teller T<sup><</sup> ⇄ T<sup>></sup> resonance transitions are discussed in depth and are implemented in the stellar rate calculations. Results of the calculations are presented on an abbreviated grid of temperature and density and comparison is made to terrestrial weak transition rates where possible. Neutron shell blocking of allowed electron capture on heavy nuclei during stellar core collapse
is discussed along with several unblocking mechanisms operative at high temperature and density. The results of one-zone collapse calculations are presented which suggest that the effect of neutron shell blocking is to produce a larger core lepton fraction at neutrino trapping which leads to a larger inner-core mass and hence a stronger post-bounce shock.</p>https://thesis.library.caltech.edu/id/eprint/78401. The Origin of the Kirkwood Gaps: A Mapping for Asteroidal Monitor Near the 3/1 Commensurability. 2. The Resonance Overlap Criterion and the Onset of Stochastic Behavior in the Restricted Three-Body Problem
https://resolver.caltech.edu/CaltechTHESIS:08282017-145742321
Authors: {'items': [{'email': 'wisdom@mit.edu', 'id': 'Wisdom-Jack-Leach', 'name': {'family': 'Wisdom', 'given': 'Jack Leach'}, 'show_email': 'YES'}]}
Year: 1981
DOI: 10.7907/s1r9-ff38
<p>Paper 1:</p>
<p>A mapping of the phase space onto itself with the same low order resonance structure as the 3/1 commensurability in the planar elliptic three-body problem is derived. This mapping is approximately one thousand (1000) times faster than the usual method of numerically integrating the averaged equations of motion (as used by Schubart, Froeschlé and Scholl in their studies of the asteroid belt). This mapping exhibits some very surprising behavior that might provide the key to the origin of the gaps. A test asteroid placed in the gap may evolve for a million years with low eccentricity (< 0.05) and then suddenly jump to large eccentricity (> 0.3) becoming a Mars crosser. The asteroid can then be removed by a close encounter with Mars. To test this hypothesis a distribution of 300 test asteroids in the neighborhood of the 3/1 commensurability was evolved for two million years. When the Mars crossers are removed the distribution of initial conditions displays a gap at the location of the 3/1 Kirkwood gap. While this is the first real demonstration of the formation of a gap, the gap is too narrow. The planar elliptic mapping is then extended to include the inclinations and the secular perturbations of Jupiter's orbit. The two million year evolution of the 300 test asteroids is repeated using the full mapping. The resulting gap is somewhat larger yet still too small. Finally the possibility that over longer times more asteroids will become Mars crossers is tested by studying the evolution of one test asteroid near the border of the gap for a much longer time. A jump in its eccentricity occurs after 18 million years indicating that indeed it may simply be a matter of time for the full width of the gap to open.</p>
<p>Paper 2:</p>
<p>The resonance overlap criterion for the onset of stochastic behavior is applied to the planar circular-restricted three-body problem with small mass ratio (µ). Its predictions for µ = 10<sup>-3</sup>, µ = 10<sup>-4</sup> and µ = 10<sup>-5</sup> are compared to the transitions in the numerically determined Kolmogorov-Sinai entropy and found to be in remarkably good agreement. In addition, an approximate scaling law for the onset of stochastic behavior is derived.</p>https://thesis.library.caltech.edu/id/eprint/10394Stationary Spherical Optically Thick Accretion into Black Holes
https://resolver.caltech.edu/CaltechTHESIS:08252017-133002176
Authors: {'items': [{'id': 'Flammang-Richard-Alan', 'name': {'family': 'Flammang', 'given': 'Richard Alan'}, 'show_email': 'NO'}]}
Year: 1982
DOI: 10.7907/t73p-2e81
<p>As its title indicates, this thesis treats the problem of stationary, spherical, optically thick accretion into black holes. By the phrase "optically thick" it is meant that (1) radiative energy transport can be adequately described by the diffusion approximation and (2) the photons are everywhere in local energy equilibrium (LTE) with the accreting gas particles.</p>
<p>In Chapter 1, a general set of equations governing time-independent spherical accretion into black holes is formulated. The equations are fully general relativistic and are applicable to optically thick regions, optically thin regions, and the transition regions which join them. The radiation is treated using frequency-integrated moments. The full, infinite series of moment equations is given, together with the limiting forms the equations take in the optically thick regime.</p>
<p>In Chapter 2, we present the mathematical theory of stationary spherical optically thick accretion. We analyze the integral curves of the differential equations describing the problem. We find a one-parameter family of critical points, where the inflow velocity equals the isothermal sound speed. Physical solutions must pass through one of these critical points. We obtain a complete set of boundary conditions which the solution must satisfy at the horizon of the black hole, and show that these, plus the requirement that the solution pass through a critical point, determine a unique solution to the problem. This analysis leads to a generalization of the well-known Bondi critical point constraint, which arises in the adiabatic accretion problem and which is effective at the point where the inflow velocity equals the adiabatic sound speed. We show that this point can be regarded as a "diffused critical point" in our problem. The analysis also yields a simple expression for the diffusive luminosity at radial infinity. Finally, we find a satisfying explanation for the rather peculiar critical point structure of this problem in an analysis of the characteristics and subcharacteristics present in the problem and in a "hierarchical" analysis of the waves which propagate along them.</p>
<p>In Chapter 3, we apply the theory of optically thick accretion developed in Chapter 2 to a wide range of physically different accretion regimes. Numerical solutions are presented and their physical properties are discussed. For solutions in which radiation pressure P<sub>R</sub> dominates gas pressure P<sub>G</sub>, but in which gas energy density (including its rest-mass) ρ<sub>G</sub> dominates radiation energy density ρ<sub>R</sub>, we pay particular attention to the adabaticity of the flow. Our quantitative results in this regime agree very well with Begelman's (1978) theory. We find the dimensionless number which governs the importance of heat diffusion in our problem and show that it reduces to the idea of "trapping of photons" and to the Péclet number in the appropriate limits. We find that solutions with P<sub>R</sub> > P<sub>G</sub> and ρ<sub>R</sub> > ρ<sub>G</sub> are always essentially adiabatic, owing in part to a relativistic suppression of heat flux which becomes important in this regime. The diffusive luminosity at infinity for these solutions is the Eddington limit of the black hole; with the adiabatic accretion rate, "efficiencies" of up to order unity are possible. We give preliminary consideration to the question of the stability of our solutions against convection and conclude that the Schwarzschild criterion is applicable, even for our non-static accretion flows. We show that solutions with P<sub>R</sub> > P<sub>G</sub> are everywhere stable against convection. On the other hand, solutions which start out at radial infinity with P<sub>G</sub> > P<sub>R</sub> are unstable to convection (if the adiabatic index of the gas γ<sub>G</sub> exceeds 17/12) from radial infinity down to the point where P<sub>R</sub> ~ P<sub>G</sub> and the radiation-gas mixture has attained an adiabatic index of 17/12. The diffusive luminosity at infinity for these solutions is reduced from the Eddington limit of the black hole by the factor (γ<sub>G</sub> - 1)4P<sub>R∞</sub>/γ<sub>G</sub>P<sub>G∞</sub>; it is further reduced by the ratio of the electron scattering opacity to the actual opacity at infinity, if this differs from unity. In most cases, energy diffusion has a negligible effect on the accretion rate of these solutions.</p>https://thesis.library.caltech.edu/id/eprint/10391Radiative Mass Structure in Unified Models and Fermions in the Desert
https://resolver.caltech.edu/CaltechTHESIS:09272018-120912826
Authors: {'items': [{'id': 'Bowick-Mark-John', 'name': {'family': 'Bowick', 'given': 'Mark John'}, 'show_email': 'NO'}]}
Year: 1983
DOI: 10.7907/11jn-dn31
<p>The radiative mass structure of some Grand Unified Models is discussed. They contain fermions with SU(2)-invariant masses in the desert. The possibility of such fermions is examined in detail with the conclusion that their mass can be low enough (~ 20 GeV) to be found in accelerators today. The mixing of such fermions with ordinary fermions is analysed and their contribution to rare processes calculated. They do not upset standard GUT predictions. Finally an analysis of their contribution to the μ → eγ rate is an interesting illustration of decoupling.</p>https://thesis.library.caltech.edu/id/eprint/11206Stability of Spherically Symmetric, Charged Black Holes and Multipole Moments for Stationary Systems
https://resolver.caltech.edu/CaltechETD:etd-03132009-081222
Authors: {'items': [{'id': 'Gürsel-Halis-Yekta', 'name': {'family': 'Gürsel', 'given': 'Halis Yekta'}, 'show_email': 'NO'}]}
Year: 1983
DOI: 10.7907/e9t6-dr05
<p>This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. NoVikov, Vernon D. Sandberg and A. A. Starobinsky. In these papers we describe the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. We conclude that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with muitipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne despite the fact that his name does not appear on one of them. The first one (Paper III in this thesis) shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second (Paper IV in this thesis) proves a conjecture by Kip S. Thorne: In the limit of "slow" motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. We prove this conjecture by giving an algorithm for generating rigidly rotating solutions of Einstein's equations from nonrotating, static solutions.</p>
https://thesis.library.caltech.edu/id/eprint/945Topics in Black-Hole Physics: Geometric Constraints on Noncollapsing, Gravitating Systems and Tidal Distortions of a Schwarzschild Black Hole
https://resolver.caltech.edu/CaltechTHESIS:08232017-105535039
Authors: {'items': [{'id': 'Redmount-Ian-H', 'name': {'family': 'Redmount', 'given': 'Ian H.'}, 'show_email': 'NO'}]}
Year: 1984
DOI: 10.7907/mp3n-4r06
<p>This dissertation consists of two studies on the general-relativistic theory of black holes. The first work concerns the fundamental issue of black-hole formation: in it I seek geometric constraints on gravitating matter systems, in the special case of axial symmetry, which determine whether or not those systems undergo gravitational collapse to form black holes. The second project deals with mechanical behavior of a black hole: specifically, I study the tidal deformation of a static black hole by the gravitational fields of external bodies.</p>
<p>In the first paper I approach the problem of geometric constraints determining gravitational collapse or non-collapse through the initial-value formalism of general relativity. I construct initial-value data representing noncollapsing, nonsingular, axisymmetric matter systems and examine the constraints imposed on this construction by the initial-value equation derived from the Einstein field equations. The construction consists of a nonsingular, momentarily static interior geometry with nonnegative mass-energy density, matched smoothly to a static, vacuum exterior geometry (described by a Weyl solution of the Einstein field equations) at a boundary surface. The initial-value equation is found to impose restrictions on the choice of the boundary surface for such a system. Two such constraints are obtained here, appropriate to spherical and toroidal interior-region topologies. These constraints are studied by applying them to simple examples of Weyl exterior geometries. The "hoop conjecture" for the general geometric-constraints problem states that a system must collapse to a black hole unless its circumference in some direction exceeds a lower bound of the order of the system's mass. The examples examined here show, however, that the constraints derived in this study are not generally correlated with any simple measure of system size, and thus that they do not embody the hoop conjecture.</p>
<p>The second paper examines the tidal distortion of a Schwarzschild black hole by bodies ("moons") suspended above the horizon on "ropes." A solution of the Einstein field equations is constructed describing this configuration, using the Weyl formalism for axisymmetric, static, vacuum geometries. The intrinsic geometry of the tidally deformed black-hole horizon is obtained from this solution; I construct embedding diagrams to represent the shape of the horizon and the tidal bulges raised on it for both weak and strong perturbations. The relations among the masses of the hole and moons, the binding energy of the system, and the rope density and tension are calculated from the solution and shown to be mutually consistent. Also, the Riemann curvature tensor representing the tidal fields near the horizon is calculated. This solution is found to agree with a previous calculation by Hartle of black-hole tides, in the limit of perturbing moons far from the horizon. In the opposite case of moons very near the horizon, this solution approaches the static limit of the distorted horizon in Rindler space calculated by Suen and Price. The results of this study thus support the use of the Rindler approximation to Schwarzschild spacetime in calculating static black-hole tides, and its extension to dynamical situations.</p>https://thesis.library.caltech.edu/id/eprint/10385Black-Hole Electrodynamics
https://resolver.caltech.edu/CaltechTHESIS:09012017-133647841
Authors: {'items': [{'id': 'Macdonald-Douglas-Alan', 'name': {'family': 'Macdonald', 'given': 'Douglas Alan'}, 'show_email': 'NO'}]}
Year: 1984
DOI: 10.7907/vv78-at49
<p>This dissertation considers several aspects of the structure and dynamics of electromagnetic fields around black holes. The four-dimensional, covariant laws of electrodynamics are reformulated in a 3 + 1 (space+time) language in which the key quantities are three-dimensional vectors lying in hypersurfaces of a constant global time <i>t</i>. This formulation is applied to the Blandford-Znajek model of power generation in quasars, which consists of a supermassive black hole surrounded by an accretion disk that holds a magnetic field on the hole, with the rotational energy and angular momentum of the hole and disk being extracted by electromagnetic torques. The 3 + 1 formalism allows the theory of stationary, axisymmetric black holes and their magnetospheres to be couched in an "absolute-space/universal-time" language very similar to the flat spacetime theory of pulsar electrodynamics; and this similarity allows fiat-space pulsar concepts to be extended to curved-space black holes. The Blandford-Znajek quasar model is reformulated in terms of a DC circuit-theory analysis, and action principles describing the overall structure of the magnetosphere and the field distribution on the horizon are developed. A general prescription for constructing global models of force-free magnetospheres is developed and this prescription is used to generate numerical models of black-hole magnetospheres for a variety of field configurations and black-hole angular velocities. The electromagnetic boundary conditions at the horizon of a black hole are described in terms of a recently developed "membrane viewpoint". The necessity and efficacy of using a "stretched horizon" in the membrane viewpoint is discussed, and is illustrated by two simple dynamical problems involving electromagnetic fields near black-hole horizons.</p>https://thesis.library.caltech.edu/id/eprint/10410Dynamical Electromagnetic Fields Near Black Holes and Multipole Moments of Stationary, General Relativistic Systems
https://resolver.caltech.edu/CaltechTHESIS:09012017-090944275
Authors: {'items': [{'id': 'Suen-Wai-Mo', 'name': {'family': 'Suen', 'given': 'Wai Mo'}, 'show_email': 'NO'}]}
Year: 1985
DOI: 10.7907/xayq-7806
<p>This dissertation contains two works; one of the behavior of dynamical electromagnetic fields in the stationary spacetime generated by a black hole, and the other on the structure of a general stationary vacuum spacetime itself.</p>
<p>The study of electromagnetic field is carried out in terms of the "membrane formalism" for black holes; and it is part of a series of papers with the aim of developing that formalism into a complete, self-consistent description of electromagnetic and gravitational fields in a black hole background. Various model problems are presented as aids in understanding the interactions of electromagnetic fields with a black hole, and special attention is paid to the concept of the "stretched horizon" which is vital for the membrane formalism.</p>
