Multipole moments in general relativity and dynamical perturbations of black-hole magnetospheres

This thesis consists of two parts. In Part I, we develop a multipole moment formalism in general relativity and use it to analyze the motion and precession of compact bodies. More specifically, the generic, vacuum, dynamical gravitational field of the exterior universe in the vicinity of a freely moving body is expanded in positive powers of the distance r away from the body's spatial origin (i.e., in the distance r from its timelike-geodesic world line). The expansion coefficients, called "external multipole moments,'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives evaluated on the body's central world line. In a carefully chosen class of de Donder coordinates, the expansion of the external field involves only integral powers of r ; no logarithmic terms occur. The expansion is used to derive higher-order corrections to previously known laws of motion and precession for black holes and other bodies. The resulting laws of motion and precession are expressed in terms of couplings of the time derivatives of the body's quadrupole and octopole moments to the external moments, i.e., to the external curvature and its gradient.

In part II, we study the interaction of magnetohydrodynamic (MHD) waves in a black-hole magnetosphere with the "dragging of inertial frames" effect of the hole's rotation - i.e., with the hole's "gravitomagnetic field." More specifically: we first rewrite the laws of perfect general relativistic magnetohydrodynamics (GRMHD) in 3+1 language in a general spacetime, in terms of quantities (magnetic field, flow velocity, ...) that would be measured by the ''fiducial observers” whose world lines are orthogonal to (arbitrarily chosen) hypersurfaces of constant time. We then specialize to a stationary spacetime and MHD flow with one arbitrary spatial symmetry (e.g., the stationary magnetosphere of a Kerr black hole); and for this spacetime we reduce the GRMHD equations to a set of algebraic equations. The general features of the resulting stationary, symmetric GRMHD magnetospheric solutions are discussed, including the Blandford-Znajek effect in which the gravitomagnetic field interacts with the magnetosphere to produce an outflowing jet. Then in a specific model spacetime with two spatial symmetries, which captures the key features of the Kerr geometry, we derive the GRMHD equations which govern weak, linealized perturbations of a stationary magnetosphere with outflowing jet. These perturbation equations are then Fourier analyzed in time t and in the symmetry coordinate x, and subsequently solved numerically. The numerical solutions describe the interaction of MHD waves with the gravitomagnetic field. It is found that, among other features, when an oscillatory external force is applied to the region of the magnetosphere where plasma (e⁺e^-) is being created, the magnetosphere responds especially strongly at a particular, resonant, driving frequency. The resonant frequency is that for which the perturbations appear to be stationary (time independent) in the common rest frame of the freshly created plasma and the rotating magnetic field lines. The magnetosphere of a rotating black hole, when buffeted by nonaxisymmetric magnetic fields anchored in a surrounding accretion disk, might exhibit an analogous resonance. If so then the hole's outflowing jet might be modulated at resonant frequencies ω=(m/2) Ω_H where m is an integer and Ω_H is the hole's angular velocity.

A Multiwavelength Study of the Intracluster Medium and the Characterization of the Multiwavelength Sub/millimeter Inductance Camera

The first part of this thesis combines Bolocam observations of the thermal Sunyaev-Zel’dovich (SZ) effect at 140 GHz with X-ray observations from Chandra, strong lensing data from the Hubble Space Telescope (HST), and weak lensing data from HST and Subaru to constrain parametric models for the distribution of dark and baryonic matter in a sample of six massive, dynamically relaxed galaxy clusters. For five of the six clusters, the full multiwavelength dataset is well described by a relatively simple model that assumes spherical symmetry, hydrostatic equilibrium, and entirely thermal pressure support. The multiwavelength analysis yields considerably better constraints on the total mass and concentration compared to analysis of any one dataset individually. The subsample of five galaxy clusters is used to place an upper limit on the fraction of pressure support in the intracluster medium (ICM) due to nonthermal processes, such as turbulent and bulk flow of the gas. We constrain the nonthermal pressure fraction at r500c to be less than 0.11 at 95% confidence, where r500c refers to radius at which the average enclosed density is 500 times the critical density of the Universe. This is in tension with state-of-the-art hydrodynamical simulations, which predict a nonthermal pressure fraction of approximately 0.25 at r500c for the clusters in this sample.

