On the Resonance of a Lined Tire Cavity

This thesis investigates the direct measurement of the thermal noise spectral distribution. Long base line gravitational wave detectors, being commissioned around the world, are limited in sensitivity in the intermediate frequencies by the thermal noise. These detectors are utilising suspended test mirrors for the detection of gravitational waves by measuring their relative displacement. One of the fundamental noise sources in these detectors is the thermally induced displacement of the suspension onto and within the mirrors. This thermally induced motion of the test mirrors limits the displacement sensitivity of the gravitational wave detectors. Knowledge of the spectral behavior of thermal noise over a wide frequency range will improve predictions and understanding of the behavior of the suspension and test mirrors. ¶ In this thesis the direct measurement of the thermal noise spectral distribution of a mechanical flexure resonator is described. The mechanical flexure resonator is an unidirectional ’wobbly table’ made from copper-beryllium, which hinges around four thin flexures 15 mm wide, 1 mm high and ~116 µm thick. The mechanical flexure resonator has a resonant frequency of 192 Hz, with a quality factor of ~3000. ¶ ...

Low temperature detectors have been a subject of intense interest to the scientific community over the last decade. These detectors work at very low temperatures, often well below 1 Kelvin, to minimize the noise in the measurement of photons. This leads to very powerful detectors applicable to a broad wavelength range. Since these detectors are so sensitive even single pixels and small arrays (up to several hundred pixels) enable deeper explorations of the cosmos than ever before. Instruments based on these technologies have been used at submillimeter, optical, and X-ray wavelengths. The scientific prospects for these detectors increase as they grow in pixel count. For some applications, especially for Cosmic Microwave Background (CMB) polarization work, a large focal plane will not only increase efficiency but will also enable new and vital science. Current superconducting technologies, such as Transition Edge Sensors (TESs), can currently deliver extremely high sensitivity in the submillimeter and read-noise free imaging spectroscopy at Optical/UV and X-ray wavelengths, but the largest arrays contain less that 100 pixels. In order to make real progress these arrays must contain many thousands of pixels. This is a formidable technical challenge. This thesis will explore a promising emerging technology called Microwave Kinetic Inductance Detectors (MKIDs). MKIDs make use of the change in the surface impedance of a superconductor as incoming photons break up Cooper pairs. This is accomplished by making the strip of superconductor part of a microwave resonant circuit, and monitoring the phase of a signal transmitted through (or past) the resonator. The primary advantage of this technology is that by using resonant circuits with high quality factors, passive frequency domain multiplexing will allow up to thousands of resonators to be read out through a single coaxial cable and a single HEMT amplifier. This eliminates the cryogenic electronics (SQUIDS) and wiring problems associated with current superconducting devices. Inexpensive and powerful room-temperature readout electronics can leverage the microwave integrated circuits developed for wireless communications. When this project started four years ago MKIDs were just a concept. In this thesis I will recount the progress we have made in taking this concept and turning it into a detector technology, building on the work we published in Nature in 2003. I will demonstrate that we have overcome the major technical obstacles and shown conclusively that MKIDs work, and should provide much larger arrays than are possible with other technologies. Due to our work at Caltech and JPL, MKIDs are considered one of the leading technologies to reach the ambitious goals set for future ground and space missions. The noise performance is already good enough for sky-limited, ground-based, submillimeter astronomy. Despite MKIDs acceptable noise performance for ground-based astronomy, there are many applications which require lower detector noise. The simple MKIDs we measure in this thesis still exhibit a noise higher than theory would predict which could limit their usefulness for some applications. In Chapters 7-9 we perform several experiments which identify the source of the excess noise as the substrate. In the course of these experiments to characterize and identify the noise, we successfully demonstrate two distinct approaches which dramatically reduce the noise excess.