<p>The second work develops a multipole moment formalism for a general stationary system in general relativity. The multipole moments are defined in terms of a general formal series solution of the stationary Einstein equation, in analogy to multipole moments in the Newtonian theory of gravity. These relativistic moments exhibit many desirable properties and are shown to be useful in studying the interactions between a gravitating body and an external gravitational field. A model calculation applying the formalism to a black hole interacting with an external multipole field shows that the interaction can be understood in terms of "elastic moduli" of the black-hole horizon.</p>https://thesis.library.caltech.edu/id/eprint/10408Theoretical Investigations in Nonlinear Quantum Optics, Theory of Measurement, and Pulsations of General Relativistic Models of Neutron Stars
https://resolver.caltech.edu/CaltechTHESIS:09062017-132307035
Authors: {'items': [{'id': 'Schumaker-Bonny-Laura', 'name': {'family': 'Schumaker', 'given': 'Bonny Laura'}, 'show_email': 'NO'}]}
Year: 1985
DOI: 10.7907/fwvz-7t26
<p>This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and moment um variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two-photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the ouput modes arise from two-photon transitions, i.e., are created or destroyed two at a time. The states produced by such devices are single-mode and two-mode "squeezed states", special kinds of GPS whose low-noise properties make them attractive for applications in such fields as optical communications and gravitational wave detection. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed as an improved signal-to-noise ratio relative to that obtained with coherent states (the states produced, e.g., by a laser).</p>
<p>The fifth and sixth papers deal with problems of a different nature from that of the previous papers. The fifth paper considers the validity of the "standard quantum limit" (SQL) for measurements which monitor the position of a free mass. It shows specifically that when the pre-measurement wave functions of the free mass and the measuring apparatus(es) are Gaussian (in the general sense, which includes so-called "contractive states"), measurements described by linear couplings to the position or to both the position and momentum are limited by the SQL. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models, and of the gravitational waves they emit.</p>https://thesis.library.caltech.edu/id/eprint/10414Interactions of Strings Compactified on Orbifolds
https://resolver.caltech.edu/CaltechTHESIS:08012017-135315454
Authors: {'items': [{'id': 'Hamidi-Shahram', 'name': {'family': 'Hamidi', 'given': 'Shahram'}, 'show_email': 'NO'}]}
Year: 1987
DOI: 10.7907/gvyt-8e89
<p>It is very important to understand the process of string compactification before one can extract any reliable phenomenology. We consider an exactly solvable method of string compactification, in which the internal space is an orbifold. We compute various interaction amplitudes and describe how other amplitudes can be calculated.</p>
<p>Multi-valued string variables are handled by formulating the amplitudes on covering spaces where they become single-valued. In the computation of the amplitudes, stretched string intermediate states give rise to expressions that are non-perturbative from the non-linear sigma model point of view.</p>
<p>We also discuss, in the context of Z orbifold, the "blowing up" of the fixed points of an orbifold, to give rise to a Calabi-Yau manifold. The resulting Calabi-Yau manifold is shown to be non-perturbatively stable.</p>https://thesis.library.caltech.edu/id/eprint/10358Quantum and Inflationary Cosmology with Higher Derivative Gravity
https://resolver.caltech.edu/CaltechTHESIS:08022017-083105707
Authors: {'items': [{'id': 'Mijić-Milan-B', 'name': {'family': 'Mijić', 'given': 'Milan B.'}, 'show_email': 'NO'}]}
Year: 1987
DOI: 10.7907/1sz4-gt36
<p>The subject of this thesis is the description of the Very Early Universe, from the Big Bang to the beginning of the radiation-dominated Friedman-Roberston-Walker era. We examine a pure gravity inflationary model for the Universe which is based on adding ƐR<sup>2</sup> term to the usual gravitational Lagrangian ("improved Starobinsky model"). We find the classical inflationary solution essentially independent of initial conditions. The model has only one free parameter, which is bounded from above by observational constraints on scalar and tensorial perturbations and from below by both the need for standard baryogenesis and the need for galaxy formation. This requires 10<sup>11</sup>GeV < Ɛ<sup>-1/2</sup> < 10<sup>13</sup>GeV.</p>
<p>The model is interpreted as a Chaotic Inflationary model, with initial conditions for classical evolution being generated by the quantum fluctuations in metric and curvature in Very Early Universe. We discuss those fluctuations using a particular solution of the Wheeler-De Witt equation and find that the inflationary phase is a highly typical event.</p>https://thesis.library.caltech.edu/id/eprint/10359Relativistic Stellar Pulsations
https://resolver.caltech.edu/CaltechETD:etd-08262008-093129
Authors: {'items': [{'email': 'lsfinn@psu.edu', 'id': 'Finn-Lee-Samuel', 'name': {'family': 'Finn', 'given': 'Lee Samuel'}, 'show_email': 'YES'}]}
Year: 1987
DOI: 10.7907/T7VS-8648
<p>This thesis consists of studies on the topic of relativistic stellar pulsations.</p>
<p><i>i)</i> A new formalism for the numerical study of <i>g</i>-modes in neutron stars is developed. This formalism avoids pitfalls associated with previous formalisms when applied to the study of these low-frequency modes. The formalism involves a new choice of perturbation variables, the introduction of an "instantaneous gravity" approximation to the field outside the star, and an energy principle for determining gravitational radiation damping times. The formalism is used to study <i>g</i>-modes that arise because of chemical inhomogeneities in neutron star crusts. <i>g</i>-mode frequencies associated with chemical inhomogeneities are found to be much higher than those associated with finite temperature.</p>
<p><i>ii)</i> The relativistic Cowling approximation, introduced by McDermott, Van Horn, and Scholl (1983) and analogous to the Newtonian Cowling approximation, is refined to make it more accurate in the regime of highly relativistic stars. The approximation is used to prove a host of useful theorems regarding the non-radial modes of relativistic stars.</p>
<p><i>iii)</i> Realistic neutron stars have a solid crust, and this will seriously affect their <i>g</i>-modes. The first steps toward developing a theory of non-radial relativistic pulsations in stars with a solid crust is reported on here: the calculation of the shear strain and stress during a pulsation, the introduction of the shear stress into the Einstein field equations as a source and to the equations of motion as a force, and the development of a Lagrangian and variational principle for studying non-radial relativistic pulsations in stars with a solid crust.</p>
<p><i>iv)</i> Solar five-minute oscillations are a weak source of gravitational radiation. The inner part of the solar system is actually in the transition zone of the solar oscillation gravitational field, and future space-based beam detectors might be able to measure the solar "transition-zone radiation." The transition-zone gravitational field is explored for four relativistic gravity theories: a spin-zero theory (Nordstøm's theory), a spin-one theory (analogous to electromagnetism), a spin-two theory (general relativity), and a mixed spin-zero/spin-one theory (Jordan-Brans-Dicke theory). From the transition-zone gravitational field, it is possible to determine experimentally the spin content of relativistic gravity.</p>
https://thesis.library.caltech.edu/id/eprint/3230Excitation and Damping of Solar P-Modes
https://resolver.caltech.edu/CaltechETD:etd-09092008-090628
Authors: {'items': [{'id': 'Kumar-Pawan', 'name': {'family': 'Kumar', 'given': 'Pawan'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/q6y2-3263
<p>I have carried out detailed analysis of the interaction of acoustic radiation with homogeneous turbulence in order to understand the excitation of solar p-modes by turbulent convection. The most significant outcome of this investigation is the finding that, for certain types of forced turbulences, the absorption of acoustic waves is no greater than a free turbulence, whereas the emission is always enhanced by a factor M⁻², where M is the Mach number of the turbulence. Turbulent convection in the sun is an example of this kind of turbulence. This leads to the conclusion that energies in solar p-modes, due to their interaction with the convection, should be approximately equal to the thermal energy in a resonant eddy. This is found to be in good agreement with the observations. The ideas developed in the above work have been applied to explain the recently observed absorption of acoustic waves by sunspots as well. Work has also been carried out to determine the probability distribution function for the time averaged energy of stochastically excited modes. We hope to learn about the nature of the excitation and damping processes for the solar modes by comparing this theoretically determined distribution with the observations.</p>
<p>In an effort towards resolving the overstability question of solar p-modes, I have investigated the effectiveness of 3-mode couplings, the most plausible process for limiting the amplitudes of overstable modes. The 3-mode coupling mechanism is also a good candidate for exciting fundamental modes which are found to be linearly stable, but are observed to have energies comparable to p-modes of similar frequencies. The issue of mode stability remains inconclusive due to the unknown energies of modes with period ~3.5 minutes. However, we find the fundamental modes to be damped as a result of mode couplings and hence they require excitation by a mechanism other than the overstability.</p>
https://thesis.library.caltech.edu/id/eprint/3407The R +ɛR² Cosmology
https://resolver.caltech.edu/CaltechTHESIS:02202013-144403198
Authors: {'items': [{'id': 'Morris-Michael-Scott', 'name': {'family': 'Morris', 'given': 'Michael Scott'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/h44f-9639
<p>This thesis presents the study of a model cosmology based on the R +ɛR² gravitational Lagrangian. It may be roughly divided into two distinct parts. First, the classical inflationary scenario is developed. Then, the formalism of quantum cosmology is employed to determine initial conditions for the classical model.</p>
<p>In the work on the classical model, the evolution equations for an isotropic and homogeneous universe are solved to exhibit both early-time inflation and a smooth transition to subsequent radiation-dominated behavior. Then perturbations on this isotropic background are evolved through the model to provide constraints on the model parameters from the observational limits on anisotropy today. This study concludes that such an inflationary model will prove a viable description for our universe if the initial Hubble parameter <i>H<sub>i</sub></i> is bounded from below, <i>H<sub>i</sub></i> > 10⁻⁵ <i>l</i><sub>Pl</sub>⁻¹, and if ɛ > 10¹¹ <i>l</i><sub>Pl</sub>².</p>
<p>In the work on the wave function, the two boundary conditions of Vilenkin ("tunneling from nothing") and Hartle and Hawking ("no boundary") are compared. The wave functions obtained are restricted to the initial edge of classical Lorentzian inflationary trajectories as distributions over initial conditions for the classical inflationary model. It is found that Vilenkin's wave function prefers the universe to undergo a great deal of inflation, whereas Hartle and Hawking's wave function prefers the universe to undergo little inflation. Finally, both boundary conditions are shown to require that inhomogeneous perturbative modes start out in their ground states.</p>https://thesis.library.caltech.edu/id/eprint/7486Novel Quantum States and Measurements
https://resolver.caltech.edu/CaltechETD:etd-06192009-150752
Authors: {'items': [{'id': 'Braunstein-Samuel-Leon', 'name': {'family': 'Braunstein', 'given': 'Samuel Leon'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/9K1B-7X39
<p>i) The quantum mechanics of higher order parametric amplifiers is studied. It is shown that these devices produce meaningful quantum states; numerical calculations are performed that demonstrate the convergence of matrix elements associated with these states. Further, the correspondence between the classical and quantum evolution for these devices is studied and the differences explained by a kind of "quantum diffusion." Finally, the possibility of producing ordinary squeezed light with these devices is noted.</p>
<p>ii) The generation of squeezed light always involves some scheme that amounts to pumping electromagnetic modes at near twice their natural frequency. When the pump is itself treated quantum mechanically, extra noise is introduced that ultimately limits the amount of squeezing achievable. Detailed calculations are carried out in this regard for the parametric amplifier. It is found that the pump's initial phase noise is responsible for this limit.</p>
<p>iii) Quantum-mechanical measurements are usually described by applying the standard quantum rules to a measurement model. They can also be described by a formalism that uses mathematical objects called Effects and Operations. These two descriptions should be equivalent. D'Espagnat has raised a question about the usage of this formalism of Effects and Operations for repeated measurements. This question is cleared up, and the source of the discrepancy is given a simple interpretation.</p>
<p>iv) Usually, an inequality that is chained becomes a weaker inequality. Chaining the Bell inequality, however, leads to stronger violations by quantum mechanics. Further, a new kind of Bell inequality, based on the information obtained in a measurement, is derived. This information Bell inequality can be used to formulate tests of local realism in very general circumstances, e.g., higher spin versions of the EPR experiment. These new inequalities yield an interpretation for the size of their violation and lead to the formulation of a hierarchy of Bell inequalities for which two-particle Bell inequalities play a special role.</p>
https://thesis.library.caltech.edu/id/eprint/2651A Theoretical Study of the Generation of Squeezed-State Light via Degenerate Parametric Amplification
https://resolver.caltech.edu/CaltechETD:etd-11022007-131309
Authors: {'items': [{'id': 'Crouch-David-Dale', 'name': {'family': 'Crouch', 'given': 'David Dale'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/55jn-f921
<p>This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light.</p>
<p>i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on <i>spatial</i> differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed.</p>
<p>ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ<sup>(2)</sup> nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy.</p>
<p>iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier.</p>
<p>iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.</p>
https://thesis.library.caltech.edu/id/eprint/4376Diffraction-Limited Imaging on the 200-Inch Telescope
https://resolver.caltech.edu/CaltechTHESIS:06032013-115455313
Authors: {'items': [{'id': 'Nakajima-Tadashi', 'name': {'family': 'Nakajima', 'given': 'Tadashi'}, 'show_email': 'NO'}]}
Year: 1989
DOI: 10.7907/hgnx-x451
<p>We have used the technique of non-redundant masking at the Palomar 200-inch telescope and radio VLBI imaging software to make optical aperture synthesis maps of two binary stars, β Corona Borealis and σ Herculis. The dynamic range of the map of β CrB, a binary star with a separation of 230 milliarcseconds is 50:1. For σ Her, we find a separation of 70 milliarcseconds and the dynamic range of our image is 30:1. These demonstrate the potential of the non-redundant masking technique for diffraction-limited imaging of astronomical objects with high dynamic range.</p>
<p>We find that the optimal integration time for measuring the closure phase is longer than that for measuring the fringe amplitude. There is not a close relationship between amplitude errors and phase errors, as is found in radio interferometry. Amplitude self calibration is less effective at optical wavelengths than at radio wavelengths. Primary beam sensitivity correction made in radio aperture synthesis is not necessary in optical aperture synthesis.</p>