The second part of this thesis focuses on the characterization of the Multiwavelength Sub/millimeter Inductance Camera (MUSIC), a photometric imaging camera that was commissioned at the Caltech Submillimeter Observatory (CSO) in 2012. MUSIC is designed to have a 14 arcminute, diffraction-limited field of view populated with 576 spatial pixels that are simultaneously sensitive to four bands at 150, 220, 290, and 350 GHz. It is well-suited for studies of dusty star forming galaxies, galaxy clusters via the SZ Effect, and galactic star formation. MUSIC employs a number of novel detector technologies: broadband phased-arrays of slot dipole antennas for beam formation, on-chip lumped element filters for band definition, and Microwave Kinetic Inductance Detectors (MKIDs) for transduction of incoming light to electric signal. MKIDs are superconducting micro-resonators coupled to a feedline. Incoming light breaks apart Cooper pairs in the superconductor, causing a change in the quality factor and frequency of the resonator. This is read out as amplitude and phase modulation of a microwave probe signal centered on the resonant frequency. By tuning each resonator to a slightly different frequency and sending out a superposition of probe signals, hundreds of detectors can be read out on a single feedline. This natural capability for large scale, frequency domain multiplexing combined with relatively simple fabrication makes MKIDs a promising low temperature detector for future kilopixel sub/millimeter instruments. There is also considerable interest in using MKIDs for optical through near-infrared spectrophotometry due to their fast microsecond response time and modest energy resolution. In order to optimize the MKID design to obtain suitable performance for any particular application, it is critical to have a well-understood physical model for the detectors and the sources of noise to which they are susceptible. MUSIC has collected many hours of on-sky data with over 1000 MKIDs. This work studies the performance of the detectors in the context of one such physical model. Chapter 2 describes the theoretical model for the responsivity and noise of MKIDs. Chapter 3 outlines the set of measurements used to calibrate this model for the MUSIC detectors. Chapter 4 presents the resulting estimates of the spectral response, optical efficiency, and on-sky loading. The measured detector response to Uranus is compared to the calibrated model prediction in order to determine how well the model describes the propagation of signal through the full instrument. Chapter 5 examines the noise present in the detector timestreams during recent science observations. Noise due to fluctuations in atmospheric emission dominate at long timescales (less than 0.5 Hz). Fluctuations in the amplitude and phase of the microwave probe signal due to the readout electronics contribute significant 1/f and drift-type noise at shorter timescales. The atmospheric noise is removed by creating a template for the fluctuations in atmospheric emission from weighted averages of the detector timestreams. The electronics noise is removed by using probe signals centered off-resonance to construct templates for the amplitude and phase fluctuations. The algorithms that perform the atmospheric and electronic noise removal are described. After removal, we find good agreement between the observed residual noise and our expectation for intrinsic detector noise over a significant fraction of the signal bandwidth.

Effect of La3+ on microwave dielectric properties of (Pb0.45Ca0.55) (Fe0.5Nb0.5)O-3 ceramics

In this work, microwave dielectric properties of A-site substitution by La3+ in (Pb0.45Ca0.55) (Fe0.5Nb0.5) 03 system were investigated. Microwave dielectric properties of A-site charge unbalance substitution of [(Pb0.45Ca0.55)(1-x) La-x] (Fe0.5Nb0.5)O-3(+) (P45CLFN) were improved because the solid solution of small amount of surplus La3+ with (Pb, Ca)(2+) could eliminate oxygen vacancies, and the formation of secondary phase (pyrochlore) was also caused by surplus La3+. The decreasing of dielectric constant with the increase of La3+ content is due to the formation of pyrochlore. The grain size is changed slightly and Q(f) values (7000 similar to 7300 GHz) are almost unchanged at x = 0.02 similar to 0.10, but the temperature coefficient of resonant frequency (TCF) are increased and changed from negative to positive. TCF is zero at x 0.075 with Q(f) = 7267 GHz and K = 89. TCF of all specimens are within +/- 5 x 10(-6)degrees C-1.

Controle a estrutura variável para atenuar modos ressonantes em servomecanismos.

