2,4-dimethylene-1,3-cyclobutanediyl and 2,4-dimethylenebicyclobutane. Synthesis, spectroscopy, and reactivity of a triplet biradical and its covalent isomer

The preparation and direct observation of triplet 2,4-dimethylene-1,3- cyclobutanediyl (1), the non-Kekule isomer of benzene, is described. The biradical was generated by photolysis of 5,6-dimethylene-2,3- diazabicyclo[2.1.1]hex-2-ene (2) (which was synthesized in several steps from benzvalene) under cryogenic, matrix-isolation conditions. Biradical 1 was characterized by EPR spectroscopy (‌‌‌‌‌│D/hc│ =0.0204 cm^(-1), │E/hc│ =0.0028 cm^(-1)) and found to have a triplet ground state. The Δm_s= 2 transition displays hyperfine splitting attributed to a 7.3-G coupling to the ring methine and a 5.9-G coupling to the exocyclic methylene protons. Several experiments, including application of the magnetophotoselection (mps) technique in the generation of biradical 1, have allowed a determination of the zero-field triplet sublevels as x = -0.0040, y = +0.0136, and z = -0.0096 cm^(-1), where x and y are respectively the long and short in-plane axes and z the out-of-plane axis of 1.

Triplet 1 is yellow-orange and displays highly structured absorption (λ_(max)= 506 nm) and fluorescence (λ_(max) = 510 nm) spectra, with vibronic spacings of 1520 and 620 cm^(-1) for absorption and 1570 and 620 cm^(-1) for emission. The spectra were unequivocally assigned to triplet 1 by the use of a novel technique that takes advantage of the biradical's photolability. The absorption є = 7200 M^(-1) cm^(-1) and f = 0.022, establishing that the transition is spin-allowed. Further use of the mps technique has demonstrated that the transition is x-polarized, and the excited state 1s therefore of B_(1g) symmetry, in accord with theoretical predictions.

Thermolysis or direct photolysis of diazene 2 in fluid solution produces 2,4- dimethylenebicyclo[l.l.0]butane (3), whose ^(l)H NMR spectrum (-80°C, CD_(2)Cl_(2)) consists of singlets at δ 4.22 and 3.18 in a 2:1 ratio. Compound 3 is thermally unstable and dimerizes with second-order kinetics between -80 and -25°C (∆H^(‡) = 6.8 kcal mol^(-1), (∆s^(‡) = -28 eu) by a mechanism involving direct combination of two molecules of 3 in the rate-determining step. This singlet-manifold reaction ultimately produces a mixture of two dimers, 3,8,9- trimethylenetricyclo[5.1.1.0^(2,5)]non-4-ene (75) and trans-3,10-dimethylenetricyclo[6.2.0.0^(2,5)]deca-4,8-diene (76t), with the former predominating. In contrast, triplet-sensitized photolysis of 2, which leads to triplet 1, provides, in addition to 75 and 76t, a substantial amount of trans-5,10- dimethylenetricyclo[6.2.0.0^(3,6)]deca-3,8-diene (77t) and small amounts of two unidentified dimers.

In addition, triplet biradical 1 ring-closes to 3 in rigid media both thermally (77-140 K) and photochemically. In solution 3 forms triplet 1 upon energy transfer from sensitizers having relatively low triplet energies. The implications of the thermal chemistry for the energy surfaces of the system are discussed.

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

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

Macaque lateral intraparietal area and oculomotor behaviors

Neurons in the primate lateral intraparietal area (area LIP) carry visual, saccade-related and eye position activities. The visual and saccade activities are anchored in a retinotopic framework and the overall response magnitude is modulated by eye position. It was proposed that the modulation by eye position might be the basis of a distributed coding of target locations in a head-centered space. Other recording studies demonstrated that area LIP is involved in oculomotor planning. These results overall suggest that area LIP transforms sensory information for motor functions. In this thesis I further explore the role of area LIP in processing saccadic eye movements by observing the effects of reversible inactivation of this area. Macaque monkeys were trained to do visually guided and memory saccades and a double saccade task to examine the use of eye position signal. Finally, by intermixing visual saccades with trials in which two targets were presented at opposite sides of the fixation point, I examined the behavior of visual extinction.