<p>The effects of atmospheric disturbances on optical aperture synthesis have been studied by Monte Carlo simulations based on the Kolmogorov theory of refractive-index fluctuations. For the non-redundant masking with τ<sub>c</sub>-sized apertures, the simulated fringe amplitude gives an upper bound of the observed fringe amplitude. A smooth transition is seen from the non-redundant masking regime to the speckle regime with increasing aperture size. The fractional reduction of the fringe amplitude according to the bandwidth is nearly independent of the aperture size. The limiting magnitude of optical aperture synthesis with τ<sub>c</sub>-sized apertures and that with apertures larger than τ<sub>c</sub> are derived.</p>
<p>Monte Carlo simulations are also made to study the sensitivity and resolution of the bispectral analysis of speckle interferometry. We present the bispectral modulation transfer function and its signal-to-noise ratio at high light levels. The results confirm the validity of the heuristic interferometric view of image-forming process in the mid-spatial-frequency range. The signal-to-noise ratio of the bispectrum at arbitrary light levels is derived in the mid-spatial-frequency range.</p>
<p>The non-redundant masking technique is suitable for imaging bright objects with high resolution and high dynamic range, while the faintest limit will be better pursued by speckle imaging.</p>https://thesis.library.caltech.edu/id/eprint/7823A Balloon Measurement of the Isotopic Composition of Galactic Cosmic Ray Iron
https://resolver.caltech.edu/CaltechETD:etd-05312007-121425
Authors: {'items': [{'id': 'Grove-Jon-Eric', 'name': {'family': 'Grove', 'given': 'Jon Eric'}, 'show_email': 'NO'}]}
Year: 1989
DOI: 10.7907/3cr8-jv31
<p>We have measured the isotopic composition of galactic cosmic ray iron in the energy interval ~1550-2200 MeV/nucleon using a balloon-borne mass spectrometer. The instrument was flown from Palestine, Texas, in May 1984 for >35 hours at an atmospheric depth of ~6 g/cm². Masses were derived by the Cerenkov-Energy technique. The Cerenkov counter employed a silica aerogel radiator with index of refraction n = 1.1. Particle energies were measured in a stack of NaI(Tl) scintillators, which also provided particle trajectories. The calibration of the detectors is discussed, along with the algorithms we have used to calculate velocities, energies, and masses. The limitations of aerogels as Cerenkov radiators, particularly the stability of their light yield, are considered. A detailed discussion of the sources of mass uncertainty is presented, including an analytic model of the contribution from fluctuations in the Cerenkov yield from knock-on electrons. The achieved mass resolution is ~0.65 amu, which is consistent with the theoretical estimate. We report an ⁵⁴Fe/⁵⁶Fe abundance ratio of 0.14<sup>+0.18</sup><sub>-0.11</sub> and an 84% confidence upper limit of ⁵⁸Fe/⁵⁶Fe ≤ 0.07 at the top of the atmosphere. Combining our data with those of previous measurements of the composition of iron at lower energies, and using a model of the galactic propagation, we derive cosmic-ray source abundance ratios of ⁵⁴Fe/⁵⁶Fe = 0.064<sup>+0.032</sup><sub>-0.027</sub> and ⁵⁸Fe/⁵⁶Fe ≤ 0.062. These values are consistent with the composition of solar-system iron and place restrictions on the conditions under which cosmic-ray iron is synthesized.</p>https://thesis.library.caltech.edu/id/eprint/2338Singularities and Horizons in the Collisions of Gravitational Waves
https://resolver.caltech.edu/CaltechTHESIS:10242013-145903390
Authors: {'items': [{'id': 'Yurtsever-Ulvi-Hamit', 'name': {'family': 'Yurtsever', 'given': 'Ulvi Hamit'}, 'show_email': 'NO'}]}
Year: 1989
DOI: 10.7907/zm5n-g882
<p>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 <i>exactly plane-symmetric</i> gravitational waves? Second, under what conditions will the collisions of almost-plane gravitational waves (waves with large but finite transverse sizes) produce singularities?</p>
<p>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.</p>
<p>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 <i>finite</i> 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.</p>https://thesis.library.caltech.edu/id/eprint/8009A model of the olfactory bulb and beyond
https://resolver.caltech.edu/CaltechTHESIS:02192014-080819270
Authors: {'items': [{'email': 'z.li@ucl.ac.uk', 'id': 'Li-Z', 'name': {'family': 'Li', 'given': 'Zhaoping'}, 'show_email': 'YES'}]}
Year: 1990
DOI: 10.7907/1Q5F-X469
<p>The olfactory bulb of mammals aids in the discrimination of odors. A mathematical
model based on the bulbar anatomy and electrophysiology is described. Simulations of the
highly non-linear model produce a 35-60 Hz modulated activity, which is coherent across
the bulb. The decision states (for the odor information) in this system can be thought
of as stable cycles, rather than as point stable states typical of simpler neuro-computing
models. Analysis shows that a group of coupled non-linear oscillators are responsible for
the oscillatory activities. The output oscillation pattern of the bulb is determined by the
odor input. The model provides a framework in which to understand the transformation
between odor input and bulbar output to the olfactory cortex. This model can also be
extended to other brain areas such as the hippocampus, thalamus, and neocortex, which
show oscillatory neural activities. There is significant correspondence between the model
behavior and observed electrophysiology.</p>
<p>It has also been suggested that the olfactory bulb, the first processing center after the
sensory cells in the olfactory pathway, plays a role in olfactory adaptation, odor sensitivity
enhancement by motivation, and other olfactory psychophysical phenomena. The input
from the higher olfactory centers to the inhibitory cells in the bulb are shown to be able
to modulate the response, and thus the sensitivity, of the bulb to odor input. It follows
that the bulb can decrease its sensitivity to a pre-existing and detected odor (adaptation)
while remaining sensitive to new odors, or can increase its sensitivity to discover interesting
new odors. Other olfactory psychophysical phenomena such as cross-adaptation are also
discussed.</p>https://thesis.library.caltech.edu/id/eprint/8083Radiative processes in active galactic nuclei
https://resolver.caltech.edu/CaltechETD:etd-06202007-132612
Authors: {'items': [{'email': 'paolo.coppi@yale.edu', 'id': 'Coppi-Paolo-Severo', 'name': {'family': 'Coppi', 'given': 'Paolo Severo'}, 'show_email': 'NO'}]}
Year: 1991
DOI: 10.7907/GDMQ-Q829
A study of processes relevant to the electron-positron pair plasmas thought to exist in Active Galactic Nuclei is undertaken. The processes considered include: Compton scattering, pair annihilation, two photon pair production, synchrotron emission, e-e bremsstrahlung, and Coulomb scattering. Approximations used in the past to treat these processes in the context of a kinetic code are examined, and improvements are presented. A two-moment scattering formalism is presented to allow for important energy dispersion effects in scattering. This improved treatment of microphysical processes is implemented in a time-dependent, kinetic code incorporating Klein-Nishina effects on both the pair and photon distributions, relativistic thermal Comptonization, and synchrotron reabsorption.
The effects of pair plasma reprocessing on the emergent radiation spectrum are examined. Time-varying and stationary spectra are computed. Good qualitative agreement with previous calculations is found, except when the differences are attributable to the improved treatment of the microphysics. These differences can be substantial, particularly in the "photon-starved" regime where the effects of Coulomb scattering by suprathermal pairs off thermal pairs significantly modify the spectra. The spectral response of the pair plasma to variations in the particle injection is found to depend sensitively on the plasma parameters. A transitional spectrum may look very different from the spectra of either the stationary initial or final states. The highest energies (gamma-rays) are found to respond most rapidly to changes and should vary more than the X-rays. Pair plasmas can produce soft X-ray excesses. This happens under conditions independently favored by current pair plasma-Compton reflection models of the hard X-ray spectrum.
https://thesis.library.caltech.edu/id/eprint/2662Topics in general relativity theory : gravitational-wave measurements of black-hole parameters; gravitational collapse of a cylindrical body; and classical-particle evolution in the presence of closed, timelike curves
https://resolver.caltech.edu/CaltechETD:etd-12082008-095402
Authors: {'items': [{'id': 'Echeverria-F', 'name': {'family': 'Echeverria', 'given': 'Fernando'}, 'show_email': 'NO'}]}
Year: 1993
DOI: 10.7907/BEV7-NS85
In this thesis I present three separate studies on three different topics in General Relativity.
The first study investigates the accuracy with which the mass and angular momentum of a black hole can be determined by measurements of gravitational waves from the hole, using a laser-interferometer gravitational-wave detector. The black hole is assumed to have been strongly perturbed, perhaps by coalescence with a binary companion, and the detector measures the waves produced by its resulting vibration and ring-down. The uncertainties in the measured mass and angular momentum arise from the unavoidable presence of noise in the detector. It is found that the faster the hole rotates, the more accurate the measurements will be, with the uncertainty in the angular momentum decreasing rapidly with increasing rotation speed. It is also found that the errors in the mass and angular momentum are highly correlated.
The second study is an analysis of the gravitational collapse of an infinitely long, cylindrical dust shell. This analysis is expected to be helpful in understanding the behavior during collapse of more realistic, finite-length bodies. It is found that the collapse evolves into a naked singularity in finite time, as measured by a distant observer or by one riding on the shell. Analytical expressions for the variables describing the collapse are found at late times, near the singularity. The picture is completed with a numerical simulation that follows the collapse from the start until very close to the singularity. The singularity is found to be strong, in the sense that an observer riding on the shell will be infinitely stretched in the direction parallel to the symmetry axis, and infinitely compressed in the azimuthal direction. The gravitational waves emitted from the collapse are also analyzed.
The last study focuses on a different kind of phenomenon, namely, the consequences of the existence of closed timelike curves in a spacetime that contains a wormhole. One might expect that the closed timelike curves would cause difficulty for the initial value problem for systems that evolve in such a spacetime: a system with apparently well-posed initial conditions might have no self-consistent solutions to its evolution equations. We study the simple case of a macroscopic, classical particle with a hard-sphere potential (a "billiard ball"), and we focus attention on initial conditions for which the evolution, if followed naively, is self- inconsistent: the ball enters one mouth of the wormhole and then comes out of the other mouth at an earlier time, then collides with its younger self, preventing itself from ever entering the first mouth. We find, surprisingly, that for all such "dangerous" initial conditions, there are an infinite number of self-consistent evolutionary solutions, involving a glancing collision and any number of wormhole traversals. We also find that for many non-dangerous initial conditions, there also exist an infinity of possible evolutions.
https://thesis.library.caltech.edu/id/eprint/4882Topics in general relativity : the hoop conjecture and theoretical aspects of gravitational wave detection
https://resolver.caltech.edu/CaltechETD:etd-11132006-095610
Authors: {'items': [{'email': 'eef3@cornell.edu', 'id': 'Flanagan-E-E', 'name': {'family': 'Flanagan', 'given': 'Eanna E.'}, 'show_email': 'YES'}]}
Year: 1994
DOI: 10.7907/7SW7-8076
The body of this thesis consists of four chapters (2 through 5), each of which is a paper that has been published in or submitted for publication to Physical Review D. I am the sole author of chapters 2, 3, and 4; Curt Cutler coauthored chapter 5 with me.
These four chapters deal with two topics in general relativity: the formation of horizons in nonspherical gravitational collapse (chapters 2 and 3), and some theoretical aspects of the effort to detect gravitational waves from cosmic sources (chapters 4 and 5). These four chapters were written largely for experts in the topics they cover. As an aid to general readers, I shall give in this introductory chapter some background information about chapters 2 through 5 and a nontechnical overview of their contents.https://thesis.library.caltech.edu/id/eprint/4534Topics in general relativity : naked singularities, and theoretical aspects of gravitational waves from merging compact binaries
https://resolver.caltech.edu/CaltechETD:etd-09112007-132644
Authors: {'items': [{'id': 'Apostolatos-T-A', 'name': {'family': 'Apostolatos', 'given': 'Theocaris A.'}, 'show_email': 'NO'}]}
Year: 1995
DOI: 10.7907/2x5m-b994
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Two topics in classical general relativity are discussed: a) The clothing of singularities by event horizons, and b) various issues in the evolution of coalescing compact binaries, as sources of gravitational waves to be detected by the LIGO/VIRGO/GEO ground-based detectors and/or the LISA space-based detector. More specifically:
We investigate a problem related to an important conjecture of classical relativity, namely the existence of a "cosmic censorship" that forbids the formation of naked singularities, and always clothes them with event horizons that causally hide them from the rest of the Universe. Under consideration is the role of rotation in an infinite cylindrical shell consisting of collisionless dust particles, half of which rotate clockwise and half counterclockwise. We show that, although such a shell without any rotation is known to collapse into a line singularity, the presence of an arbitrarily small amount of rotation is sufficient to halt the collapse. Such a shell, starting from a non equibrium configuration, will "breath" radially, emitting gravitational waves, and will finally settle down to an equilibrium radius at which gravity is balanced by centrifugal forces. This suggests the essential role that rotation might play in halting the gravitational collapse of an elongated distribution of mass and preventing the formation of a naked singularity. However, this is a highly idealized example, and it can, by no means, ensure the validity of the "cosmic censorship" hypothesis.
On a separate topic, we explore the details of how gravitational radiation reaction drives the evolution of a slightly eccentric orbit of a small body around nonrotating supermassive black holes. A combination of analytic and numerical results arise from the solution of the Teukolsky perturbation equation. It is shown that in the fully relativistic situation, as in the Newtonian quadrupole approximation, there is a tendency for circularization of the orbit down to an orbital radius [...], where M is the mass of the black hole, and G and c are Newton's gravitation constant and the speed of light. It is further shown that for radii smaller than [...] the eccentricity increases.
Finally, an attempt is made to understand and construct analytic expressions that, based on the laws of general relativity, approximately describe the simultaneous precession in rapidly spinning black hole and/or neutron star and inspiral binaries with circular orbits. The precession is produced by general relativistic spin-orbit and spin-spin coupling; the inspiral, by gravitational radiation reaction. We derive the corresponding approximate waveforms to be received by the network of LIGO, VIRGO, and GEO earth-based gravitational-wave detectors. We then go on to investigate the adequateness of various "families of templates," to detect these spin-modulated waveforms by the method of "matching filters," We introduce a "fitting factor" FF as a measure of templates' adequateness, and show the complete inadequateness, for the task of detection, of the "Newtonian template family" (the set of the waveforms derived from the Newtonian, quadrupole approximation formalism). Another template family with an extra parameter is suggested that performs much better.https://thesis.library.caltech.edu/id/eprint/3472Electron energy loss spectroscopic study of small molecules on transition metal surfaces
https://resolver.caltech.edu/CaltechETD:etd-10122007-112248
Authors: {'items': [{'id': 'Wang-Youqi', 'name': {'family': 'Wang', 'given': 'Youqi'}, 'show_email': 'NO'}]}
Year: 1995
DOI: 10.7907/h31m-na55
The scheme of ultrahigh-resolution electron energy loss spectroscopy (UNREELS) is described in detail with graphical examples of the real data processing. On the basis of modern digital information processing techniques, this method promises to yield EEL spectra with the ultimate resolution and superior signal to noise ratio.