Nesta dissertação é mostrada experimentalmente a existência de modos ressonantes em servomotores de corrente contínua sem núcleo de ferro. Até onde se sabe, não já publicações ou documentos técnicos de fabricantes que relatam esse efeito neste tipo de motor. Foi observado também que a frequência da ressonância é variável e que possivelmente depende da temperatura interna do motor. Conforme e mostrado em simulações técnicas tradicionais para o controle de motores podem não ser eficazes para lidar com esses modos ressonantes. Com o objetivo de amortecer a ressonância e obter o controle de velocidade e posição desses motores, são desenvolvidos controladores por modo deslizante baseados em funções de chaveamento obtidas por observadores de alto ganho. Esse controle e robusto a incertezas paramétricas e perturbações. Com o auxílio de simulações são mostrados os pontos fortes e limitações de cada um dos controladores.

Optimisation of a piezoelectric system for energy harvesting from traffic vibrations

Piezoelectric systems are viewed as a promising approach to energy harvesting from environmental vibrations. The energy harvested from real vibration sources is usually difficult to estimate analytically. Therefore, it is hard to optimise the associated energy harvesting system. This work investigates the optimisation of a piezoelectric cantilever system using a genetic algorithm based approach with numerical simulations. The genetic algorithm globally considers the effects of each parameter to produce an optimal frequency response to scavenge more energy from the real vibrations while the conventional sinusoidal based method can only optimise the resistive load for a given resonant frequency. Experimental acceleration data from the vibrations of a vehicle-excited manhole cover demonstrates that the optimised harvester automatically selects the right frequency and also synchronously optimises the damper and the resistive load. This method shows great potential for optimizing the energy harvesting systems with real vibration data. ©2009 IEEE.

Electrical actuation and readout in a nanoelectromechanical resonator based on a laterally suspended zinc oxide nanowire.

In this paper, we present experimental results describing enhanced readout of the vibratory response of a doubly clamped zinc oxide (ZnO) nanowire employing a purely electrical actuation and detection scheme. The measured response suggests that the piezoelectric and semiconducting properties of ZnO effectively enhance the motional current for electromechanical transduction. For a doubly clamped ZnO nanowire resonator with radius ~10 nm and length ~1.91 µm, a resonant frequency around 21.4 MHz is observed with a quality factor (Q) of ~358 in vacuum. A comparison with the Q obtained in air (~242) shows that these nano-scale devices may be operated in fluid as viscous damping is less significant at these length scales. Additionally, the suspended nanowire bridges show field effect transistor (FET) characteristics when the underlying silicon substrate is used as a gate electrode or using a lithographically patterned in-plane gate electrode. Moreover, the Young's modulus of ZnO nanowires is extracted from a static bending test performed on a nanowire cantilever using an AFM and the value is compared to that obtained from resonant frequency measurements of electrically addressed clamped–clamped beam nanowire resonators.

Protein functionalized ZnO thin film bulk acoustic resonator as an odorant biosensor

ZnO thin film bulk acoustic resonators (FBARs) with resonant frequency of ∼1.5 GHz have been fabricated to function as an odorant biosensor. Physical adsorption of an odorant binding protein (AaegOBP22 from Aedes aegypti) resulted in frequency down shift. N,N-diethyl-meta-toluamide (DEET) has been selected as a ligand to the odorant binding protein (OBP). Alternate exposure of the bare FBARs to nitrogen flow with and without DEET vapor did not cause any noticeable frequency change. However, frequency drop was detected when exposing the OBP loaded FBAR sensors to the nitrogen flow containing DEET vapor against nitrogen flow alone (control) and the extent of frequency shift was proportional to the amount of the protein immobilized on the FBAR surface, indicating a linear response to DEET binding. These findings demonstrate the potential of binding protein functionalized FBARs as odorant biosensors. © 2012 Elsevier B.V. All rights reserved.

Mode-localized displacement sensing

We report the construction of a new class of micromachined displacement sensors that employ the phenomenon of vibration-mode localization for monitoring minute inertial displacements. It is demonstrated both theoretically and experimentally that the eigenstate-shifted output signal of such mode-localized displacement sensors may be as high as 1000 times greater than corresponding resonant-frequency variations that serve as the output in the more traditional vibratory resonant micromechanical displacement/motion sensors. The high parametric sensitivities attainable in such mode-localized displacement sensors, together with their inherent advantages of improved environmental robustness and electrical tunability, suggest an alternative approach in achieving improved sensitivity and stability in high-resolution displacement transduction. © 1992-2012 IEEE.