In chapter 2, I will show that lesion of area LIP results in increased latency of contralesional visual and memory saccades. Contralesional memory saccades are also hypometric and slower in velocity. Moreover, the impairment of memory saccades does not vary with the duration of the delay period. This suggests that the oculomotor deficits observed after inactivation of area LIP is not due to the disruption of spatial memory.

In chapter 3, I will show that lesion of area LIP does not severely affect the processing of spontaneous eye movement. However, the monkeys made fewer contralesional saccades and tended to confine their gaze to the ipsilesional field after inactivation of area LIP. On the other hand, lesion of area LIP results in extinction of the contralesional stimulus. When the initial fixation position was varied so that the retinal and spatial locations of the targets could be dissociated, it was found that the extinction behavior could best be described in a head-centered coordinate.

In chapter 4, I will show that inactivation of area LIP disrupts the use of eye position signal to compute the second movement correctly in the double saccade task. If the first saccade steps into the contralesional field, the error rate and latency of the second saccade are both increased. Furthermore, the direction of the first eye movement largely does not have any effect on the impairment of the second saccade. I will argue that this study provides important evidence that the extraretinal signal used for saccadic localization is eye position rather than a displacement vector.

In chapter 5, I will demonstrate that in parietal monkeys the eye drifts toward the lesion side at the end of the memory saccade in darkness. This result suggests that the eye position activity in the posterior parietal cortex is active in nature and subserves gaze holding.

Overall, these results further support the view that area LIP neurons encode spatial locations in a craniotopic framework and is involved in processing voluntary eye movements.

On the Mumford-Tate conjecture for Abelian varieties with reduction conditions

In this thesis we study Galois representations corresponding to abelian varieties with certain reduction conditions. We show that these conditions force the image of the representations to be "big," so that the Mumford-Tate conjecture (:= MT) holds. We also prove that the set of abelian varieties satisfying these conditions is dense in a corresponding moduli space.

The main results of the thesis are the following two theorems.

Theorem A: Let A be an absolutely simple abelian variety, End° (A) = k : imaginary quadratic field, g = dim(A). Assume either dim(A) ≤ 4, or A has bad reduction at some prime ϕ, with the dimension of the toric part of the reduction equal to 2r, and gcd(r,g) = 1, and (r,g) ≠ (15,56) or (m -1, m(m+1)/2). Then MT holds.

Theorem B: Let M be the moduli space of abelian varieties with fixed polarization, level structure and a k-action. It is defined over a number field F. The subset of M(Q) corresponding to absolutely simple abelian varieties with a prescribed stable reduction at a large enough prime ϕ of F is dense in M(C) in the complex topology. In particular, the set of simple abelian varieties having bad reductions with fixed dimension of the toric parts is dense.

Besides this we also established the following results:

(1) MT holds for some other classes of abelian varieties with similar reduction conditions. For example, if A is an abelian variety with End° (A) = Q and the dimension of the toric part of its reduction is prime to dim( A), then MT holds.

(2) MT holds for Ribet-type abelian varieties.

(3) The Hodge and the Tate conjectures are equivalent for abelian 4-folds.

(4) MT holds for abelian 4-folds of type II, III, IV (Theorem 5.0(2)) and some 4-folds of type I.

(5) For some abelian varieties either MT or the Hodge conjecture holds.

Topics in gravitational-wave science : macroscopic quantum mechanics and black hole physics

The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics.

Gravitational waves are "ripples of space-time", long predicted by general relativity. Although indirect evidence of gravitational waves has been discovered from observations of binary pulsars, direct detection of these waves is still actively being pursued. An international array of laser interferometer gravitational-wave detectors has been constructed in the past decade, and a first generation of these detectors has taken several years of data without a discovery. At this moment, these detectors are being upgraded into second-generation configurations, which will have ten times better sensitivity. Kilogram-scale test masses of these detectors, highly isolated from the environment, are probed continuously by photons. The sensitivity of such a quantum measurement can often be limited by the Heisenberg Uncertainty Principle, and during such a measurement, the test masses can be viewed as evolving through a sequence of nearly pure quantum states.

The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities.

The second part of this thesis (Chapters 3-7) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects - as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function.

In Chapters 4-5, we build theoretical tools for analyzing the so-called "non-Markovian" quantum measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a non-Markovian bath (i.e., one with a memory) while at the same time being under continuous quantum measurement (by the probe field). This aims at providing a general framework for analyzing a large class of non-Markovian measurement processes. Chapter 5 develops a way of characterizing the non-Markovianity of a bath (i.e.,whether and to what extent the bath remembers information about the plant) by perturbing the plant and watching for changes in the its subsequent evolution. Chapter 6 re-analyzes a recent measurement of a mechanical oscillator's zero-point fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rack-action noise.