The interaction of ammonia with clean and chemically modified Ru(001) surfaces were studied by using HREELS, TPD, and LEED techniques under UHV condition. Ammonia is found to interact with the surface chiefly through its lone-pair electrons, evidenced by the blue-shift of ammonia symmetric deformation mode and the increase of thermal desorption temperature of ammonia on both oxygen and nitrogen modified surfaces. No detectable dissociation of ammonia is found under the specified conditions.
The reactions of gas-phase atomic hydrogen with oxygen and carbon monoxide pre-adsorbed on Ru(001) surface at low temperature were studied via HREELS technique. The experimental results can be understood via an Eley-Rideal-like mechanism.
The decomposition mechanism of methylamine on Ru(001) surface was investigated by HREELS and TPD techniques. The cyanide adspecies was found to be side-on bonded on the ruthenium surface and its bond order is reduced from three to two.
https://thesis.library.caltech.edu/id/eprint/4055Signal Extraction and Optical Design for an Advanced Gravitational Wave Interferometer
https://resolver.caltech.edu/CaltechTHESIS:04302012-152752095
Authors: {'items': [{'id': 'Mason-James-Edward', 'name': {'family': 'Mason', 'given': 'James Edward'}, 'show_email': 'NO'}]}
Year: 2001
DOI: 10.7907/amrv-a028
<p>The LIGO project is two 4 km baseline interferometers which are currently being
constructed in the quest to directly detect gravitational radiation. Concurrent with
this effort is research aimed at increasing the strain sensitivity of the initial interferometers to 2.5 x 10^(-23)/√Hz. The optical configuration, which defines the detector gain and bandwidth, is one such area of research. Resonant sideband extraction (RSE) is the configuration which is proposed for advanced LIGO. RSE allows for much more freedom in the optimization of the detector response compared to the
initial configuration.</p>
<p>The principle of RSE is examined in the context of a three mirror coupled cavity.
The effect of optical losses on the design of an RSE interferometer is discussed. Two
model optimizations of the interferometer design are done: one for binary inspiral
sources and one for periodic sources at 1 kHz.</p>
<p>An optical heterodyne signal extraction scheme is proposed to sense the deviation
of the mirrors away from their nominal positions, and to read out the gravitational
wave signal. The scheme is applied to the two model interferometers previously
designed, and its performance is analyzed for each case. Allowable residual deviations of the common mode degrees of freedom are also derived.</p>
<p>A tabletop prototype of an RSE interferometer has been constructed to demonstrate
both the viability of the proposed signal extraction scheme and the tunability
of the RSE interferometer. Good agreement on both counts is found between the
measured experimental data and the modeled predictions.</p>
<p>The coupling of laser frequency and amplitude noise into the gravitational wave
readout port is analyzed for the RSE configuration assuming the proposed gravitational
wave signal readout scheme. Specifications for the allowable laser frequency
and amplitude noise, as well as allowable residual deviations of the differential mode
degrees of freedom, are derived for the two model interferometers.</p>
https://thesis.library.caltech.edu/id/eprint/6994Modeling and Detecting Gravitational Waves from Compact Stellar Objects
https://resolver.caltech.edu/CaltechETD:etd-05292002-113750
Authors: {'items': [{'email': 'vallis@vallis.org', 'id': 'Vallisneri-Michele', 'name': {'family': 'Vallisneri', 'given': 'Michele'}, 'orcid': '0000-0002-4162-0033', 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/JN6M-BW40
<p>In the next few years, the first detections of gravity-wave signals using Earth-based interferometric detectors will begin to provide precious new information about the structure, dynamics, and evolution of compact bodies, such as neutron stars and black holes, both isolated and in binary systems. The intrinsic weakness of gravity-wave signals requires a proactive approach to modeling the prospective sources and anticipating the shape of the signals that we seek to detect. Full-blown 3-D numerical simulations of the sources are playing and will play an important role in planning the gravity-wave data-analysis effort. This thesis explores the interplay between numerical source modeling and data analysis, looking closely at three case studies.</p>
<p>1. I evaluate the prospects for extracting equation-of-state information from neutron-star tidal disruption in neutron-star–black-hole binaries with LIGO-II, and I estimate that the observation of disrupting systems at distances that yield about one event per year should allow the determination of the neutron-star radius to about 15%, which compares favorably to the currently available electromagnetic determinations.</p>
<p>2. In collaboration with Lee Lindblom and Joel Tohline, I perform numerical simulations of the nonlinear dynamics of the <i>r</i>-mode instability in young, rapidly spinning neutron stars, and I find evidence that nonlinear couplings to other modes will not pose a significant limitation to the growth of the <i>r</i>-mode amplitude.</p>
<p>3. In collaboration with Alessandra Buonanno and Yanbei Chen, I study the problem of detecting gravity waves from solar-mass black-hole–black-hole binaries with LIGO-I, and I construct two families of <i>detection</i> templates that address the inadequacy of standard post-Newtonian theory to predict reliable waveforms for these systems.</p>
https://thesis.library.caltech.edu/id/eprint/2226Controlling Quantum Information
https://resolver.caltech.edu/CaltechTHESIS:03142012-093815562
Authors: {'items': [{'id': 'Landahl-Andrew-John', 'name': {'family': 'Landahl', 'given': 'Andrew John'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/BJ0Q-C297
<p>Quantum information science explores ways in which quantum physical laws can be harnessed to control the acquisition, transmission, protection, and processing
of information. This field has seen explosive growth in the past several years from progress on both theoretical and experimental fronts. Essential to this endeavor are methods for controlling quantum information.</p>
<p>In this thesis, I present three new approaches for controlling quantum information. First, I present a new protocol for continuously protecting unknown quantum
states from noise. This protocol combines and expands ideas from the theories of quantum error correction and quantum feedback control. The result can outperform either approach by itself. I generalize this protocol to all known quantum
stabilizer codes, and study its application to the three-qubit repetition code in detail via Monte Carlo simulations.</p>
<p>Next, I present several new protocols for controlling quantum information that are fault-tolerant. These protocols require only local quantum processing due to
the topological properties of the quantum error correcting codes upon which they are built. I show that each protocol's fault-dependence behavior exhibits an order-disorder phase transition when mapped onto an associated statistical-mechanical model. I review the critical error rates of these protocols found by numerical study
of the associated models, and I present new analytic bounds for them using a self-avoiding random walk argument. Moreover, I discuss fault-tolerant procedures for encoding, error-correction, computing, and decoding quantum information using these protocols, and calculate the accuracy threshold of fault-tolerant quantum memory for protocols using them.</p>
<p>I end by presenting a new class of quantum algorithms that solve combinatorial optimization problems solely by measurement. I compute the running times of
these algorithms by establishing an explicit dynamical model for the measurement process. This model, the digitized version of von Neumann's measurement model,
is recognized as Kitaev's phase estimation algorithm. I show that the running times of these algorithms are closely related to the running times of adiabatic quantum algorithms. Finally, I present a two-measurement algorithm that achieves a quadratic speedup for Grover's unstructured search problem.</p>https://thesis.library.caltech.edu/id/eprint/6851Topics in General Relativity: Binary Black Holes and Hyperbolic Formulations of Einstein's Equations
https://resolver.caltech.edu/CaltechTHESIS:01202012-112836824
Authors: {'items': [{'id': 'Alvi-Kashif-Siddiq', 'name': {'family': 'Alvi', 'given': 'Kashif Siddiq'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/5S0S-MF65
<p>This thesis consists of three projects in general relativity on topics related to binary black holes
and the gravitational waves they emit. The first project involves calculating a four-metric that is an approximate solution to Einstein's equations representing two widely separated nonrotating black holes in a circular orbit. This metric is constructed by matching a post-Newtonian metric to
two tidally distorted Schwarzschild metrics using the framework of matched asymptotic expansions. The four-metric presented here provides physically realistic initial data that are tied to the binary's inspiral phase and can be evolved numerically to determine the gravitational wave output during the late stages of inspiral as well as the merger.</p>
<p>The second project is on the tidal interaction of binary black holes during the inspiral phase. The holes' tidal distortion results in the flow of energy and angular momentum into or out of the holes in a process analogous to Newtonian tidal friction in a planet-moon system. The changes in the black holes' masses, spins, and horizon areas during inspiral are calculated for a circular binary with holes of possibly comparable masses. The absorption or emission of energy and angular momentum by the holes is shown to have a negligible influence on the binary 's orbital evolution when the holes have comparable masses. The tidal-interaction analysis presented in this thesis is applicable to a black hole in a binary with any companion body (e.g., a neutron star) that is well separated from
the hole.</p>
<p>The final project is on first-order hyperbolic formulations of Einstein's equations, which are promising as a basis for numerical simulation of binary black holes. This thesis presents two first-order symmetrizable hyperbolic systems that include the lapse and shift as dynamical fields and have only physical characteristic speeds. The first system may be useful in numerical work; the second system allows one to show that any solution to Einstein's equations in any gauge can be obtained
using hyperbolic evolution of the entire metric, including the gauge fields.</p>https://thesis.library.caltech.edu/id/eprint/6771Lock Acquisition in Resonant Optical Interferometers
https://resolver.caltech.edu/CaltechETD:etd-12062004-115632
Authors: {'items': [{'email': 'mevans@ligo.caltech.edu', 'id': 'Evans-Matthew-John', 'name': {'family': 'Evans', 'given': 'Matthew John'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/N1J2-M098
The LIGO (Laser Interferometric Gravitational-wave Observatory) project, and other projects around the world, are currently planning to use long-baseline (> 1 km) interferometers to directly detect gravitational radiation from astrophysical sources. In this work we present a framework for lock acquisition, the process by which an initially uncontrolled resonant interferometer is brought to its operating point. Our approach begins with the identification of a path which takes the detector from the uncontrolled state to the operational state. The properties of the detector's outputs along this path, embodied in the sensing matrix, must be determined and parameterized in terms of measureables. Finally, a control system which can compute the inverse of the sensing matrix, apply it to the incoming signals, and make the resulting signals available for feedback is needed to close the control loop. This formalism was developed and explored extensively in simulation and was subsequently applied to the LIGO interferometers. Results were in agreement with expectation within error, typically ±20% on the sensing matrix elements, and the method proved capable of bringing a high-finesse power-recycled Fabry-Perot-Michelson interferometer (a LIGO detector) to its operating point.https://thesis.library.caltech.edu/id/eprint/4806Quantum Transport and Dynamics of Phonons in Mesoscopic Systems
https://resolver.caltech.edu/CaltechETD:etd-05272003-152136
Authors: {'items': [{'email': 'dsantamore@desu.edu@desu.edu', 'id': 'Santamore-Deborah-Hannah', 'name': {'family': 'Santamore', 'given': 'Deborah Hannah'}, 'orcid': '0000-0001-6305-7096', 'show_email': 'YES'}]}
Year: 2003
DOI: 10.7907/E62V-PR26
<p>Recent advances in nanotechnology have shrunk the size of mesoscopic structures. This allows us to investigate the quantum mechanics of mechanical oscillators. In this thesis we focus on two aspects.</p>
<p>In Part I, an individual discrete mode structure of an oscillator and its effect to thermal conductance have been thoroughly examined: Specifically, we investigated the reduction in the thermal conductance in the quantum limit due to phonon scattering by surface roughness, first using scalar waves, then using full three dimensional elasticity theory for an elastic beam with a rectangular cross section. At low frequencies, we find power laws for the scattering coefficients that are strongly mode dependent, and different from the results deriving from Rayleigh scattering of scalar waves, that is often assumed. The scattering gives temperature dependent contributions to the reduction in thermal conductance with the same power laws. At higher frequencies, the scattering coefficient becomes large at the onset frequency of each mode due to the flat dispersion. We use our results to attempt a quantitative understanding of the suppression of the thermal conductance from the universal value observed in experiment.</p>
<p>As individual phonon energy becomes comparable to or greater than the thermal energy, the individual phonon dynamics within each mode can be resolved. In Part II, we examine a possibility of detecting individual quanta of a system: We investigate a scheme that makes a quantum non-demolition measurement of the excitation level of a mesoscopic mechanical oscillator by utilizing the anharmonic coupling between two bending modes of an elastic beam. The non-linear coupling between the two modes shifts the resonant frequency of the readout oscillator proportionate to the excitation of the system oscillator. This frequency shift may be detected as a phase shift of the readout oscillation when driven on resonance. We show that in an appropriate regime this measurement approaches a quantum non-demolition measurement of the phonon number of the system oscillator. As a result it should be possible to monitor jumps between Fock states caused by the coupling of the system to the thermal reservoirs.</p>https://thesis.library.caltech.edu/id/eprint/2123Pulsar Searches: From Radio to Gamma-Rays
https://resolver.caltech.edu/CaltechETD:etd-01232003-213508
Authors: {'items': [{'id': 'Chandler-Adam-Matthew', 'name': {'family': 'Chandler', 'given': 'Adam Matthew'}, 'show_email': 'NO'}]}
Year: 2003
DOI: 10.7907/MDJX-M255
<p>We report the results of four different pulsar searches, covering radio, X-ray, and gamma-ray wavelengths. These searches targeted pulsars in virtually all of their guises: young and old, long-period and short-period, accretion-powered and rotation-powered. Ten new pulsars were discovered.</p>
<p>There are very few known gamma-ray pulsars, all of which were found by folding gamma-ray data with a pulse period known from other wavelengths. Some emission models indicate that there may be a large number of gamma-ray pulsars that are undetectable at lower energies. We searched several of the brightest unidentified gamma-ray sources for pulsations. This was the first attempt to identify gamma-ray pulsars by a direct search of gamma-ray data. No new identifications resulted and we report upper limits.</p>
<p>Even more rare than gamma-ray pulsars are accreting millisecond pulsars. We searched for coherent pulsations from Aql X-1, a low-mass X-ray binary suspected of harboring such an object. No pulsations were detected, and we argue that the quiescent emission of this system has a thermal origin (i.e., it is not due to low-level accretion).</p>
<p>The two radio searches included here were both designed to detect millisecond pulsars. First, we report the results of a large area survey from Arecibo. Five new slow pulsars were discovered, including an apparent orthogonal rotator and an extremely unusual bursting radio pulsar. No short-period pulsars were discovered and we place some of the first useful observational constraints on the limiting spin period of a neutron star.</p>
<p>We also performed pointed searches of several globular clusters using the new Green Bank Telescope. Three new binary millisecond pulsars were found in M62. These were the first new objects found with the GBT, and they bring the total pulsar population in M62 to six. We also discovered two isolated pulsars, one each in NGC 6544 and NGC 6624.</p>
<p>Many of the methods we developed will be relevant to future searches. Perhaps the most significant contribution is a dynamic power spectrum-based technique that finally allows sensitive searches for binary pulsars whose orbital periods are of the same order as the observation time.</p>https://thesis.library.caltech.edu/id/eprint/286Topics of LIGO Physics: Quantum Noise in Advanced Interferometers and Template Banks for Compact-Binary Inspirals
https://resolver.caltech.edu/CaltechETD:etd-05302003-044325
Authors: {'items': [{'email': 'yanbei@tapir.caltech.edu', 'id': 'Chen-Yanbei', 'name': {'family': 'Chen', 'given': 'Yanbei'}, 'orcid': '0000-0002-9730-9463', 'show_email': 'NO'}]}
Year: 2003
DOI: 10.7907/VQH0-QA78
This thesis deals with the planning for advanced interferometric gravitational-wave detectors, as well as the detection of inspiral waves using first-generation interferometers.
