Innovations of wide-field optical-sectioning fluorescence microscopy : toward high-speed volumetric bio-imaging with simplicity

Optical microscopy has become an indispensable tool for biological researches since its invention, mostly owing to its sub-cellular spatial resolutions, non-invasiveness, instrumental simplicity, and the intuitive observations it provides. Nonetheless, obtaining reliable, quantitative spatial information from conventional wide-field optical microscopy is not always intuitive as it appears to be. This is because in the acquired images of optical microscopy the information about out-of-focus regions is spatially blurred and mixed with in-focus information. In other words, conventional wide-field optical microscopy transforms the three-dimensional spatial information, or volumetric information about the objects into a two-dimensional form in each acquired image, and therefore distorts the spatial information about the object. Several fluorescence holography-based methods have demonstrated the ability to obtain three-dimensional information about the objects, but these methods generally rely on decomposing stereoscopic visualizations to extract volumetric information and are unable to resolve complex 3-dimensional structures such as a multi-layer sphere.

The concept of optical-sectioning techniques, on the other hand, is to detect only two-dimensional information about an object at each acquisition. Specifically, each image obtained by optical-sectioning techniques contains mainly the information about an optically thin layer inside the object, as if only a thin histological section is being observed at a time. Using such a methodology, obtaining undistorted volumetric information about the object simply requires taking images of the object at sequential depths.

Among existing methods of obtaining volumetric information, the practicability of optical sectioning has made it the most commonly used and most powerful one in biological science. However, when applied to imaging living biological systems, conventional single-point-scanning optical-sectioning techniques often result in certain degrees of photo-damages because of the high focal intensity at the scanning point. In order to overcome such an issue, several wide-field optical-sectioning techniques have been proposed and demonstrated, although not without introducing new limitations and compromises such as low signal-to-background ratios and reduced axial resolutions. As a result, single-point-scanning optical-sectioning techniques remain the most widely used instrumentations for volumetric imaging of living biological systems to date.

In order to develop wide-field optical-sectioning techniques that has equivalent optical performance as single-point-scanning ones, this thesis first introduces the mechanisms and limitations of existing wide-field optical-sectioning techniques, and then brings in our innovations that aim to overcome these limitations. We demonstrate, theoretically and experimentally, that our proposed wide-field optical-sectioning techniques can achieve diffraction-limited optical sectioning, low out-of-focus excitation and high-frame-rate imaging in living biological systems. In addition to such imaging capabilities, our proposed techniques can be instrumentally simple and economic, and are straightforward for implementation on conventional wide-field microscopes. These advantages together show the potential of our innovations to be widely used for high-speed, volumetric fluorescence imaging of living biological systems.

Wave interactions in periodic structures and periodic dielectric waveguides

This work is concerned with a general analysis of wave interactions in periodic structures and particularly periodic thin film dielectric waveguides.

The electromagnetic wave propagation in an asymmetric dielectric waveguide with a periodically perturbed surface is analyzed in terms of a Floquet mode solution. First order approximate analytical expressions for the space harmonics are obtained. The solution is used to analyze various applications: (1) phase matched second harmonic generation in periodically perturbed optical waveguides; (2) grating couplers and thin film filters; (3) Bragg reflection devices; (4) the calculation of the traveling wave interaction impedance for solid state and vacuum tube optical traveling wave amplifiers which utilize periodic dielectric waveguides. Some of these applications are of interest in the field of integrated optics.

A special emphasis is put on the analysis of traveling wave interaction between electrons and electromagnetic waves in various operation regimes. Interactions with a finite temperature electron beam at the collision-dominated, collisionless, and quantum regimes are analyzed in detail assuming a one-dimensional model and longitudinal coupling.

The analysis is used to examine the possibility of solid state traveling wave devices (amplifiers, modulators), and some monolithic structures of these devices are suggested, designed to operate at the submillimeter-far infrared frequency regime. The estimates of attainable traveling wave interaction gain are quite low (on the order of a few inverse centimeters). However, the possibility of attaining net gain with different materials, structures and operation condition is not ruled out.

The developed model is used to discuss the possibility and the theoretical limitations of high frequency (optical) operation of vacuum electron beam tube; and the relation to other electron-electromagnetic wave interaction effects (Smith-Purcell and Cerenkov radiation and the free electron laser) are pointed out. Finally, the case where the periodic structure is the natural crystal lattice is briefly discussed. The longitudinal component of optical space harmonics in the crystal is calculated and found to be of the order of magnitude of the macroscopic wave, and some comments are made on the possibility of coherent bremsstrahlung and distributed feedback lasers in single crystals.