Chapter 7 describes a model in which gravity is classical and matter motions are quantized, elaborating how the quantum motions of matter are affected by the fact that gravity is classical. It offers an experimentally plausible way to test this model (hence the nature of gravity) by measuring the center-of-mass motion of a macroscopic object.

The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes - a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray binary objects, detecting gravitational waves emitted by systems containing black holes will offer a much more direct way of observing black holes, providing unprecedented details of space-time geometry in the black-holes' strong-field region.

The third part of this thesis (Chapters 8-11) studies black-hole physics in connection with gravitational-wave detection.

Chapter 8 applies black hole perturbation theory to model the dynamics of a light compact object orbiting around a massive central Schwarzschild black hole. In this chapter, we present a Hamiltonian formalism in which the low-mass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasi-normal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weakly-damped QNMs, with relative error O(1/L^2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on near-extremal Kerr black holes, we discuss a bifurcation in their QNM spectra for certain ranges of (l,m) (the angular quantum numbers) as a/M → 1. With tools prepared in Chapter 9 and 10, in Chapter 11 we obtain an analytical approximate for the scalar Green function in Kerr spacetime.

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

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

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

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

Where Tori fear to tread : hypermassive neutron star remnants and absolute event horizons Or topics in computational general relativity

Computational general relativity is a field of study which has reached maturity only within the last decade. This thesis details several studies that elucidate phenomena related to the coalescence of compact object binaries. Chapters 2 and 3 recounts work towards developing new analytical tools for visualizing and reasoning about dynamics in strongly curved spacetimes. In both studies, the results employ analogies with the classical theory of electricity and magnitism, first (Ch. 2) in the post-Newtonian approximation to general relativity and then (Ch. 3) in full general relativity though in the absence of matter sources. In Chapter 4, we examine the topological structure of absolute event horizons during binary black hole merger simulations conducted with the SpEC code. Chapter 6 reports on the progress of the SpEC code in simulating the coalescence of neutron star-neutron star binaries, while Chapter 7 tests the effects of various numerical gauge conditions on the robustness of black hole formation from stellar collapse in SpEC. In Chapter 5, we examine the nature of pseudospectral expansions of non-smooth functions motivated by the need to simulate the stellar surface in Chapters 6 and 7. In Chapter 8, we study how thermal effects in the nuclear equation of state effect the equilibria and stability of hypermassive neutron stars. Chapter 9 presents supplements to the work in Chapter 8, including an examination of the stability question raised in Chapter 8 in greater mathematical detail.

Branes and supersymmetric quantum field theories

Since the discovery of D-branes as non-perturbative, dynamic objects in string theory, various configurations of branes in type IIA/B string theory and M-theory have been considered to study their low-energy dynamics described by supersymmetric quantum field theories.

One example of such a construction is based on the description of Seiberg-Witten curves of four-dimensional N = 2 supersymmetric gauge theories as branes in type IIA string theory and M-theory. This enables us to study the gauge theories in strongly-coupled regimes. Spectral networks are another tool for utilizing branes to study non-perturbative regimes of two- and four-dimensional supersymmetric theories. Using spectral networks of a Seiberg-Witten theory we can find its BPS spectrum, which is protected from quantum corrections by supersymmetry, and also the BPS spectrum of a related two-dimensional N = (2,2) theory whose (twisted) superpotential is determined by the Seiberg-Witten curve. When we don’t know the perturbative description of such a theory, its spectrum obtained via spectral networks is a useful piece of information. In this thesis we illustrate these ideas with examples of the use of Seiberg-Witten curves and spectral networks to understand various two- and four-dimensional supersymmetric theories.

First, we examine how the geometry of a Seiberg-Witten curve serves as a useful tool for identifying various limits of the parameters of the Seiberg-Witten theory, including Argyres-Seiberg duality and Argyres-Douglas fixed points. Next, we consider the low-energy limit of a two-dimensional N = (2, 2) supersymmetric theory from an M-theory brane configuration whose (twisted) superpotential is determined by the geometry of the branes. We show that, when the two-dimensional theory flows to its infra-red fixed point, particular cases realize Kazama-Suzuki coset models. We also study the BPS spectrum of an Argyres-Douglas type superconformal field theory on the Coulomb branch by using its spectral networks. We provide strong evidence of the equivalence of superconformal field theories from different string-theoretic constructions by comparing their BPS spectra.