In Chapters 2 -- 4 (in collaboration with Alessandra Buonanno), the the signal recycling interferometer proposed for LIGO-II is studied in the two-photon formalism. This study reveals the optical spring effect, which allows the interferometer to beat the standard quantum limit, while in the same time introduces a dynamical instability. A classical control system is designed to suppress this instability. In Chapter 5 (in collaboration with Alessandra Buonanno and Nergis Mavalvala), the quantum noise in heterodyne readout schemes for advanced interferometers is studied. In Chapter 6 (in collaboration with Patricia Purdue), a QND Speed-Meter interferometer with Michelson topology is proposed, analyzed and shown to be a promising candidate for third-generation interferometers (LIGO-III or EURO). This design requires adding a kilometer-scale cavity into the interferometer. In Chapter 7, Sagnac interferometers are analyzed and shown to exhibit a similar broadband QND performance without the need of additional cavity --- as expected since these interferometers are sensitive only to time-dependent mirror displacement, and are automatic speed meters.
In Chapter 8 (in collaboration with Alessandra Buonanno and Michele Vallisneri), the Post-Newtonian (PN) breakdown at late-stage inspirals of non-spinning binary black holes is studied. We propose the use of Detection Template Families (DTFs) --- extensions of ordinary PN templates that can mimic all different PN waveforms and hence are plausible to catch the real waveform, yet do not provide straightforward parameter estimation. In Chapter 9 (in collaboration with Alessandra Buonanno and Michele Vallisneri), binaries carrying spins are studied using an adiabatic PN model. Based on features of the precession dynamics, we construct a DTF, using a modified Apostolatos' ansatz, that can mimic the modulated waveforms reasonably well, while keeping a small number of parameters to be searched over one by one, with the rest searched over automatically. We also propose a (computationally) plausible way of searching over the entire physical parameter space of neutron-star--black-hole binaries.https://thesis.library.caltech.edu/id/eprint/2286Mirror Thermal Noise in Interferometric Gravitational Wave Detectors
https://resolver.caltech.edu/CaltechETD:etd-05092003-153759
Authors: {'items': [{'id': 'Rao-Shanti-Raja', 'name': {'family': 'Rao', 'given': 'Shanti Raja'}, 'show_email': 'NO'}]}
Year: 2003
DOI: 10.7907/5W0V-QB90
<p>The LIGO (Laser Interferometer Gravitational-wave Observatory) project has begun its search for gravitational waves, and efforts are being made to improve its ability to detect these. The LIGO observatories are long, Fabry-Perot-Michelson interferometers, where the interferometer mirrors are also the gravitational wave test masses. LIGO is designed to detect the ripples in spacetime caused by cataclysmic astrophysical events, with a target gravitational wave minimum strain sensitivity of 4 x 10^-22 around 100 Hz. The Advanced LIGO concept calls for an order of magnitude improvement in strain sensitivity, with a better signal to noise ratio to increase the rate of detection of events. Some of Advanced LIGO's major requirements are improvements over the LIGO design for thermal noise in the test mass substrates and reflective coatings.</p>
<p>Thermal noise in the interferometer mirrors is a significant challenge in LIGO's development. This thesis reviews the theory of test mass thermal noise and reports on several experiments conducted to understand this theory.v
<p>Experiments to measure the thermal expansion of mirror substrates and coatings use the photothermal effect in a cross-polarized Fabry-Perot interferometer, with displacement sensitivity of 10^-15 m/rHz. Data are presented from 10 Hz to 4kHz on solid aluminum, and on sapphire, BK7, and fused silica, with and without commercial TiO2/SiO2 dielectric mirror coatings. The substrate contribution to thermal expansion is compared to theories by Cerdonio et al. and Braginsky, Vyatchanin, and Gorodetsky. New theoretical models are presented for estimating the coating contribution to the thermal expansion. These results can also provide insight into how heat flows between coatings and substrates relevant to predicting coating thermoelastic noise.</p>
<p>The Thermal Noise Interferometer (TNI) project is a interferometer built specifically to study thermal noise, and this thesis describes its construction and commissioning. Using LIGO-like designs, components, and processes, the TNI has a minimum length noise in each of two arm cavities of 5 x 10^-18 m/rHz around 1 kHz.</p>https://thesis.library.caltech.edu/id/eprint/1696Dynamics of Spinning Compact Binaries in General Relativity
https://resolver.caltech.edu/CaltechETD:etd-05222003-161626
Authors: {'items': [{'email': 'mhartl@post.harvard.edu', 'id': 'Hartl-Michael-David', 'name': {'family': 'Hartl', 'given': 'Michael David'}, 'show_email': 'NO'}]}
Year: 2003
DOI: 10.7907/KZ5M-MR27
<p>This thesis investigates the dynamics of binary systems composed of spinning compact objects (such as white dwarfs, neutron stars, and black holes) in the context of general relativity. In particular, we use the method of Lyapunov exponents to determine whether such systems are chaotic. Compact binaries are promising sources of gravitational radiation for both ground- and space-based gravitational-wave detectors, and radiation from chaotic orbits would be difficult to detect and analyze. For chaotic orbits, the number of waveform templates needed to match a given gravitational-wave signal would grow exponentially with increasing detection sensitivity, rendering the preferred matched filter detection method computationally impractical. It is therefore urgent to understand whether the binary dynamics can be chaotic, and, if so, how prevalent this chaos is.</p>
<p>We first consider the dynamics of a spinning compact object orbiting a much more massive rotating black hole, as modeled by the Papapetrou equations in Kerr spacetime. We find that many initial conditions lead to positive Lyapunov exponents, indicating chaotic dynamics. The Lyapunov exponents come in positive/negative pairs, a characteristic of Hamiltonian dynamical systems. Despite the formal existence of chaotic solutions, we find that chaos occurs only for physically unrealistic values of the small body's spin. As a result, chaos will not affect theoretical templates in the extreme mass-ratio limit for which the Papapetrou equations are valid. Chaos will therefore not affect the ability of space-based gravitational-wave detectors (such as LISA, the Laser Interferometer Space Antenna) to perform precision tests of general relativity using extreme mass-ratio inspirals.</p>
<p>We next consider the dynamics of spinning black-hole binaries, as modeled by the post-Newtonian (PN) equations, which are valid for orbital velocities much smaller than the speed of light. We study thoroughly the special case of quasi-circular orbits with comparable mass ratios, which are particularly relevant from the perspective of gravitational wave generation for LIGO (the Laser Interferometer Gravitational-wave Observatory) and other ground-based interferometers. In this case, unlike the extreme mass-ratio case, we find chaotic solutions for physically realistic values of the spin. On the other hand, our survey shows that chaos occurs in a negligible fraction of possible configurations, and only for such small radii that the PN approximation is likely to be invalid. As a result, at least in the case of comparable mass black-hole binaries, theoretical templates will not be significantly affected by chaos.</p>
<p>In a final, self-contained chapter, we discuss various methods for the calculation of Lyapunov exponents in systems of ordinary differential equations. We introduce several new techniques applicable to constrained dynamical systems, developed in the course of studying the dynamics of spinning compact binaries.</p>
<p>Considering the Papapetrou and post-Newtonian systems together, our most important general conclusion is that we find no chaos in any relativistic binary system for orbits that clearly satisfy the approximations required for the equations of motion to be physically valid.</p>https://thesis.library.caltech.edu/id/eprint/1940Quantum Information Theory: Classical Communication Over Quantum Channels
https://resolver.caltech.edu/CaltechETD:etd-02172004-173217
Authors: {'items': [{'email': 'jcort@ll.mit.edu', 'id': 'Cortese-John-Anthony', 'name': {'family': 'Cortese', 'given': 'John Anthony'}, 'show_email': 'NO'}]}
Year: 2004
DOI: 10.7907/V68W-YK95
This thesis studies classical communication over quantum channels. Chapter 1 describes an algebraic technique which extends several previously known qubit channel capacity results to the qudit quantum channel case. Chapter 2 derives a formula for the relative entropy function of two qubit density matrices in terms of their Bloch vectors. The application of the Bloch vector relative entropy formula to the determination of Holevo-Schumacher-Westmoreland (HSW) capacities for qubit quantum channels is discussed. Chapter 3 outlines several numerical simulation results which support theoretical conclusions and conjectures discussed in Chapters 1 and 2. Chapter 4 closes the thesis with comments, examples and discussion on the additivity of Holevo Chi and the HSW channel capacity.https://thesis.library.caltech.edu/id/eprint/649Radiative Transfer in Accreting Environments
https://resolver.caltech.edu/CaltechETD:etd-05262004-231543
Authors: {'items': [{'email': 'abroderick@uwaterloo.ca', 'id': 'Broderick-Avery-Earl', 'name': {'family': 'Broderick', 'given': 'Avery Earl'}, 'orcid': '0000-0002-3351-760X', 'show_email': 'NO'}]}
Year: 2004
DOI: 10.7907/H2PF-K590
<p>Accretion onto compact objects plays a central role in high-energy astrophysics. The process of accretion can substantially affect the magnetic field strength and geometry (e.g, via the magneto-rotational instability or dynamo processes) and the accreting plasma density. The presence of the compact object itself can significantly affect the character and structure of the accreting plasma as well as its emission. This is especially true, in the case of an accreting black hole, when a significant fraction of the emission originates or passes near the horizon. To address this, we develop a manifestly covariant magnetoionic theory, capable of tracing rays in the geometric optics approximation through a magnetized plasma in a general relativistic environment. This is discussed for both the cold and warm, ion and pair plasmas. We also address the problem of performing polarized radiative transfer covariantly in these environments, considering in particular the anisotropic nature of magnetized plasmas, the gravitational redshift and Doppler shift, the transport of the polarization vector along the ray, and the ellipticity of the plasma eigenmodes.</p>
<p>The presence of relativity qualitatively changes the dispersion relation, introducing a third branch. In addition it significantly augments various polarized emission and transfer effects in strongly sheared flows, such as jets. Additionally, we demonstrate that it is possible, due to refraction coupled with the existence of a horizon, to generate a net circular polarization regardless of the intrinsic polarization of the emission mechanism. We find that this is not likely to be of significant importance for circular polarization in AGN (including the Galactic center and M81). However, in the context of X-ray binaries, this may produce measurable circular polarizations in the infrared.</p>
<p>We also develop a formalism for performing polarized radiative transfer through tangled magnetic fields. We find that for Faraday thick plasmas with a net magnetic helicity (but not necessarily a net magnetic field) it is possible to generate a circular polarization fraction which increases with frequency, as is observed to be the case in the Galactic center. In this case the handedness of the circular polarization is determined by the angular momentum of the accretion disk. This mechanism can be applied to extragalactic AGN and naturally explains the low degrees of circular polarization observed. As with the refractive mechanism, this may also be applied to X-ray binaries, and predicts ~10% polarization fractions at infrared wavelengths. Again, this provides a significant motivation for the development of infrared polarimetry.</p>https://thesis.library.caltech.edu/id/eprint/2085Topics in Gravitational-Wave Astronomy
https://resolver.caltech.edu/CaltechETD:etd-08052003-161044
Authors: {'items': [{'email': 'richard.oshaughnessy@ligo.org', 'id': "O'Shaughnessy-Richard-William", 'name': {'family': "O'Shaughnessy", 'given': 'Richard William'}, 'orcid': '0000-0001-5832-8517', 'show_email': 'YES'}]}
Year: 2004
DOI: 10.7907/4C1K-VZ17
<p>Both the Laser Interferometer Gravitational Wave Observatory (LIGO) and the Laser Interferometer Space Antenna (LISA) will over the next decade detect gravitational waves emitted by the motion of compact objects (e.g. black hole and neutron star binaries). This thesis presents methods to improve (i) LIGO detector quality, (ii) our knowledge of waveforms for certain LIGO and LISA sources, and (iii) models for the rate of detectability of a particular LISA source.</p>
<p>1) Plunge of compact object into a supermassive black hole: LISA should detect many inspirals of compact objects into supermassive black holes (~ 10⁵-10⁷ M<sub>⊙</sub>). Since the inspiral of each compact object terminates shortly after the inspiralling object reaches its last stable orbit, the late-stage inspiral waveform provides insight into the location of the last stable orbit and strong-field relativity. I discovered that while LISA will easily see the overall inspiral (consisting of many cycles before plunge), the present LISA design will just miss detecting the waves emitted from the transition from inspiral to plunge.</p>
<p>2) Scheme to reduce thermoelastic noise in advanced LIGO: After its first upgrade, LIGO will have its sensitivity limited by thermoelastic noise. [Thermoelastic noise occurs because milimeter-scale thermal fluctuations in the mirror bulk expand and contract, causing the mirror surface to shimmer.] The interferometer's sensitivity could be enhanced substantially by reducing thermoelastic noise. In collaboration with Kip Thorne, Erika d'Ambrosio, Sergey Vyatchanin, and Sergey Strigin, I developed a proposal to reduce thermoelastic noise in advanced-LIGO by switching the LIGO cavity optics from simple spherical mirrors to a new, Mexican-hat shape.</p>
<p>3) Geometric-optics-based analysis of stability of symmetric-hyperbolic formulations of Einstein's equations: Einstein's equations must be evolved numerically to predict accurate waveforms for the late stages of binary black hole inspiral and merger. But no matter which representation of Einstein's equations is used, numerical simulations rarely run long. For examle, for first-order symmetric-hyperbolic (FOSH) formulations of Einstein's evolution equations, sometimes exact but unphysical solutions grow so large that the evolution fails. For FOSH formulations, I found easily-understood solutions (wave packets) and used them to predict which formulations will be particularly ill-behaved.</p>https://thesis.library.caltech.edu/id/eprint/3017Variations on the Standard Model of the Universe
https://resolver.caltech.edu/CaltechETD:etd-05272005-141451
Authors: {'items': [{'email': 'krs@phas.ubc.ca', 'id': 'Sigurdson-Kris-Raymond', 'name': {'family': 'Sigurdson', 'given': 'Kris Raymond'}, 'orcid': '0000-0002-6729-0765', 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/52QC-H668
In the past decade, due to compelling measurements of the angular power spectrum of the cosmic microwave background (CMB) radiation, the large-scale matter distribution, the recent acceleration of the expansion rate of the Universe over cosmic time, and the current expansion rate (the Hubble constant), cosmology has culminated in a standard model of the Universe. By connecting this standard cosmological model with predictive theories of physics we can hope to look for signatures of these theories in the data. Along this line of inquiry we consider in this thesis: (i) the effects on CMB temperature and polarization anisotropies of spatial fluctuations of the fine-structure parameter alpha between causally disconnected regions of the Universe at the time of recombination, (ii) the suppression of the small-scale matter power spectrum due to the decay of charged matter to dark matter prior to recombination, (iii) the consequences of a neutral dark-matter particle with a nonzero electric and/or magnetic dipole moment, (iv) how charged-particles decaying in the early Universe can induce a scale-dependent or 'running' spectral index in the small-scale matter power spectrum and examples of this effect in minimal supersymmetric models in which the lightest neutralino is a viable cold-dark-matter candidate. With improved tests and cross-checks of standard-cosmological-model predictions we can search for anomalies that may reveal the character of the underlying physics. In this direction we propose in this thesis: (v) a new method for removing the effect of gravitational lensing from maps of CMB polarization anisotropies using observations of anisotropies or structures in the cosmic 21-cm radiation, (vi) that measurements of fluctuations in the absorption of CMB photons by hydrogen in the 21-cm line and deuterium in the 92-cm line during the cosmic dark ages could be used to determine the primordial deuterium abundance.https://thesis.library.caltech.edu/id/eprint/2153Raman Transitions in Cavity QED