Propagation of the fast magnetosonic wave in a tokamak plasma

The propagation of the fast magnetosonic wave in a tokamak plasma has been investigated at low power, between 10 and 300 watts, as a prelude to future heating experiments.

The attention of the experiments has been focused on the understanding of the coupling between a loop antenna and a plasma-filled cavity. Special emphasis has been given to the measurement of the complex loading impedance of the plasma. The importance of this measurement is that once the complex loading impedance of the plasma is known, a matching network can be designed so that the r.f. generator impedance can be matched to one of the cavity modes, thus delivering maximum power to the plasma. For future heating experiments it will be essential to be able to match the generator impedance to a cavity mode in order to couple the r.f. energy efficiently to the plasma.

As a consequence of the complex impedance measurements, it was discovered that the designs of the transmitting antenna and the impedance matching network are both crucial. The losses in the antenna and the matching network must be kept below the plasma loading in order to be able to detect the complex plasma loading impedance. This is even more important in future heating experiments, because the fundamental basis for efficient heating before any other consideration is to deliver more energy into the plasma than is dissipated in the antenna system.

The characteristics of the magnetosonic cavity modes are confirmed by three different methods. First, the cavity modes are observed as voltage maxima at the output of a six-turn receiving probe. Second, they also appear as maxima in the input resistance of the transmitting antenna. Finally, when the real and imaginary parts of the measured complex input impedance of the antenna are plotted in the complex impedance plane, the resulting curves are approximately circles, indicating a resonance phenomenon.

The observed plasma loading resistances at the various cavity modes are as high as 3 to 4 times the basic antenna resistance (~ .4 Ω). The estimated cavity Q’s were between 400 and 700. This means that efficient energy coupling into the tokamak and low losses in the antenna system are possible.

Damping and saturation of a second order electron plasma wave echo

A description is given of experimental work on the damping of a second order electron plasma wave echo due to velocity space diffusion in a low temperature magnetoplasma. Sufficient precision was obtained to verify the theoretically predicted cubic rather than quadratic or quartic dependence of the damping on exciter separation. Compared to the damping predicted for Coulomb collisions in a thermal plasma in an infinite magnetic field, the magnitude of the damping was approximately as predicted, while the velocity dependence of the damping was weaker than predicted. The discrepancy is consistent with the actual non-Maxwellian electron distribution of the plasma.

In conjunction with the damping work, echo amplitude saturation was measured as a function of the velocity of the electrons contributing to the echo. Good agreement was obtained with the predicted J₁ Bessel function amplitude dependence, as well as a demonstration that saturation did not influence the damping results.

Radiation from a short electric dipole antenna in a hot uniaxial plasma

The effects of electron temperature on the radiation fields and the resistance of a short dipole antenna embedded in a uniaxial plasma have been studied. It is found that for ω < ω_p the antenna excites two waves, a slow wave and a fast wave. These waves propagate only within a cone whose axis is parallel to the biasing magnetostatic field B_o and whose semicone angle is slightly less than sin ^(-1) (ω/ω_p). In the case of ω > ω_p the antenna excites two separate modes of radiation. One of the modes is the electromagnetic mode, while the other mode is of hot plasma origin. A characteristic interference structure is noted in the angular distribution of the field. The far fields are evaluated by asymptotic methods, while the near fields are calculated numerically. The effects of antenna length ℓ, electron thermal speed, collisional and Landau damping on the near field patterns have been studied.

The input and the radiation resistances are calculated and are shown to remain finite for nonzero electron thermal velocities. The effect of Landau damping and the antenna length on the input and radiation resistances has been considered.

The radiation condition for solving Maxwell's equations is discussed and the phase and group velocities for propagation given. It is found that for ω < ω_p in the radial direction (cylindrical coordinates) the power flow is in the opposite direction to that of the phase propagation. For ω > ω_p the hot plasma mode has similar characteristics.

Part I - The radiation of elastic waves from a spherical cavity in a half space. Part II - Precision determination of focal depths and epicenters of earthquakes.