Phase conjugation via four-wave mixing in a resonant medium

This thesis describes the theoretical solution and experimental verification of phase conjugation via nondegenerate four-wave mixing in resonant media. The theoretical work models the resonant medium as a two-level atomic system with the lower state of the system being the ground state of the atom. Working initially with an ensemble of stationary atoms, the density matrix equations are solved by third-order perturbation theory in the presence of the four applied electro-magnetic fields which are assumed to be nearly resonant with the atomic transition. Two of the applied fields are assumed to be non-depleted counterpropagating pump waves while the third wave is an incident signal wave. The fourth wave is the phase conjugate wave which is generated by the interaction of the three previous waves with the nonlinear medium. The solution of the density matrix equations gives the local polarization of the atom. The polarization is used in Maxwell's equations as a source term to solve for the propagation and generation of the signal wave and phase conjugate wave through the nonlinear medium. Studying the dependence of the phase conjugate signal on the various parameters such as frequency, we show how an ultrahigh-Q isotropically sensitive optical filter can be constructed using the phase conjugation process.

In many cases the pump waves may saturate the resonant medium so we also present another solution to the density matrix equations which is correct to all orders in the amplitude of the pump waves since the third-order solution is correct only to first-order in each of the field amplitudes. In the saturated regime, we predict several new phenomena associated with degenerate four-wave mixing and also describe the ac Stark effect and how it modifies the frequency response of the filtering process. We also show how a narrow bandwidth optical filter with an efficiency greater than unity can be constructed.

In many atomic systems the atoms are moving at significant velocities such that the Doppler linewidth of the system is larger than the homogeneous linewidth. The latter linewidth dominates the response of the ensemble of stationary atoms. To better understand this case the density matrix equations are solved to third-order by perturbation theory for an atom of velocity v. The solution for the polarization is then integrated over the velocity distribution of the macroscopic system which is assumed to be a gaussian distribution of velocities since that is an excellent model of many real systems. Using the Doppler broadened system, we explain how a tunable optical filter can be constructed whose bandwidth is limited by the homogeneous linewidth of the atom while the tuning range of the filter extends over the entire Doppler profile.

Since it is a resonant system, sodium vapor is used as the nonlinear medium in our experiments. The relevant properties of sodium are discussed in great detail. In particular, the wavefunctions of the 3S and 3P states are analyzed and a discussion of how the 3S-3P transition models a two-level system is given.

Using sodium as the nonlinear medium we demonstrate an ultrahigh-Q optical filter using phase conjugation via nondegenerate four-wave mixing as the filtering process. The filter has a FWHM bandwidth of 41 MHz and a maximum efficiency of 4 x 10^-3. However, our theoretical work and other experimental work with sodium suggest that an efficient filter with both gain and a narrower bandwidth should be quite feasible.

Bright-field and fluorescence chip-scale microscopy for biological imaging

Optical microscopy is an essential tool in biological science and one of the gold standards for medical examinations. Miniaturization of microscopes can be a crucial stepping stone towards realizing compact, cost-effective and portable platforms for biomedical research and healthcare. This thesis reports on implementations of bright-field and fluorescence chip-scale microscopes for a variety of biological imaging applications. The term “chip-scale microscopy” refers to lensless imaging techniques realized in the form of mass-producible semiconductor devices, which transforms the fundamental design of optical microscopes.

Our strategy for chip-scale microscopy involves utilization of low-cost Complementary metal Oxide Semiconductor (CMOS) image sensors, computational image processing and micro-fabricated structural components. First, the sub-pixel resolving optofluidic microscope (SROFM), will be presented, which combines microfluidics and pixel super-resolution image reconstruction to perform high-throughput imaging of fluidic samples, such as blood cells. We discuss design parameters and construction of the device, as well as the resulting images and the resolution of the device, which was 0.66 µm at the highest acuity. The potential applications of SROFM for clinical diagnosis of malaria in the resource-limited settings is discussed.