https://resolver.caltech.edu/CaltechETD:etd-05272005-160246
Authors: {'items': [{'id': 'Boozer-Allen-David', 'name': {'family': 'Boozer', 'given': 'Allen David'}, 'show_email': 'NO'}]}
Year: 2005
DOI: 10.7907/F2WH-X491
<p>In order to study quantum effects such as state superposition and entanglement, one would like to construct simple systems for which the damping rates are slow relative to the rate of coherent evolution. One such system is strong-coupling cavity quantum electrodynamics (QED), in which a single atom is coupled to a single mode of a high finesse optical cavity. In recent years, optical trapping techniques have been applied to the cavity QED system, allowing an individual atom to remain coupled to the cavity for long periods of time. For the purpose of future cavity QED experiments, one would like to gain as much control over the trapped atom as possible; in particular, one would like to cool the center of mass motion of the atom, to measure the magnetic field at the location of the atom, and to be able to prepare the atom in a given internal state. In the first part of this thesis, I present a scheme for driving Raman transitions inside the cavity that can be used to achieve these goals. After giving a detailed theoretical treatment of the Raman scheme, I describe how it can be implemented in the lab and discuss some preliminary experimental results.</p>
<p>In the second part of this thesis, I present a number of simple field theory models. These models were developed in an attempt to understand some of the central ideas of theoretical physics by looking at how the ideas work in a highly simplified context. The hope is that by reducing the mathematical complexity of an actual theory, the underlying physical concepts can be more easily understood.</p>https://thesis.library.caltech.edu/id/eprint/2157Magnetic Microtraps for Cavity QED, Bose-Einstein Condensates, and Atom Optics
https://resolver.caltech.edu/CaltechETD:etd-09202005-205733
Authors: {'items': [{'email': 'benlev@stanford.edu', 'id': 'Lev-Benjamin-Leonard', 'name': {'family': 'Lev', 'given': 'Benjamin Leonard'}, 'show_email': 'YES'}]}
Year: 2006
DOI: 10.7907/YP00-7Z87
<p>The system comprised of an atom strongly coupled to photons, known as cavity quantum electrodynamics (QED), provides a rich experimental setting for quantum information processing, both in the implementation of quantum logic gates and in the development of quantum networks. Moreover, studies of cavity QED will help elucidate the dynamics of continuously observed open quantum systems with quantum-limited feedback.</p>
<p>To achieve these goals in cavity QED, a neutral atom must be tightly confined inside a high-finesse cavity with small mode volume for long periods of time. Microfabricated wires on a substrate---known as an atom chip---can create a sufficiently high-curvature magnetic potential to trap atoms in the Lamb-Dicke regime. We have recently integrated an optical fiber Fabry-Perot cavity with such a device. The microwires allow the on-chip collection and laser cooling of neutral atoms, and allow the magnetic waveguiding of these atoms to an Ioffe trap inside the cavity mode. Magnetically trapped intracavity atoms have been detected with this cavity QED system. A similar experiment employing microdisks and photonic bandgap cavities is nearing completion. With these more exotic cavities, a robust and scalable atom-cavity chip system will deeply probe the strong coupling regime of cavity QED with magnetically trapped atoms.</p>
<p>Atom chips have found great success in producing and manipulating Bose-Einstein condensates and in creating novel atom optical elements. An on-chip BEC has been attained in a miniaturized system incorporating an atom chip designed for atom interferometry and for studies of Josephson effects of a BEC in a double-well potential.</p>
<p>Using similar microfabrication techniques, we created and demonstrated a specular magnetic atom mirror formed from a standard computer hard drive. This device, in conjunction with micron-sized charged circular pads, can produce a 1-D ring trap which may prove useful for studying Tonks gases in a ring geometry and for creating devices such as a SQUID-like system for neutral atoms.</p>
<p>This thesis describes the fabrication and employment of these atoms chips in experiments at both Caltech and Munich, the latter in collaboration with Professors Theodore Haensch and Jakob Reichel at the Max Planck Institute for Quantum Optics.</p>https://thesis.library.caltech.edu/id/eprint/3658Topics of LIGO Physics: Template Banks for the Inspiral of Precessing, Compact Binaries, and Design of the Signal-Recycling Cavity for Advanced LIGO
https://resolver.caltech.edu/CaltechETD:etd-05242006-025220
Authors: {'items': [{'email': 'ypan@tapir.caltech.edu', 'id': 'Pan-Yi', 'name': {'family': 'Pan', 'given': 'Yi'}, 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/TJB1-PQ24
<p>In the next decade, the detection of gravitational-wave signals by ground-based laser interferometric detectors (e.g., the Laser Interferometer Gravitational-Wave Observatory, or LIGO) will provide new information on the structure and dynamics of compact objects such as neutron stars (NS) and black holes (BH), both isolated and in binary systems. Efforts to detect the intrinsically weak gravitational-wave signals involve the development of high-quality detectors, the precise modeling of expected signals, and the development of efficient data analysis techniques. This thesis concerns two topics in these areas: methods to detect signals from the inspiral of precessing NS-BH and BH-BH binaries, and the design of the signal-recycling cavity for Advanced LIGO (the second generation LIGO detector).</p>
<p>The detection of signals from the inspiral of precessing binaries using the standard matched filter technique, is complicated by the large number (12 at least) of parameters required to describe the complex orbital-precession dynamics of the binary and the consequent modulations of the gravitational-wave signals. To extract these signals from the noisy detector output requires a discrete bank of a huge number of signal templates that cover the 12-dimensional parameter space; and processing data with all these templates requires computational power far exceeding what is available with current technology. To solve this problem, Buonanno, Chen, and Vallisneri (BCV) proposed the use of detection template families (DTFs) --- phenomenological templates that are capable of mimicking rather accurately the inspiral waveform calculated by the post-Newtonian (PN) approach, while having a simpler functional form to reduce the computational cost. In particular, BCV proposed the so called BCV2 DTF for the precessing-binary inspiral, which has 12 parameters (most of them phenomenological). Of these, 8 are extrinsic parameters that can be searched over analytically, and only four of them are intrinsic parameters that need be searched over in a numerical one-by-one manner. The signal-matching efficiency of the BCV2 DTF has been shown to be satisfactory for signals from comparable mass BH-BH binaries.</p>
<p>In Chapter 2 (in collaboration with Alessandra Buonanno, Yanbei Chen, Hideyuki Tagoshi, and Michele Vallisneri), I test the signal-matching efficiency of the BCV2 DTF for signals from a wide sample of precessing BH-BH and NS-BH binaries that covers the parameter range of interest for LIGO and other ground-based gravitational-wave detectors, and I study the mapping between the physical and phenomenological parameters. My colleagues and I calculate the template-match metric, propose the template-placement strategy in the intrinsic parameter space and estimate the number of templates needed (and thus equivalently the computational cost) to cover the parameter space. We also propose a so called BCV2P DTF that replaces the phenomenological parameters in the BCV2 DTF by physical parameters, which can be used to estimate the actual parameters of the binary that emitted any detected signal.</p>
<p>In Chapters 3 and 4 (in collaboration with Alessandra Buonanno, Yanbei Chen, and Michele Vallisneri), I investigate a physical template family (PTF) suggested by BCV. This PTF uses the most accurate known waveforms for inspiraling, precessing binaries (the adiabatic PN waveforms), formulated using a new precessing convention such that five parameters become extrinsic. PTF has the obvious advantages over the DTFs of a perfect match with target signals, a lower false-alarm rate at fixed threshold, and an ability to directly estimate the physical parameters of any detected signal.</p>
<p>In Chapter 3, we focus on the simpler single-spin binaries in which only four parameters out of nine remain intrinsic. We propose a two-stage scheme to search over the five extrinsic parameters quickly, and investigate the false-alarm statistics in each of the two stages. We define and calculate the metric of the full template space, and the projected metric and average metric of the intrinsic parameter subspace, and use these metrics to develop the method of template placement. Finally, we estimate that the number of templates needed to detect single-spin binary inspirals is within the reach of the current available computational power.</p>
<p>In Chapter 4, we generalize the use of the single-spin PTF to double-spin binaries, based on the fact that most double-spin binaries have similar dynamics to the single-spin ones. Since the PTF in this case is, strictly speaking, only quasi-physical, we test and eventually find satisfactory signal-matching performance. We also investigate, both analytically and numerically, the difference between the single-spin and double-spin dynamics, and gain an intuition into where in the parameter space the PTF works well. We estimate the number of templates needed to cover all BH-BH and NS-BH binaries of interest to ground-based detectors, which turns out to be roughly at the limit of currently available computational power. Since the PTF is not exactly physical for double-spin binaries, it introduces systematic errors in parameter estimation. We investigate these, and find that they are either comparable to or overwhelmed by statistical errors, for events with moderate signal-to-noise ratio. BCV and I are currently systematically investigating parameter estimation with the PTF.</p>
<p>The second part of this thesis concerns the design of the signal-recycling cavity for Advanced LIGO. In the planned Advanced-LIGO-detector upgrades from the first-generation LIGO, a signal-recycling mirror (SRM) is introduced at the dark output port. This SRM forms a signal-recycling cavity (SRC) with the input test masses. This signal-recycling design offers several advantages and brings new physics to LIGO. However, there is a problem in the current design of the SRC: the SRC is nearly degenerate, i.e., it does not distinguish transverse optical modes; and as a result, mode coupling due to mirror deformation will strongly reduce the optical power in the fundamental mode, and thus reduce the signal strength, which is roughly proportional to it.</p>
<p>In Chapter 5, I investigate this problem using a numerical simulation of the propagation of the optical field in an Advanced LIGO interferometer. I find that if the current degenerate design for the SRC is used, there will be a serious and perhaps unattainable constraint on the magnitude of mirror deformations, in order to keep the reduction of signal-to-noise ratio below a few percent. This conclusion is consistent with previous order of magnitude estimates. This constraint poses practical difficulties on the quality of mirror polishing and the control of thermal aberration of the mirrors. Based on my simulation results, for a range of degeneracies of the SRC, I find the optimal level of degeneracy, which minimizes the reduction of signal-to-noise ratio. That optimum is nearly non-degenerate. I also discuss possible modifications to the current design that can achieve this optimal degeneracy.</p>https://thesis.library.caltech.edu/id/eprint/2007Quantitative Model of Calcium/Calmodulin- Dependent Protein Kinase II Activation
https://resolver.caltech.edu/CaltechETD:etd-06052006-142955
Authors: {'items': [{'id': 'Mihalas-Stefan', 'name': {'family': 'Mihalas', 'given': 'Stefan'}, 'orcid': '0000-0002-2629-7100', 'show_email': 'NO'}]}
Year: 2006
DOI: 10.7907/d0zv-g984
<p>Calcium/calmodulin-dependent protein kinase II (CaMKII) is a key element in the calcium second messenger cascades that lead to long term potentiation (LTP) of synaptic strength. In this thesis, I have constructed kinetic models of activation of CaMKII and measured some of the unknown parameters of the model. I used the models to elucidate mechanisms of activation of CaMKII and to study the kinetics of its activation under conditions similar to those in dendritic spines.</p>
<p>In chapter 2, I developed a new experimental method to rapidly stop the autophosphorylation reaction. I used this method to measure the catalytic turnover number of CaMKII. To quantitatively characterize CaMKII atophosphorylation in nonsaturating calcium, I also measured the autophosphorylation turnover number when CaMKII is activated by calmodulin mutants that can bind calcium ions only in either the amino or the carboxyl lobes.</p>
<p>Previous models of CaMKII activation assumed that binding of calmodulins to individual CaMKII subunits is independent and that autophosphorylation occurs within a ring of 6 subunits. However, a recent structure of CaMKII suggests that pairs of subunits cooperate in binding calmodulin and raises the possibility that the autophosphorylation occurs within pairs of subunits. In chapter 3, I constructed a model in which CaMKII subunits cooperate in binding calmodulin. This model reconciled previous experimental results from the literature that appeared contradictory. In chapter 4, I constructed two models for CaMKII autophosphorylation, in which autophosphorylation can occur either in rings or pairs, and used them to design experiments aimed at differentiating between these possibilities. Previously published measurements and the measurements that I performed are more consistent with autophosphorylation occurring within pairs.</p>
<p>In chapter 5, I constructed a model for simultaneous interactions among calcium, calmodulin, and CaMKII, and I used an automatic parameter search algorithm to fit the parameters for this model. I used it to characterize which of the parameters of calcium transients are critical for CaMKII activation.</p>
<p>This modeling work is part of a continuing effort to realistically model the spatial and temporal aspects of calcium second messenger signaling in dendritic spines.</p>https://thesis.library.caltech.edu/id/eprint/2462Topics in Numerical Relativity: The Periodic Standing-Wave Approximation, the Stability of Constraints in Free Evolution, and the Spin of Dynamical Black Holes
https://resolver.caltech.edu/CaltechETD:etd-05252007-143511
Authors: {'items': [{'email': 'owen@tapir.caltech.edu', 'id': 'Owen-Robert-Philip', 'name': {'family': 'Owen', 'given': 'Robert Philip'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/464A-4Y76
<p>This thesis concerns numerical relativity, the attempt to study Einstein's theory of gravitation using numerical discretization. The goal of the field, the study of gravitational dynamics in cases where symmetry reduction or perturbation theory are not possible, finally seems to be coming to fruition, at least for the archetypal problem of the inspiral and coalescence of binary black hole systems. This thesis presents three episodes that each bear some relationship to this story.</p>
<p>Chapters 2 and 3 present previously published work in collaboration with Richard Price and others on the so-called periodic standing-wave (PSW) approximation for binary inspiral. The approximation is to balance outgoing radiation with incoming radiation, stabilizing the orbit and making the problem stationary in a rotating frame. Chapters 2 and 3 apply the method to the problem of co-orbiting charges coupled to a nonlinear scalar field in three dimensions.</p>
<p>Chapters 4, 5, and 6 concern the stability of constraint fields in conventional numerical relativity simulations. Chapter 4 (also previously published work, in collaboration with the Caltech numerical relativity group, along with Michael Holst and Lawrence Kidder) presents a method for immediately correcting violations of constraints after they have arisen. Chapters 5 and 6 present methods to "damp" away constraint violations dynamically in two specific contexts. Chapter 5 (previously published work in collaboration with the Caltech numerical relativity group and Lawrence Kidder) presents a first-order linearly degenerate symmetric hyperbolic representation of Einstein's equations in generalized harmonic gauge. A representation is presented that stabilizes all constraints, including those that appear when the system is written in first-order form. Chapter 6 presents a generalization of the Kidder-Scheel-Teukolsky evolution systems that provides much-improved stability. This is investigated with numerical simulations of a single black hole spacetime.</p>
<p>Finally, chapter 7 presents work in progress to implement code to calculate the spin of black holes in numerical simulations. This requires a well-defined generalization of the concept of "rotation generators" on topological two-spheres that may not have any true Killing vectors. I present a new method for defining these fields, and results of a numerical code that computes them.</p>https://thesis.library.caltech.edu/id/eprint/2073Topics in Gravitational Physics: Tidal Coupling in Gravitational Wave Searches and Mach’s Principle