Part I: The dynamic response of an elastic half space to an explosion in a buried spherical cavity is investigated by two methods. The first is implicit, and the final expressions for the displacements at the free surface are given as a series of spherical wave functions whose coefficients are solutions of an infinite set of linear equations. The second method is based on Schwarz's technique to solve boundary value problems, and leads to an iterative solution, starting with the known expression for the point source in a half space as first term. The iterative series is transformed into a system of two integral equations, and into an equivalent set of linear equations. In this way, a dual interpretation of the physical phenomena is achieved. The systems are treated numerically and the Rayleigh wave part of the displacements is given in the frequency domain. Several comparisons with simpler cases are analyzed to show the effect of the cavity radius-depth ratio on the spectra of the displacements.

Part II: A high speed, large capacity, hypocenter location program has been written for an IBM 7094 computer. Important modifications to the standard method of least squares have been incorporated in it. Among them are a new way to obtain the depth of shocks from the normal equations, and the computation of variable travel times for the local shocks in order to account automatically for crustal variations. The multiregional travel times, largely based upon the investigations of the United States Geological Survey, are confronted with actual traverses to test their validity.

It is shown that several crustal phases provide control enough to obtain good solutions in depth for nuclear explosions, though not all the recording stations are in the region where crustal corrections are considered. The use of the European travel times, to locate the French nuclear explosion of May 1962 in the Sahara, proved to be more adequate than previous work.

A simpler program, with manual crustal corrections, is used to process the Kern County series of aftershocks, and a clearer picture of tectonic mechanism of the White Wolf fault is obtained.

Shocks in the California region are processed automatically and statistical frequency-depth and energy depth curves are discussed in relation to the tectonics of the area.

Exploring the Dynamic Radio Sky: The Search for Slow Transients with the VLA

While synoptic surveys in the optical and at high energies have revealed a rich discovery phase space of slow transients, a similar yield is still awaited in the radio. Majority of the past blind surveys, carried out with radio interferometers, have suffered from a low yield of slow transients, ambiguous transient classifications, and contamination by false positives. The newly-refurbished Karl G. Jansky Array (Jansky VLA) offers wider bandwidths for accurate RFI excision as well as substantially-improved sensitivity and survey speed compared with the old VLA. The Jansky VLA thus eliminates the pitfalls of interferometric transient search by facilitating sensitive, wide-field, and near-real-time radio surveys and enabling a systematic exploration of the dynamic radio sky. This thesis aims at carrying out blind Jansky VLA surveys for characterizing the radio variable and transient sources at frequencies of a few GHz and on timescales between days and years. Through joint radio and optical surveys, the thesis addresses outstanding questions pertaining to the rates of slow radio transients (e.g. radio supernovae, tidal disruption events, binary neutron star mergers, stellar flares, etc.), the false-positive foreground relevant for the radio and optical counterpart searches of gravitational wave sources, and the beaming factor of gamma-ray bursts. The need for rapid processing of the Jansky VLA data and near-real-time radio transient search has enabled the development of state-of-the-art software infrastructure. This thesis has successfully demonstrated the Jansky VLA as a powerful transient search instrument, and it serves as a pathfinder for the transient surveys planned for the SKA-mid pathfinder facilities, viz. ASKAP, MeerKAT, and WSRT/Apertif.

The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.

Instrumentation for Kinetic-Inductance-Detector-Based Submillimeter Radio Astronomy

A substantial amount of important scientific information is contained within astronomical data at the submillimeter and far-infrared (FIR) wavelengths, including information regarding dusty galaxies, galaxy clusters, and star-forming regions; however, these wavelengths are among the least-explored fields in astronomy because of the technological difficulties involved in such research. Over the past 20 years, considerable efforts have been devoted to developing submillimeter- and millimeter-wavelength astronomical instruments and telescopes.

The number of detectors is an important property of such instruments and is the subject of the current study. Future telescopes will require as many as hundreds of thousands of detectors to meet the necessary requirements in terms of the field of view, scan speed, and resolution. A large pixel count is one benefit of the development of multiplexable detectors that use kinetic inductance detector (KID) technology.

This dissertation presents the development of a KID-based instrument including a portion of the millimeter-wave bandpass filters and all aspects of the readout electronics, which together enabled one of the largest detector counts achieved to date in submillimeter-/millimeter-wavelength imaging arrays: a total of 2304 detectors. The work presented in this dissertation has been implemented in the MUltiwavelength Submillimeter Inductance Camera (MUSIC), a new instrument for the Caltech Submillimeter Observatory (CSO).