Next, the implementations of ePetri, a self-imaging Petri dish platform with microscopy resolution, are presented. Here, we simply place the sample of interest on the surface of the image sensor and capture the direct shadow images under the illumination. By taking advantage of the inherent motion of the microorganisms, we achieve high resolution (~1 µm) imaging and long term culture of motile microorganisms over ultra large field-of-view (5.7 mm × 4.4 mm) in a specialized ePetri platform. We apply the pixel super-resolution reconstruction to a set of low-resolution shadow images of the microorganisms as they move across the sensing area of an image sensor chip and render an improved resolution image. We perform longitudinal study of Euglena gracilis cultured in an ePetri platform and image based analysis on the motion and morphology of the cells. The ePetri device for imaging non-motile cells are also demonstrated, by using the sweeping illumination of a light emitting diode (LED) matrix for pixel super-resolution reconstruction of sub-pixel shifted shadow images. Using this prototype device, we demonstrate the detection of waterborne parasites for the effective diagnosis of enteric parasite infection in resource-limited settings.

Then, we demonstrate the adaptation of a smartphone’s camera to function as a compact lensless microscope, which uses ambient illumination as its light source and does not require the incorporation of a dedicated light source. The method is also based on the image reconstruction with sweeping illumination technique, where the sequence of images are captured while the user is manually tilting the device around any ambient light source, such as the sun or a lamp. Image acquisition and reconstruction is performed on the device using a custom-built android application, constructing a stand-alone imaging device for field applications. We discuss the construction of the device using a commercial smartphone and demonstrate the imaging capabilities of our system.

Finally, we report on the implementation of fluorescence chip-scale microscope, based on a silo-filter structure fabricated on the pixel array of a CMOS image sensor. The extruded pixel design with metal walls between neighboring pixels successfully guides fluorescence emission through the thick absorptive filter to the photodiode layer of a pixel. Our silo-filter CMOS image sensor prototype achieves 13-µm resolution for fluorescence imaging over a wide field-of-view (4.8 mm × 4.4 mm). Here, we demonstrate bright-field and fluorescence longitudinal imaging of living cells in a compact, low-cost configuration.

Topics in LIGO-related physics: interferometric speed meters and tidal work

In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors, one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. The most straightforward design for a speed-meter interferometer that accomplishes this is described and analyzed in Chapter 2. This design (due to Braginsky, Gorodetsky, Khalili, and Thorne) is analogous to a microwave-cavity speed meter conceived by Braginsky and Khalili. A mathematical mapping between the microwave speed meter and the optical interferometric speed meter is developed and used to show (in accord with the speed being a quantum nondemolition observable) that in principle the interferometric speed meter can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies . However, in practice, to reach or beat the SQL, this specific speed meter requires exorbitantly high input light power. The physical reason for this is explored, along with other issues such as constraints on performance due to optical dissipation.

Chapter 3 proposes a more sophisticated version of a speed meter. This new design requires only a modest input power and appears to be a fully practical candidate for third-generation LIGO. It can beat the SQL (the approximate sensitivity of second-generation LIGO interferometers) over a broad range of frequencies (~ 10 to 100 Hz in practice) by a factor h/h_SQL ~ √W^(SQL)_(circ)/W_circ. Here W_circ is the light power circulating in the interferometer arms and W_SQL ≃ 800 kW is the circulating power required to beat the SQL at 100 Hz (the LIGO-II power). If squeezed vacuum (with a power-squeeze factor e^-2R) is injected into the interferometer's output port, the SQL can be beat with a much reduced laser power: h/h_SQL ~ √W^(SQL)_(circ)/W_circe^-2R. For realistic parameters (e^-2R ≃ 10 and W_circ ≃ 800 to 2000 kW), the SQL can be beat by a factor ~ 3 to 4 from 10 to 100 Hz. [However, as the power increases in these expressions, the speed meter becomes more narrow band; additional power and re-optimization of some parameters are required to maintain the wide band.] By performing frequency-dependent homodyne detection on the output (with the aid of two kilometer-scale filter cavities), one can markedly improve the interferometer's sensitivity at frequencies above 100 Hz.

Chapters 2 and 3 are part of an ongoing effort to develop a practical variant of an interferometric speed meter and to combine the speed meter concept with other ideas to yield a promising third- generation interferometric gravitational-wave detector that entails low laser power.