Self-excited circumferential instabilities in a model annular gas turbine combustor: Global flame dynamics

In this paper the global flame dynamics of a model annular gas turbine combustor undergoing strong self-excited circumferential instabilities is presented. The combustor consisted of either 12, 15 or 18 turbulent premixed bluff-body flames arranged around an annulus of fixed circumference so that the effect of flame separation distance, S, on the global heat release dynamics could be investigated. Reducing S was found to produce both an increase in the resonant frequency and the limit-cycle amplitudes of pressure and heat release for the same equivalence ratio. The phase-averaged global heat release, obtained from high-speed OH- chemiluminescence imaging from above, showed that these changes are caused by large-scale modifications to the flame structure around the annulus. For the largest S studied (12 flame configuration) the azimuthal instability produced a helical-like global heat release structure for each flame. When S was decreased, large-scale merging or linking between adjacent flames occurred spanning approximately half of the annulus with the peak heat release concentrated at the outer annular wall. The circumferential nature of the instability was evident from both the pressure measurements and the phase-averaged OH- chemiluminescence showing the phase of the heat release on either side of the annulus to be ≈180°apart and spinning in the counter clockwise direction. Both spinning and standing modes were found but only spinning modes are considered in this paper. To the best of the authors knowledge, these are the first experiments to provide a phase-averaged picture of self-excited azimuthal instabilities in a laboratory-scale annular combustor relevant to gas turbines. © 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Direct comparison of the gravimetric responsivities of ZnO-based FBARs and SMRs

Film bulk acoustic resonators (FBARs) and solidly mounted resonators (SMRs) have the potential to significantly improve upon the sensitivity and minimum detection limit of traditional gravimetric sensors based on quartz crystal microbalances (QCMs) and surface acoustic wave resonators (SAWs). To date, neither FBAR nor SMR devices have been demonstrated to be superior to the other; hence the choice between them depends primarily on the users' ability to design/fabricate membranes and/or Bragg reflectors. In this work, it is shown that identically designed FBAR and SMR devices resonating at the same frequency exhibit different responsivities to mass loadings, Rm, and that the SMRs are less responsive than the FBARs. For the specific device design and resonant frequency (~2 GHz) of the resonators presented here, the FBARs' mass responsivity is ~20% greater than that of the SMRs', and although this value is not universal for all possible device designs, it clearly shows that FBAR devices should be favoured over SMRs in gravimetric sensing applications where the FBARs' fragility is not an issue. Numerical calculations based on Mason's model offer an insight into the physical mechanisms behind the greater FBARs responsivity, and it was shown that the Bragg reflector has an effect on the acoustic load at one of the facets of the piezoelectric films which is in turn responsible for the SMRs' lower responsivity to mass loadings. © 2013 Elsevier B.V.

A flexural crack model for damage detection in reinforced concrete structures

The use of changes in vibration data for damage detection of reinforced concrete structures faces many challenges that obstruct its transition from a research topic to field applications. Among these is the lack of appropriate damage models that can be deployed in the damage detection methods. In this paper, a model of a simply supported reinforced concrete beam with multiple cracks is developed to examine its use for damage detection and structural health monitoring. The cracks are simulated by a model that accounts for crack formation, propagation and closure. The beam model is studied under different dynamic excitations, including sine sweep and single excitation frequency, for various damage levels. The changes in resonant frequency with increasing loads are examined along with the nonlinear vibration characteristics. The model demonstrates that the resonant frequency reduces by about 10% at the application of 30% of the ultimate load and then drops gradually by about 25% at 70% of the ultimate load. The model also illustrates some nonlinearity in the dynamic response of damaged beams. The appearance of super-harmonics shows that the nonlinearity is higher when the damage level is about 35% and then decreases with increasing damage. The restoring force-displacement relationship predicted the reduction in the overall stiffness of the damaged beam. The model quantitatively predicts the experimental vibration behaviour of damaged RC beams and also shows the damage dependency of nonlinear vibration behaviour. © 2011 Published under licence by IOP Publishing Ltd.