https://resolver.caltech.edu/CaltechETD:etd-05212007-004257
Authors: {'items': [{'id': 'Fang-Hua', 'name': {'family': 'Fang', 'given': 'Hua'}, 'show_email': 'NO'}]}
Year: 2007
DOI: 10.7907/D99H-J577
<p>The gravitational waves emitted by a compact object inspirling into a massive central body (e.g., a massive black hole) contain exquisite information about the spacetime geometry around that body and the tidal interaction (energy and angular momentum transfer) between the body and the inspiraling object's orbit. The first part (chapter 2--4) of this thesis studies several topics in the frame work of gravitation-wave search. In chapter 2 (in collaboration with G. Lovelace), we study the tidal interaction between a non-rotating black hole and circularly orbiting moon. Our analysis shows that the static induced quadrupole moment of the black hole is inherently ambiguous. In chapter 3, we give a survey of initial explorations of the prospects for using Advanced LIGO to detect gravitational waves from intermediate-mass-ratio inspirals (IMRIs))---analogous to the extreme-mass-ratio inspirals (EMRIs) targeted by LISA. We describe initial estimates of the detection range and the number of IMRI wave cycles in the Advanced LIGO band. We also give a detailed analysis of Advanced LIGO's accuracy for measuring the tide-induced energy transfer between the central black hole and the orbit. In chapter 4 (in collaboration with S. Babak, J. R. Gair, K. Glampedakis, and S. Hughes), we describe a new waveform-generating scheme in the context of LISA's data analysis for EMRI waves. The result is a family of "Numerical Kludge" waveforms, which share remarkable agreement with the more rigorous, but more computational-intensive Teukolsky-based waveforms.</p>
<p>The second part (chapter 5) of this thesis (in collaboration with K. S. Thorne) discusses another prediction from general relativity, the dragging of inertial frames, in connection with Mach's principle. We idealize our universe as a homogeneous, isotropic expanding, and slowly rotating sphere, surrounded by vacuum. We find that as the universe expands, the frame dragging weakens at its center; and that at later times inertia at the center completely breaks free of the grip of the universe's rotating matter.</p>https://thesis.library.caltech.edu/id/eprint/1915Topics in Gravitational-Wave Physics
https://resolver.caltech.edu/CaltechETD:etd-05232007-115433
Authors: {'items': [{'email': 'geoffrey4444@gmail.com', 'id': 'Lovelace-Geoffrey-Mark', 'name': {'family': 'Lovelace', 'given': 'Geoffrey Mark'}, 'orcid': '0000-0002-7084-1070', 'show_email': 'YES'}]}
Year: 2007
DOI: 10.7907/94TE-3B59
<p>Together with ongoing experimental efforts to detect gravitational waves, several fronts of theoretical research are presently being pursued, including second-generation detector design, data analysis, and numerical-relativity simulations of sources. This thesis presents a study in each of these topics: i) The noise in the most sensitive frequency bands in second-generation ground-based gravitational-wave interferometers is dominated by the thermal noise of the test masses. One way to reduce test-mass thermal noise is to modify shape of the laser beam so that it better averages over the thermal fluctuations. When edge effects are neglected, the test-mass thermal noise is related to the beam shape by simple scaling laws. This thesis presents a rigorous derivation of these laws, along with estimates of the errors made by neglecting edge effects. ii) An important class of gravitational-wave sources for space-based gravitational-wave interferometers is extreme-mass-ratio inspirals (EMRIs). These are binaries in which an object of a few solar masses spirals into a (typically million-solar-mass) supermassive black hole (or, if any exist, other type of massive body). Ryan (1995) proved that, under certain simplifying assumptions, the spacetime geometry is redundantly encoded in EMRI waves. One of Ryan's assumptions was negligible tidal coupling. After first finding that only the time-varying part of the induced tide is unambiguously defined when the central body is a black hole, this thesis extends Ryan's theorem by showing that both the spacetime geometry and details of the tidal coupling are encoded in EMRI waves. iii) Merging black holes with comparable masses are important sources of gravitational waves for ground-based detectors. The gravitational waves near the time of merger can only be predicted by numerically solving the Einstein equations. Initial data in numerical simulations must contain the desired physical content but also satisfy the Einstein constraint equations. But conventional binary-black-hole initial data has physical flaws: a nonzero orbital eccentricity and an initial, unphysical pulse of spurious gravitational radiation. Using the Caltech-Cornell pseudospectral code, this thesis develops and implements methods to reduce both of these effects.</p>https://thesis.library.caltech.edu/id/eprint/1987Dissecting the Gravitational Lens B1608+656: Implications for the Hubble Constant
https://resolver.caltech.edu/CaltechETD:etd-09132007-122424
Authors: {'items': [{'email': 'suyu@mpa-garching.mpg.de', 'id': 'Suyu-Sherry-Hsuan', 'name': {'family': 'Suyu', 'given': 'Sherry Hsuan'}, 'orcid': '0000-0001-5568-6052', 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/MQS2-Y860
Strong gravitational lens systems provide a tool for probing galaxy mass distributions (independent of their light profiles) and for measuring cosmological parameters. In a strong lens system, the background source intensity distribution is multiply imaged. If the source intensity is time varying, then the multiple images of the variable source are delayed in time relative to each other due to the different light travel time along the multiple light paths. One can use lens systems to measure the Hubble constant by obtaining the relative time delays between the multiple images and modeling the lens potential. B1608+656 is a quadruply imaged gravitational lens system with a spatially extended source intensity distribution and two interacting galaxy lenses. This system is unique in that the three relative time delays between the four images were measured accurately with errors of only a few percent, and it thus provides an opportunity to measure the Hubble constant with high precision. The extended source intensity distribution in B1608+656 provides additional constraints on the lens potential, though simultaneous determination of the source intensity and lens potential distribution is needed. The presence of dust and interacting galaxy lenses further complicate this system. We present a comprehensive analysis in a Bayesian framework that takes into account the extended source intensity distribution, interacting galaxy lenses, and the presence of dust for reconstructing the lens potential. Using the deep HST ACS observations on B1608+656, the resulting statistical uncertainty on H_0 associated with the lens modeling is limited by the uncertainty in the best time delay measurement (~3%). The dominant systematic error on H_0 is due to the effects of the environment on B1608+656 (mass-sheet degeneracy). By using the measured velocity dispersion of the lens galaxies and considering the mass structures along the line of sight to B1608+656, we place constraints on the external convergence associated with galaxy groups and mass structure along the line of sight. The resulting Hubble constant from B1608+656 is H_0 = 72 ± 2 (stat.) ± 4 (syst.) km s^-1 Mpc^-1.
https://thesis.library.caltech.edu/id/eprint/3526The Gravity of the Situation
https://resolver.caltech.edu/CaltechETD:etd-05282008-153540
Authors: {'items': [{'email': 'tsmith2@swarthmore.edu', 'id': 'Smith-Tristan-Laine', 'name': {'family': 'Smith', 'given': 'Tristan Laine'}, 'orcid': '0000-0003-2685-5405', 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/SY21-6Z52
<p>In this thesis we examine several ways in which we can explore the early universe through gravitational-waves and the fundamental nature of gravity through cosmology and observations of dynamics within the solar system. Both of these topics have taken center stage, as we are living at a unique time which promises to bring fundamental insights into the nature of gravity with the discovery of new binary pulsar systems, the building of increasingly precise solar system and tabletop experiments and the birth of gravitational-wave observatories-- to name a few recent and upcoming advances.</p>
<p>We first discuss whether we may be able to directly detect gravitational waves from inflation using future space-based interferometers. We then describe how the direct detection of inflationary gravitational waves will allow us to probe the fundamental physics that operated at the earliest moments of the universe. Next, a new constraint to a general cosmological gravitational wave background is presented using the observations of the cosmic microwave background. Moving away from general relativity, we consider alternative theories of gravity. One reason to consider alternative theories of gravity is the observation that the expansion of the universe is currently accelerating. It is possible that this accelerated expansion is due to a modification of gravity. However, any theory that modifies gravity in order to produce accelerated expansion must also conform to the dynamics that we observe within the Solar System. We discuss how the observation of the deflection of light around the Sun places severe limitations on a particular modified gravity theory, known as f(R) gravity. Our discussion of f(R) gravity leads us to ask whether the parameterized post Newtonian parameter, γ<sub>PPN</sub>, takes on a universal value. We identify measurements made of strong lensing around early type galaxies in the Sloan Lens ACS (SLACS) survey as a first step in performing this new test of gravity. Finally, we explore some consequences of Chern-Simons gravity. One of the unique aspects of Chern-Simons gravity is that it introduces parity violation into the gravitational sector. As a consequence, it predicts a different gravitomagnetic field around the rotating Earth than is predicted in general relativity. We show how recent measurements of this gravitomagnetic field made by observing the two LAser GEOdynamics Satellites (LAGEOS) and Gravity Probe B satellites constrain Chern-Simons gravity. Finally, we discuss how future observations of binary pulsar systems may allow for a more general exploration of the gravitomagnetic structure around rotating objects.</p>
https://thesis.library.caltech.edu/id/eprint/2214Topics in Gravitational-Wave Physics
https://resolver.caltech.edu/CaltechTHESIS:07152021-205059459
Authors: {'items': [{'id': 'Savov-Pavlin', 'name': {'family': 'Savov', 'given': 'Pavlin'}, 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/72z7-n083
<p>While the astrophysics community is on the brink of detecting the first gravitational-wave signal [1, 2, 3], efforts continue to improve the existing detectors and develop new technologies for future-generation detectors. In parallel, the need is rapidly growing for improved analyzes and interpretations of the science data that comes from the detectors. This thesis contributes to these issues with research results related to (i) the design of possible upgrades for the Advanced detectors for the ground-based Laser Interferometer Gravitational-wave Observatory (AdvLIGO) [4, 5, 6, 7] (i.e. for improved versions of the initial LIGO detectors [9, 10]), and (ii) future data analysis techniques for the Laser Interferometer Space Antenna (LISA) [11, 12] (a planned space-based gravitational-wave mission). More specifically:</p>
<p>Currently, an international array of first-generation ground-based, laser-interferometer gravitational-wave detectors (consisting of LIGO, VIRGO [13, 14], GEO600 [15, 16] and TAMA300 [17]) is actively searching for gravitational waves in the frequency band (10 Hz { 10 kHz), with peak sensitivity at a few hundred Hertz. On September the 30th, 2007, the initial LIGO interferometers finished their Science Run 5 (S5) [18], which collected one year of triple coincidence data at the interferometers' design sensitivity. The next version of LIGO's interferometers, called Enhanced LIGO [19], with amplitude sensitivity improved by a factor about 2 (event rate increased by a factor 2³≃10), is being implemented and will
collect data in science mode in 2009-10. Advanced LIGO is expected to begin operations around 2013. At the end of commissioning, it will have a factor ten better amplitude sensitivity than initial LIGO, which translates to a thousand-fold increase in event rate. Therefore, just a few hours of observations by AdvLIGO will be worth the entire lifetime of initial LIGO. Another significant advantage of the Advanced LIGO design is that it will allow tuning of the sensitivity as a function of frequency, so as to optimize searches for specific astrophysical sources with specific expected spectra.</p>
<p>LISA, the first system of space-based gravitational-wave interferometers, is planned for launch and science operation in 2018 or perhaps somewhat later, depending on political developments. It will operate with peak sensitivity around a few milliHertz and should detect galore of signals simultaneously. The lifetime of the mission is expected to be around five years.</p>
<p>This thesis consists of four chapters: this introductory chapter, two chapters (2 and 3) dealing with research relevant to the technology for a possible upgrade of Advanced LIGO, and one chapter (4) relevant to data analysis for LISA. Specifically: Chapter 2 elucidates the influence of the shape (power profile) of an interferometer's arm-cavity light beams on a tilt instability, in which the tilt of an arm cavity mirror is driven by light pressure. Chapter 3 proves a duality relation between arm cavities with almost at mirrors (as originally planned for AdvLIGO) and cavities with almost concentric spherical mirrors (a design change that has been made, to control the tilt instability). I discovered and used this duality relation numerically in the research reported in Chapter 2, but only later, in collaboration with others, did I prove the duality relation analytically (Chapter 3). Chapter 4 reports details of and results from a Mock LISA Data Challenge in which gravitational wave signals from
(mock) supermassive black-hole binaries were sought and found in simulated LISA data.</p>https://thesis.library.caltech.edu/id/eprint/14305The Three Ss of Gravitational-Wave Astronomy: Sources, Signals, Searches
https://resolver.caltech.edu/CaltechETD:etd-03112008-012506
Authors: {'items': [{'email': 'Ilya.Mandel@monash.edu', 'id': 'Mandel-Ilya', 'name': {'family': 'Mandel', 'given': 'Ilya'}, 'orcid': '0000-0002-6134-8946', 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/GABY-T236
As gravitational wave astronomy prepares for the first detections of gravitational waves from compact-object binary inspirals, theoretical work is required on the study of (i) gravitational-wave sources, (ii) the signals emitted by those sources, and (iii) the searches for those signals in detector data. This thesis describes work on all three fronts. (i) We discuss intermediate-mass-ratio inspirals (IMRIs) of black holes or neutron stars into intermediate-mass black holes (IMBHs) that could be detected with Advanced LIGO. We analyze different mechanisms of IMRI formation and compute IMRI event rates of up to tens of events per year for Advanced LIGO. We study the spin evolution of IMBHs that grow through a series of minor mergers. We explore how a deviation of an IMRI's central body from a Kerr black hole influences geodesics, including the possibility of chaotic orbital dynamics. We also address the scientific consequences of extreme-mass-ratio inspiral (EMRI) detections by LISA for astrophysics and general relativity, and the difficulties associated with detecting and analyzing EMRI signals. (ii) We study the periodic standing-wave approximation (PSWA), which can potentially provide accurate waveforms in the last inspiral cycles of a comparable-mass black-hole binary. Using a simple model, we find that the solution to Einstein's equations for inspiraling black holes can be recovered to a high accuracy by the addition a perturbative radiation-reaction field to the standing-wave, noninspiraling solution. (iii) We demonstrate the utility of searching for and analyzing tracks in time-frequency spectrograms of a gravitational-wave signal as a means of estimating the parameters of a massive black-hole binary inspiral, as observed by LISA.https://thesis.library.caltech.edu/id/eprint/926Signatures and Dynamics of Compact Binary Coalescences and a Search in LIGO’s S5 Data
https://resolver.caltech.edu/CaltechETD:etd-05202009-115750
Authors: {'items': [{'email': 'dgkeppel@gmail.com', 'id': 'Keppel-Drew-Garvin', 'name': {'family': 'Keppel', 'given': 'Drew Garvin'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/03MS-2W96
In this thesis, we probe several aspects of compact binary environments, focusing on results of orbits and collisions of compact objects. First, we describe a search for low-mass compact-binary-coalescence gravitational-wave signals in data from the LIGO detectors' most sensitive, longest-running science run to date (S5). We also go into detail on the interpretation of the results including its development. We then investigate the bounds on the mass of the graviton that could be achieved from the detection gravitational waves from a binary black hole merger. Last, we study the flow of momentum in compact binaries using the Landau-Lifshitz formalism.