Chapter 4 is a contribution to the foundations for analyzing sources of gravitational waves for LIGO. Specifically, it presents an analysis of the tidal work done on a self-gravitating body (e.g., a neutron star or black hole) in an external tidal field (e.g., that of a binary companion). The change in the mass-energy of the body as a result of the tidal work, or "tidal heating," is analyzed using the Landau-Lifshitz pseudotensor and the local asymptotic rest frame of the body. It is shown that the work done on the body is gauge invariant, while the body-tidal-field interaction energy contained within the body's local asymptotic rest frame is gauge dependent. This is analogous to Newtonian theory, where the interaction energy is shown to depend on how one localizes gravitational energy, but the work done on the body is independent of that localization. These conclusions play a role in analyses, by others, of the dynamics and stability of the inspiraling neutron-star binaries whose gravitational waves are likely to be seen and studied by LIGO.

Cosmological consequences of dark matter interactions and vacuum fluctuations

This thesis is divided into two parts: interacting dark matter and fluctuations in cosmology. There is an incongruence between the properties that dark matter is expected to possess between the early universe and the late universe. Weakly-interacting dark matter yields the observed dark matter relic density and is consistent with large-scale structure formation; however, there is strong astrophysical evidence in favor of the idea that dark matter has large self-interactions. The first part of this thesis presents two models in which the nature of dark matter fundamentally changes as the universe evolves. In the first model, the dark matter mass and couplings depend on the value of a chameleonic scalar field that changes as the universe expands. In the second model, dark matter is charged under a hidden SU(N) gauge group and eventually undergoes confinement. These models introduce very different mechanisms to explain the separation between the physics relevant for freezeout and for small-scale dynamics.

As the universe continues to evolve, it will asymptote to a de Sitter vacuum phase. Since there is a finite temperature associated with de Sitter space, the universe is typically treated as a thermal system, subject to rare thermal fluctuations, such as Boltzmann brains. The second part of this thesis begins by attempting to escape this unacceptable situation within the context of known physics: vacuum instability induced by the Higgs field. The vacuum decay rate competes with the production rate of Boltzmann brains, and the cosmological measures that have a sufficiently low occurrence of Boltzmann brains are given more credence. Upon further investigation, however, there are certain situations in which de Sitter space settles into a quiescent vacuum with no fluctuations. This reasoning not only provides an escape from the Boltzmann brain problem, but it also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere during slow-roll inflation, suggesting that eternal inflation is much less common than often supposed. Instead, decoherence occurs during reheating, so this analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation.

Radio frequency studies of surface resistance and critical magnetic field of type I and type II superconductors

The surface resistance and the critical magnetic field of lead electroplated on copper were studied at 205 MHz in a half-wave coaxial resonator. The observed surface resistance at a low field level below 4.2°K could be well described by the BCS surface resistance with the addition of a temperature independent residual resistance. The available experimental data suggest that the major fraction of the residual resistance in the present experiment was due to the presence of an oxide layer on the surface. At higher magnetic field levels the surface resistance was found to be enhanced due to surface imperfections.

The attainable rf critical magnetic field between 2.2°K and T_c of lead was found to be limited not by the thermodynamic critical field but rather by the superheating field predicted by the one-dimensional Ginzburg-Landau theory. The observed rf critical field was very close to the expected superheating field, particularly in the higher reduced temperature range, but showed somewhat stronger temperature dependence than the expected superheating field in the lower reduced temperature range.

The rf critical magnetic field was also studied at 90 MHz for pure tin and indium, and for a series of SnIn and InBi alloys spanning both type I and type II superconductivity. The samples were spherical with typical diameters of 1-2 mm and a helical resonator was used to generate the rf magnetic field in the measurement. The results of pure samples of tin and indium showed that a vortex-like nucleation of the normal phase was responsible for the superconducting-to-normal phase transition in the rf field at temperatures up to about 0.98-0.99 T_c' where the ideal superheating limit was being reached. The results of the alloy samples showed that the attainable rf critical fields near T_c were well described by the superheating field predicted by the one-dimensional GL theory in both the type I and type II regimes. The measurement was also made at 300 MHz resulting in no significant change in the rf critical field. Thus it was inferred that the nucleation time of the normal phase, once the critical field was reached, was small compared with the rf period in this frequency range.

Magnetospheric access of solar particles and the configuration of the distant geomagnetic field

The access of 1.2-40 MeV protons and 0.4-1.0 MeV electrons from interplanetary space to the polar cap regions has been investigated with an experiment on board a low altitude, polar orbiting satellite (OG0-4).