Experimental comparison of FBARs and SMRs responsitivities to mass loadings

The utilisation of thin film technology to develop film bulk acoustic resonators (FBARs) and solidly mounted resonators (SMRs), offers great potential to outperform the sensitivity and minimum detection limit of gravimetric sensors. Up to now, the choice between FBARs and SMRs depends primarily on the users' ability to design and fabricate Bragg reflectors and/or membranes, because neither of these two types of resonators has been demonstrated to be superior to the other. In the work reported here, it is shown that identically designed FBARs and SMRs resonating at the same frequency exhibit different responsitivities, Rm, to mass loadings, being the FBARs more responsive than the SMRs. For the specific device design and resonant frequency (∼2 GHz) of the resonators presented, FBARs' mass responsitivity is ∼20% greater than that of SMRs, and although this value should not be taken as universal for all possible device designs, it clearly indicates that FBAR devices should be favoured over SMRs in gravimetric sensing applications. © 2012 IEEE.

Modal dynamics of self-excited azimuthal instabilities in an annular combustion chamber

In this paper we describe the time-varying amplitude and its relation to the global heat release rate of self-excited azimuthal instabilities in a simple annular combustor operating under atmospheric conditions. The combustor was modular in construction consisting of either 12, 15 or 18 equally spaced premixed bluff-body flames around a fixed circumference, enabling the effect of large-scale interactions between adjacent flames to be investigated. High-speed OH* chemiluminescence imaged from above the annulus and pressure measurements obtained at multiple locations around the annulus revealed that the limit cycles of the modes are degenerate in so much as they undergo continuous transitions between standing and spinning modes in both clockwise (CW) and anti-clockwise (ACW) directions but with the same resonant frequency. Similar behaviour has been observed in LES simulations which suggests that degenerate modes may be a characteristic feature of self-excited azimuthal instabilities in annular combustion chambers. By modelling the instabilities as two acoustic waves of time-varying amplitude travelling in opposite directions we demonstrate that there is a statistical prevalence for either standing m=1 or spinning m=±1 modes depending on flame spacing, equivalence ratio, and swirl configuration. Phase-averaged OH* chemiluminescence revealed a possible mechanism that drives the direction of the spinning modes under limit-cycle conditions for configurations with uniform swirl. By dividing the annulus into inner and outer annular regions it was found that the spin direction coincided with changes in the spatial distribution of the peak heat release rate relative to the direction of the bulk swirl induced along the annular walls. For standing wave modes it is shown that the globally integrated fluctuations in heat release rate vary in magnitude along the acoustic mode shape with negligible contributions at the pressure nodes and maximum contributions at the pressure anti-nodes. © 2013.

Phase-conjugation broad area twin-contact semiconductor laser

Experimental demonstration of lasing in a broad area twin-contact semiconductor laser which operates as a phase-conjugation (PC) mirror in an external cavity configuration is reported. This allows "self-aligned" and self-pumped spatially nondegenerate four-wave mixing to be achieved without the need for external optical signals. The external cavity laser system is very insensitive to tilt misalignments of the external mirror in the PC regime and exhibits very good mechanical stability. The resonant frequency of the external cavity lies in the GHz range which corresponds to a subnanosecond time response of phase conjugation processes in the semiconductor laser. © 1997 American Institute of Physics.

Label-free detection of human prostate-specific antigen (hPSA) using film bulk acoustic resonators (FBARs)

Label-free detection of cancer biomarkers using low cost biosensors has promising applications in clinical diagnostics. In this work, ZnO-based thin film bulk acoustic wave resonators (FBARs) with resonant frequency of ∼1.5 GHz and mass sensitivity of 0.015 mg/m2 (1.5 ng/cm2) have been fabricated for their deployment as biosensors. Mouse monoclonal antibody, anti-human prostate-specific antigen (Anti-hPSA) has been used to bind human prostate-specific antigen (hPSA), a model cancer used in this study. Ellipsometry was used to characterize and optimise the antibody adsorption and antigen binding on gold surface. It was found that the best amount of antibody at the gold surface for effective antigen binding is around 1 mg/m2, above or below which resulted in the reduced antigen binding due to either the limited binding sites (below 1 mg/m2) or increased steric effect (above 1 mg/m2). The FBAR data were in good agreement with the data obtained from ellipsometry. Antigen binding experiments using FBAR sensors demonstrated that FBARs have the capability to precisely detect antigen binding, thereby making FBARs an attractive low cost alternative to existing cancer diagnostic sensors. © 2013 Elsevier B.V.