Quantifying Earthquake Collapse Risk of Tall Steel Moment Frame Buildings Using Rupture-to-Rafters Simulations

There is a sparse number of credible source models available from large-magnitude past earthquakes. A stochastic source model generation algorithm thus becomes necessary for robust risk quantification using scenario earthquakes. We present an algorithm that combines the physics of fault ruptures as imaged in laboratory earthquakes with stress estimates on the fault constrained by field observations to generate stochastic source models for large-magnitude (Mw 6.0-8.0) strike-slip earthquakes. The algorithm is validated through a statistical comparison of synthetic ground motion histories from a stochastically generated source model for a magnitude 7.90 earthquake and a kinematic finite-source inversion of an equivalent magnitude past earthquake on a geometrically similar fault. The synthetic dataset comprises of three-component ground motion waveforms, computed at 636 sites in southern California, for ten hypothetical rupture scenarios (five hypocenters, each with two rupture directions) on the southern San Andreas fault. A similar validation exercise is conducted for a magnitude 6.0 earthquake, the lower magnitude limit for the algorithm. Additionally, ground motions from the Mw7.9 earthquake simulations are compared against predictions by the Campbell-Bozorgnia NGA relation as well as the ShakeOut scenario earthquake. The algorithm is then applied to generate fifty source models for a hypothetical magnitude 7.9 earthquake originating at Parkfield, with rupture propagating from north to south (towards Wrightwood), similar to the 1857 Fort Tejon earthquake. Using the spectral element method, three-component ground motion waveforms are computed in the Los Angeles basin for each scenario earthquake and the sensitivity of ground shaking intensity to seismic source parameters (such as the percentage of asperity area relative to the fault area, rupture speed, and risetime) is studied.

Under plausible San Andreas fault earthquakes in the next 30 years, modeled using the stochastic source algorithm, the performance of two 18-story steel moment frame buildings (UBC 1982 and 1997 designs) in southern California is quantified. The approach integrates rupture-to-rafters simulations into the PEER performance based earthquake engineering (PBEE) framework. Using stochastic sources and computational seismic wave propagation, three-component ground motion histories at 636 sites in southern California are generated for sixty scenario earthquakes on the San Andreas fault. The ruptures, with moment magnitudes in the range of 6.0-8.0, are assumed to occur at five locations on the southern section of the fault. Two unilateral rupture propagation directions are considered. The 30-year probabilities of all plausible ruptures in this magnitude range and in that section of the fault, as forecast by the United States Geological Survey, are distributed among these 60 earthquakes based on proximity and moment release. The response of the two 18-story buildings hypothetically located at each of the 636 sites under 3-component shaking from all 60 events is computed using 3-D nonlinear time-history analysis. Using these results, the probability of the structural response exceeding Immediate Occupancy (IO), Life-Safety (LS), and Collapse Prevention (CP) performance levels under San Andreas fault earthquakes over the next thirty years is evaluated.

Furthermore, the conditional and marginal probability distributions of peak ground velocity (PGV) and displacement (PGD) in Los Angeles and surrounding basins due to earthquakes occurring primarily on the mid-section of southern San Andreas fault are determined using Bayesian model class identification. Simulated ground motions at sites within 55-75km from the source from a suite of 60 earthquakes (Mw 6.0 − 8.0) primarily rupturing mid-section of San Andreas fault are considered for PGV and PGD data.

Noise Cancellation for Gravitational Wave Detectors

The LIGO gravitational wave detectors are on the brink of making the first direct detections of gravi- tational waves. Noise cancellation techniques are described, in order to simplify the commissioning of these detectors as well as significantly improve their sensitivity to astrophysical sources. Future upgrades to the ground based detectors will require further cancellation of Newtonian gravitational noise in order to make the transition from detectors striving to make the first direct detection of gravitational waves, to observatories extracting physics from many, many detections. Techniques for this noise cancellation are described, as well as the work remaining in this realm.