https://thesis.library.caltech.edu/id/eprint/1901The Consequences of Modifying Fundamental Cosmological Theories
https://resolver.caltech.edu/CaltechETD:etd-05292009-132414
Authors: {'items': [{'email': 'erickcek@physics.unc.edu', 'id': 'Erickcek-Adrienne-Lynn', 'name': {'family': 'Erickcek', 'given': 'Adrienne Lynn'}, 'orcid': '0000-0002-0901-3591', 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/ST6B-1S91
<p>In this work, we examine alternatives to three fundamental cosmological theories: extended Press-Schechter merger theory, general relativity, and single-field inflation, and derive their observational consequences. The extended Press-Schechter merger rate for dark matter haloes is mathematically inconsistent and double-valued, and yet it has been widely applied in cosmology. One such application is the merger rate of supermassive black holes, and we show that the two predictions for this rate from extended Press-Schechter merger theory are nearly equal. We then compare the supermassive-black-hole merger rate derived from the extended Press-Schechter merger formalism to the rate derived from an alternate theory, in which halo merger rates are obtained by inverting the coagulation equation.</p>
<p>Next, we show how two modifications to general relativity may be tested inside the Solar System. First we consider f(R) gravity, which was proposed to explain late-time cosmic acceleration. We find that several forms of f(R) gravity are inconsistent with observations, and we establish a set of criteria that determines whether or not a given form of f(R) gravity is ruled out by Solar System gravitational tests. Second, we study Chern-Simons gravity: a parity-violating theory inspired by string theory. We find that Chern-Simons gravity predicts orbital precessions that are different from those predicted by general relativity, and we use the motion of satellites to constrain the Chern-Simons coupling parameter.</p>
<p>Finally, we consider an alternative to single-field inflation; in the curvaton scenario, the inflaton does not generate all of the primordial perturbations. Using this theory, we propose an origin for the hemispherical power asymmetry that has been observed in the cosmic microwave background on large angular scales. While this asymmetry cannot be produced by a superhorizon fluctuation in the inflaton field, it may be generated by a superhorizon fluctuation in the curvaton field. A superhorizon fluctuation would also induce large-scale anisotropies in the cosmic microwave background; we analyze this effect and prove that our model is consistent with observations. We also show how the power asymmetry may be suppressed on smaller scales if the curvaton creates isocurvature perturbations when it decays.</p>https://thesis.library.caltech.edu/id/eprint/2276Experiments with Toroidal Microresonators in Cavity QED
https://resolver.caltech.edu/CaltechETD:etd-05282009-101209
Authors: {'items': [{'email': 'sk8lizzy@gmail.com', 'id': 'Connolly-Elizabeth-Wilcut', 'name': {'family': 'Connolly', 'given': 'Elizabeth Wilcut'}, 'show_email': 'YES'}]}
Year: 2009
DOI: 10.7907/78XV-CS35
Advances made pertaining to strong interactions between single photons of light and single atoms have great potential in the field of quantum information. However, scalability is a limiting factor in the applicability of current technologies (such as an atom in the mode of a Fabry-Perot resonator) due to difficulties in alignment and fabrication. Toroial resonators, however, are fabricated lithographically on silicon wafers, and are therefore easily scalable. Light is coupled into a toroid by tapered optical fiber, allowing for the efficient retrieval of photons from the resonator mode that is necessary if multiple resonators are to be eventually coupled to one another. We have demonstrated interactions between single atoms of cesium and a toroidal resonator that lie in the regime of strong coupling since the rate of coupling between an atom and the cavity mode, g0 m = (50±12) MHz, is much larger than the dissipative rates of the system (gamma, kappa)/2pi ~ (2.6, 18) MHz. To further expand upon the usefulness of toroids in cavity QED, I have striven to improve the way that toroids are characterized and coupled. An apparatus which semi-automates the characterization process reduces the length of time a toroid is outside of vacuum, thus limiting environmental degradation. To help in better understanding the process of pulling tapered fibers, the efficiency and characteristic quantities have been detailed. Similarly, the behavior of a toroid resonance as a function of coupling strength was quantified. Preliminary locking of the coupling by controlling the separation between the taper and toroid has been accomplished. This locking will allow the next generation of atom-toroid coupling to require less human intervention and therefore be more efficient. https://thesis.library.caltech.edu/id/eprint/2218Accurate Gravitational Waveforms from Binary Black-hole Systems
https://resolver.caltech.edu/CaltechETD:etd-01122009-143851
Authors: {'items': [{'email': 'michael.oliver.boyle@gmail.com', 'id': 'Boyle-Michael', 'name': {'family': 'Boyle', 'given': 'Michael'}, 'orcid': '0000-0002-5075-5116', 'show_email': 'YES'}]}
Year: 2009
DOI: 10.7907/7NSM-RW43
<p>We examine various topics involved in the creation of accurate theoretical gravitational waveforms from binary black-hole systems.</p>
<p>In Chapter 2 a pseudospectral numerical code is applied to a set of analytic or near-analytic solutions to Einstein's equations which comprise a testbed for numerical-relativity codes. We then discuss methods for extracting gravitational-wave data from numerical simulations of black-hole binary systems, and introduce a practical technique for obtaining the asymptotic form of that data from finite simulation domains in Chapter 3. A formula is also developed to estimate the size of near-field effects from a compact binary. In Chapter 4 the extrapolated data is then compared to post-Newtonian (PN) approximations. We compare the phase and amplitude of the numerical waveform to a collection of Taylor approximants, cross-validating the numerical and PN waveforms, and investigating the regime of validity of the PN waveforms. Chapter 5 extends that comparison to include Padé and effective-one-body models, and investigates components of the PN models. In each case, a careful accounting is made of errors. Finally, we construct a long post-Newtonian–numerical hybrid waveform and evaluate the performance of LIGO's current data-analysis methods with it. We suggest certain optimizations of those methods, including extending the range of template mass ratios to unphysical ranges for certain values of the total mass, and a simple analytic cutoff frequency for the templates which results in nearly optimal matches for both Initial and Advanced LIGO.</p>
https://thesis.library.caltech.edu/id/eprint/143Topics in Theoretical Astrophysics
https://resolver.caltech.edu/CaltechETD:etd-10142008-155140
Authors: {'items': [{'email': 'chaosli_8@hotmail.com', 'id': 'Li-Chao', 'name': {'family': 'Li', 'given': 'Chao'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/CWB8-VF13
This thesis presents a study of various interesting problems in theoretical astrophysics, including gravitational wave astronomy, gamma ray bursts and cosmology. Chapters 2, 3 and 4 explore prospects for detecting gravitational waves from stellar-mass compact objects spiraling into intermediate-mass black holes with ground-based observatories. It is shown in chapter 2 that if the central body is not a BH but its metric is stationary, axisymmetric, reflection symmetric and asymptotically flat, then the waves will likely be triperiodic, as for a BH. Chapters 3 and 4 show that the evolutions of the waves' three fundamental frequencies and of the complex amplitudes of their spectral components encode (in principle) details of the central body's metric, the energy and angular momentum exchange between the central body and the orbit, and the time-evolving orbital elements. Chapter 5 studies a local readout method to enhance the low frequency sensitivity of detuned signal-recycling interferometers. We provide both the results of improvement in quantum noise and the implementation details in Advanced LIGO. Chapter 6 applies and generalizes causal Wiener filter to data analysis in macroscopic quantum mechanical experiments. With the causal Wiener filter method, we demonstrate that in theory we can put the test masses in the interferometer to its quantum mechanical ground states. Chapter 7 presents some analytical solutions for expanding fireballs, the common theoretical model for gamma ray bursts and soft gamma ray repeaters. We apply our results to SGR 1806-20 and rediscover the mismatch between the model and the afterglow observations. Chapter 8 discusses the reconstruction of the scalar-field potential of the dark energy. We advocate direct reconstruction of the scalar field potential as a way to minimize prior assumptions on the shape, and thus minimize the introduction of bias in the derived potential. Chapter 9 discusses gravitational lensing modifications to cosmic microwave background anisotropies and polarization, produced by a stochastic background of primordial gravitational waves between us and the last scattering surface. Chapter 10 calculates the non-Gaussian covariance of CMB B-modes of polarization.
https://thesis.library.caltech.edu/id/eprint/4090Bifurcations in Single Atom Cavity QED
https://resolver.caltech.edu/CaltechETD:etd-05262009-100436
Authors: {'items': [{'email': 'armen@caltech.edu', 'id': 'Armen-Michael-A', 'name': {'family': 'Armen', 'given': 'Michael A.'}, 'show_email': 'NO'}]}
Year: 2009
DOI: 10.7907/2G57-2609
Current research in single-atom cavity quantum electrodynamics largely emphasizes the input-output properties of strongly coupled systems, from normal mode splitting to photon blockade. But over the last decade, experiments have, with few exceptions, focused on relatively weak driving conditions. This thesis concentrates on a range of quantum nonlinear phenomena in the strong driving regime. In particular, I discuss the observation of random-telegraph phase switching in the light transmitted through a Fabry-Perot resonator containing one strongly coupled atom and 10-100 photons, confirming long-standing predictions of a phenomenon known as single-atom phase bistability. These results highlight the relevance of cavity quantum electrodynamics in the development of attojoule nanophotonic logic and signal processing. In addition, I consider a general class of bifurcation phenomena that are manifest within this physical setting. Here, focus is placed on the investigation of quantum-classical correspondence near semiclassical bifurcation points. https://thesis.library.caltech.edu/id/eprint/2119Topics in Gravitation – Numerical Simulations of Event Horizons and Parameter Estimation for LISA
https://resolver.caltech.edu/CaltechTHESIS:08032010-144145071
Authors: {'items': [{'email': 'mcohen2@gmail.com', 'id': 'Cohen-Michael-Isaac', 'name': {'family': 'Cohen', 'given': 'Michael Isaac'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/TG6W-Z732
<p>In Part I, we consider numerical simulations of event horizons. Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to find event horizons in numerical spacetimes, and find that straightforward integration of geodesics backward in time is most robust. We apply this method to various systems, from a highly spinning Kerr hole through to an asymmetric binary black hole inspiral. We find that the exponential rate at which outgoing null geodesics diverge from the event horizon of a Kerr black hole is the surface gravity of the hole. In head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10<sup>5</sup>. In the head-on "kick" merger, we find that computing the Landau-Lifshitz velocity of the event horizon is very useful for an improved understanding of the kick behaviour. Finally, in the inspiral simulations, we find that the topological structure of the black holes does not produce an intermediate toroidal phase, though the structure is consistent with a potential re-slicing of the spacetime in order to introduce such a phase. We further discuss the topological structure of non-axisymmetric collisions.</p>
<p>In Part II, we consider parameter estimation of cosmic string burst gravitational waves in Mock LISA data. A network of observable, macroscopic cosmic (super-)strings may well have formed in the early Universe. If so, the cusps that generically develop on cosmic-string loops emit bursts of gravitational radiation that could be detectable by gravitational-wave interferometers, such as the ground-based LIGO/Virgo detectors and the planned, space-based LISA detector. We develop two versions of a LISA-oriented string-burst search pipeline within the context of the Mock LISA Data Challenges, which rely on the publicly available MultiNest and PyMC software packages, respectively. We use the F-statistic to analytically maximize over the signal’s amplitude and polarization, A and ψ, and use the FFT to search quickly over burst arrival times t<sub>C</sub>. We also demonstrate an approximate, Bayesian version of the F-statistic that incorporates realistic priors on A and ψ. We calculate how accurately LISA can expect to measure the physical parameters of string-burst sources, and compare to results based on the Fisher-matrix approximation. To understand LISA’s angular resolution for string-burst sources, we draw maps of the waveform fitting factor [maximized over (A, ψ, t<sub>C</sub>)] as a function of sky position; these maps dramatically illustrate why (for LISA) inferring
the correct sky location of the emitting string loop will often be practically impossible. In addition, we identify and elucidate several symmetries that are embedded in this search problem, and we derive the distribution of cut-off frequencies f<sub>max</sub> for observable bursts.</p>https://thesis.library.caltech.edu/id/eprint/5984