A total of 333 quiet time observations of the electron polar cap boundary give a mapping of the boundary between open and closed geomagnetic field lines which is an order of magnitude more comprehensive than previously available.

Persistent features (north/south asymmetries) in the polar cap proton flux, which are established as normal during solar proton events, are shown to be associated with different flux levels on open geomagnetic field lines than on closed field lines. The pole in which these persistent features are observed is strongly correlated to the sector structure of the interplanetary magnetic field and uncorrelated to the north/south component of this field. The features were observed in the north (south) pole during a negative (positive) sector 91% of the time, while the solar field had a southward component only 54% of the time. In addition, changes in the north/south component have no observable effect on the persistent features.

Observations of events associated with co-rotating regions of enhanced proton flux in interplanetary space are used to establish the characteristics of the 1.2 - 40 MeV proton access windows: the access window for low polar latitudes is near the earth, that for one high polar latitude region is ~250 R_⊕ behind the earth, while that for the other high polar latitude region is ~1750 R_⊕ behind the earth. All of the access windows are of approximately the same extent (~120 R_⊕). The following phenomena contribute to persistent polar cap features: limited interplanetary regions of enhanced flux propagating past the earth, radial gradients in the interplanetary flux, and anisotropies in the interplanetary flux.

These results are compared to the particle access predictions of the distant geomagnetic tail configurations proposed by Michel and Dessler, Dungey, and Frank. The data are consistent with neither the model of Michel and Dessler nor that of Dungey. The model of Frank can yield a consistent access window configuration provided the following constraints are satisfied: the merging rate for open field lines at one polar neutral point must be ~5 times that at the other polar neutral point, related to the solar magnetic field configuration in a consistent fashion, the migration time for open field lines to move across the polar cap region must be the same in both poles, and the open field line merging rate at one of the polar neutral points must be at least as large as that required for almost all the open field lines to have merged in 0 (one hour). The possibility of satisfying these constraints is investigated in some detail.

The role played by interplanetary anisotropies in the observation of persistent polar cap features is discussed. Special emphasis is given to the problem of non-adiabatic particle entry through regions where the magnetic field is changing direction. The degree to which such particle entry can be assumed to be nearly adiabatic is related to the particle rigidity, the angle through which the field turns, and the rate at which the field changes direction; this relationship is established for the case of polar cap observations.

Wide Field-of-view Microscopes and Endoscopes for Time-lapse Imaging and High-throughput Screening

Wide field-of-view (FOV) microscopy is of high importance to biological research and clinical diagnosis where a high-throughput screening of samples is needed. This thesis presents the development of several novel wide FOV imaging technologies and demonstrates their capabilities in longitudinal imaging of living organisms, on the scale of viral plaques to live cells and tissues.

The ePetri Dish is a wide FOV on-chip bright-field microscope. Here we applied an ePetri platform for plaque analysis of murine norovirus 1 (MNV-1). The ePetri offers the ability to dynamically track plaques at the individual cell death event level over a wide FOV of 6 mm × 4 mm at 30 min intervals. A density-based clustering algorithm is used to analyze the spatial-temporal distribution of cell death events to identify plaques at their earliest stages. We also demonstrate the capabilities of the ePetri in viral titer count and dynamically monitoring plaque formation, growth, and the influence of antiviral drugs.

We developed another wide FOV imaging technique, the Talbot microscope, for the fluorescence imaging of live cells. The Talbot microscope takes advantage of the Talbot effect and can generate a focal spot array to scan the fluorescence samples directly on-chip. It has a resolution of 1.2 μm and a FOV of ~13 mm². We further upgraded the Talbot microscope for the long-term time-lapse fluorescence imaging of live cell cultures, and analyzed the cells’ dynamic response to an anticancer drug.

We present two wide FOV endoscopes for tissue imaging, named the AnCam and the PanCam. The AnCam is based on the contact image sensor (CIS) technology, and can scan the whole anal canal within 10 seconds with a resolution of 89 μm, a maximum FOV of 100 mm × 120 mm, and a depth-of-field (DOF) of 0.65 mm. We also demonstrate the performance of the AnCam in whole anal canal imaging in both animal models and real patients. In addition to this, the PanCam is based on a smartphone platform integrated with a panoramic annular lens (PAL), and can capture a FOV of 18 mm × 120 mm in a single shot with a resolution of 100─140 μm. In this work we demonstrate the PanCam’s performance in imaging a stained tissue sample.