Toward Understanding Astrophysical Phenomena

Fast radio bursts (FRBs), a novel type of radio pulse, whose physics is not yet understood at all. Only a handful of FRBs had been detected when we started this project. Taking account of the scant observations, we put physical constraints on FRBs. We excluded proposals of a galactic origin for their extraordinarily high dispersion measures (DM), in particular stellar coronas and HII regions. Therefore our work supports an extragalactic origin for FRBs. We show that the resolved scattering tail of FRB 110220 is unlikely to be due to propagation through the intergalactic plasma. Instead the scattering is probably caused by the interstellar medium in the FRB's host galaxy, and indicates that this burst sits in the central region of that galaxy. Pulse durations of order $\ms$ constrain source sizes of FRBs implying enormous brightness temperatures and thus coherent emission. Electric fields near FRBs at cosmological distances would be so strong that they could accelerate free electrons from rest to relativistic energies in a single wave period. When we worked on FRBs, it was unclear whether they were genuine astronomical signals as distinct from `perytons', clearly terrestrial radio bursts, sharing some common properties with FRBs. Recently, in April 2015, astronomers discovered that perytons were emitted by microwave ovens. Radio chirps similar to FRBs were emitted when their doors opened while they were still heating. Evidence for the astronomical nature of FRBs has strengthened since our paper was published. Some bursts have been found to show linear and circular polarizations and Faraday rotation of the linear polarization has also been detected. I hope to resume working on FRBs in the near future. But after we completed our FRB paper, I decided to pause this project because of the lack of observational constraints.

The pulsar triple system, J0733+1715, has its orbital parameters fitted to high accuracy owing to the precise timing of the central $\ms$ pulsar. The two orbits are highly hierarchical, namely $P_{\mathrm{orb,1}}\ll P_{\mathrm{orb,2}}$, where 1 and 2 label the inner and outer white dwarf (WD) companions respectively. Moreover, their orbital planes almost coincide, providing a unique opportunity to study secular interaction associated purely with eccentricity beyond the solar system. Secular interaction only involves effect averaged over many orbits. Thus each companion can be represented by an elliptical wire with its mass distributed inversely proportional to its local orbital speed. Generally there exists a mutual torque, which vanishes only when their apsidal lines are parallel or anti-parallel. To maintain either mode, the eccentricity ratio, $e_1/e_2$, must be of the proper value, so that both apsidal lines precess together. For J0733+1715, $e_1\ll e_2$ for the parallel mode, while $e_1\gg e_2$ for the anti-parallel one. We show that the former precesses $\sim 10$ times slower than the latter. Currently the system is dominated by the parallel mode. Although only a little anti-parallel mode survives, both eccentricities especially $e_1$ oscillate on $\sim 10^3\yr$ timescale. Detectable changes would occur within $\sim 1\yr$. We demonstrate that the anti-parallel mode gets damped $\sim 10^4$ times faster than its parallel brother by any dissipative process diminishing $e_1$. If it is the tidal damping in the inner WD, we proceed to estimate its tidal quantity parameter ($Q$) to be $\sim 10^6$, which was poorly constrained by observations. However, tidal damping may also happen during the preceding low-mass X-ray binary (LMXB) phase or hydrogen thermal nuclear flashes. But, in both cases, the inner companion fills its Roche lobe and probably suffers mass/angular momentum loss, which might cause $e_1$ to grow rather than decay.

Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede and Enceladus-Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas-Tethys and Titan-Hyperion MMRs and their resonant arguments are the only ones to exhibit substantial librations. When a separatrix is present, tidal damping of eccentricity or inclination excites overstable librations that can lead to passage through resonance on the damping timescale. However, after investigation, we conclude that the librations in the Mimas-Tethys and Titan-Hyperion MMRs are fossils and do not result from overstability.

Rubble piles are common in the solar system. Monolithic elements touch their neighbors in small localized areas. Voids occupy a significant fraction of the volume. In a fluid-free environment, heat cannot conduct through voids; only radiation can transfer energy across them. We model the effective thermal conductivity of a rubble pile and show that it is proportional the square root of the pressure, $P$, for $P\leq \epsy^3\mu$ where $\epsy$ is the material's yield strain and $\mu$ its shear modulus. Our model provides an excellent fit to the depth dependence of the thermal conductivity in the top $140\,\mathrm{cm}$ of the lunar regolith. It also offers an explanation for the low thermal inertias of rocky asteroids and icy satellites. Lastly, we discuss how rubble piles slow down the cooling of small bodies such as asteroids.

Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation {\it before} the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method.

Experimental, Numerical and Analytical Studies of the MHD-driven plasma jet, instabilities and waves

This thesis describes a series of experimental, numerical, and analytical studies involving the Caltech magnetohydrodynamically (MHD)-driven plasma jet experiment. The plasma jet is created via a capacitor discharge that powers a magnetized coaxial planar electrodes system. The jet is collimated and accelerated by the MHD forces.

We present three-dimensional ideal MHD finite-volume simulations of the plasma jet experiment using an astrophysical magnetic tower as the baseline model. A compact magnetic energy/helicity injection is exploited in the simulation analogous to both the experiment and to astrophysical situations. Detailed analysis provides a comprehensive description of the interplay of magnetic force, pressure, and flow effects. We delineate both the jet structure and the transition process that converts the injected magnetic energy to other forms.

When the experimental jet is sufficiently long, it undergoes a global kink instability and then a secondary local Rayleigh-Taylor instability caused by lateral acceleration of the kink instability. We present an MHD theory of the Rayleigh-Taylor instability on the cylindrical surface of a plasma flux rope in the presence of a lateral external gravity. The Rayleigh-Taylor instability is found to couple to the classic current-driven instability, resulting in a new type of hybrid instability. The coupled instability, produced by combination of helical magnetic field, curvature of the cylindrical geometry, and lateral gravity, is fundamentally different from the classic magnetic Rayleigh-Taylor instability occurring at a two-dimensional planar interface.

In the experiment, this instability cascade from macro-scale to micro-scale eventually leads to the failure of MHD. When the Rayleigh-Taylor instability becomes nonlinear, it compresses and pinches the plasma jet to a scale smaller than the ion skin depth and triggers a fast magnetic reconnection. We built a specially designed high-speed 3D magnetic probe and successfully detected the high frequency magnetic fluctuations of broadband whistler waves associated with the fast reconnection. The magnetic fluctuations exhibit power-law spectra. The magnetic components of single-frequency whistler waves are found to be circularly polarized regardless of the angle between the wave propagation direction and the background magnetic field.

Mean-speed measurements in two-dimensional, incompressible, fully-developed turbulent channel flow

Mean velocity profiles were measured in the 5” x 60” wind channel of the turbulence laboratory at the GALCIT, by the use of a hot-wire anemometer. The repeatability of results was established, and the accuracy of the instrumentation estimated. Scatter of experimental results is a little, if any, beyond this limit, although some effects might be expected to arise from variations in atmospheric humidity, no account of this factor having been taken in the present work. Also, slight unsteadiness in flow conditions will be responsible for some scatter.

Irregularities of a hot-wire in close proximity to a solid boundary at low speeds were observed, as have already been found by others.

That Kármán’s logarithmic law holds reasonably well over the main part of a fully developed turbulent flow was checked, the equation u/u_t = 6.0 + 6.25 log₁₀ y^ut/v being obtained, and, as has been previously the case, the experimental points do not quite form one straight line in the region where viscosity effects are small. The values of the constants for this law for the best over-all agreement were determined and compared with those obtained by others.

The range of Reynolds numbers used (based on half-width of channel) was from 20,000 to 60,000.

Wave uplift pressures on horizontal platforms

The major objective of the study has been to investigate in detail the rapidly-varying peak uplift pressure and the slowly-varying positive and negative uplift pressures that are known to be exerted by waves against the underside of a horizontal pier or platform located above the still water level, but not higher than the crests of the incident waves.

In a "two-dimensional" laboratory study conducted in a 100-ft long by 15-in.-wide by 2-ft-deep wave tank with a horizontal smooth bottom, individually generated solitary waves struck a rigid, fixed, horizontal platform extending the width of the tank. Pressure transducers were mounted flush with the smooth soffit, or underside, of the platform. The location of the transducers could be varied.

The problem of a d equate dynamic and spatial response of the transducers was investigated in detail. It was found that unless the radius of the sensitive area of a pressure transducer is smaller than about one-third of the characteristic width of the pressure distribution, the peak pressure and the rise-time will not be recorded accurately. A procedure was devised to correct peak pressures and rise-times for this transducer defect.

The hydrodynamics of the flow beneath the platform are described qualitatively by a si1nple analysis, which relates peak pressure and positive slowly-varying pressure to the celerity of the wave front propagating beneath the platform, and relates negative slowly-varying pressure to the process by which fluid recedes from the platform after the wave has passed. As the wave front propagates beneath the platform, its celerity increases to a maximum, then decreases. The peak pressure similarly increases with distance from the seaward edge of the platform, then decreases.

Measured peak pressure head, always found to be less than five times the incident wave height above still water level, is an order of magnitude less than reported shock pressures due to waves breaking against vertical walls; the product of peak pressure and rise-time, considered as peak impulse, is of the order of 20% of reported shock impulse due to waves breaking against vertical walls. The maximum measured slowly-varying uplift pressure head is approximately equal to the incident wave height less the soffit clearance above still water level. The normalized magnitude and duration of negative pressure appears to depend principally on the ratio of soffit clearance to still water depth and on the ratio of platform length to still water depth.