Advances in nanotechnology lead to the development of nano-electro-mechanical systems (NEMS) such as nanomechanical resonators with ultra-high resonant frequencies. The ultra-high-frequency resonators have recently received significant attention for wide-ranging applications such as molecular separation, molecular transportation, ultra-high sensitive sensing, high-frequency signal processing, and biological imaging. It is well known that for micrometer length scale, first-principles technique, the most accurate approach, poses serious limitations for comparisons with experimental studies. For such larger size, classical molecular dynamics (MD) simulations are desirable, which require interatomic potentials. Additionally, a mesoscale method such as the coarse-grained (CG) method is another useful method to support simulations for even larger system sizes. Furthermore, quasi-two-dimensional (Q2D) materials have attracted intensive research interest due to their many novel properties over the past decades. However, the energy dissipation mechanisms of nanomechanical resonators based on several Q2D materials are still unknown. In this work, the addressed main issues include the development of the CG models for molybdenum disulphide (MoS2), investigation of the mechanism effects on black phosphorus (BP) nanoresonators and the application of graphene nanoresonators. The primary coverage and results of the dissertation are as follows: Method development. Firstly, a two-dimensional (2D) CG model for single layer MoS2 (SLMoS2) is analytically developed. The Stillinger-Weber (SW) potential for this 2D CG model is further parametrized, in which all SW geometrical parameters are determined analytically according to the equilibrium condition for each individual potential term, while the SW energy parameters are derived analytically based on the valence force field model. Next, the 2D CG model is further simplified to one-dimensional (1D) CG model, which describes the 2D SLMoS2 structure using a 1D chain model. This 1D CG model is applied to investigate the relaxed configuration and the resonant oscillation of the folded SLMoS2. Owning to the simplicity nature of the 1D CG model, the relaxed configuration of the folded SLMoS2 is determined analytically, and the resonant oscillation frequency is derived analytically. Considering the increasing interest in studying the properties of other 2D layered materials, and in particular those in the semiconducting transition metal dichalcogenide class like MoS2, the CG models proposed in current work provide valuable simulation approaches. Mechanism understanding. Two energy dissipation mechanisms of BP nanoresonators are focused exclusively, i.e. mechanical strain effects and defect effects (including vacancy and oxidation). Vacancy defect is intrinsic damping factor for the quality (Q)-factor, while mechanical strain and oxidation are extrinsic damping factors. Intrinsic dissipation (induced by thermal vibrations) in BP resonators (BPRs) is firstly investigated. Specifically, classical MD simulations are performed to examine the temperature dependence for the Q-factor of the single layer BPR (SLBPR) along the armchair and zigzag directions, where two-step fitting procedure is used to extract the frequency and Q-factor from the kinetic energy time history. The Q-factors of BPRs are evaluated through comparison with those of graphene and MoS2 nanoresonators. Next, effects of mechanical strain, vacancy and oxidation on BP nanoresonators are investigated in turn. Considering the increasing interest in studying the properties of BP, and in particular the lack of theoretical study for the BPRs, the results in current work provide a useful reference. Application. A novel application for graphene nanoresonators, using them to self-assemble small nanostructures such as water chains, is proposed. All of the underlying physics enabling this phenomenon is elucidated. In particular, by drawing inspiration from macroscale self-assembly using the higher order resonant modes of Chladni plates, classical MD simulations are used to investigate the self-assembly of water molecules using graphene nanoresonators. An analytic formula for the critical resonant frequency based on the interaction between water molecules and graphene is provided. Furthermore, the properties of the water chains assembled by the graphene nanoresonators are studied.

The superfluid state, often obtained in the laboratory using liquid helium at very low temperatures, provides the basis for a wide range of interesting experiments. One large field of research relates to the study of turbulence in a superfluid, referred to as quantum turbulence due to the importance of quantum mechanical behaviour in the description of this phenomenon. An important experimental tool in the study of quantum turbulence is the mechanical resonator, with many different types of oscillator seeing use. Variations in the resonance can be related to the properties of the fluid through an understanding of the drag applied to the object. The many seemingly disparate measurements reported here were performed in the hope of providing background for future development of improved experimental techniques. In an effort to develop an improved method for determining oscillator properties, measurements have been made using a multifrequency lock-in amplifier in superfluid 4He. The results obtained show that the multifrequency lock-in can be used to obtain results equivalent to the traditional method while reducing the time required. Due to the possibility of vastly increased sensitivity to changes in effective mass, tests were performed in 4He using a new form of oscillator with a 100 nm by 100 nm square cross-section, significantly smaller than other available devices. The resonant frequency of these resonators, referred to as nanobeams, was varied from 0.6 MHz to 8.5 MHz by using beams of different length. Measurements of the resonator response as a function of temperature show that the beams can successfully probe the fluid, though the current theory is found to be insufficient to exactly quantify the dependence seen. A possible observation of turbulence generated by a nanobeam is also reported. Despite an observed critical velocity significantly different to theoretical predictions, all other measurements are consistent with a turbulent transition. As the eventual goal is to use nanobeams for measurements in 3He-B, the drag on high frequency oscillators in 3He-B was also studied. Measurements on 4 devices of different frequencies found that the current model of damping remains adequate beyond the expected frequency limit for this model. Observations of anomalous increases in the damping for a single resonator in 3He-B are also discussed. As this unexpected damping is only seen for small, sensitive resonators there is concern that similar effects could hinder interpretation of future nanobeam measurements in 3He-B. Efforts were made to understand the source of this damping, and hence explain why it is seen for only one of three nominally identical oscillators, though no conclusive explanation could be found.

The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for force detection and quantum physics of macroscopic objects. In the first experiment, the dispersive mechanical resonance shift from the interaction with a Cooper-pair box qubit is studied. The measured coupling strength is large enough to satisfy one of the conditions required to perform many of the proposed quantum nanomechanical measurements. The resonance shift also probes the microwave-driven response of the qubit, showing Rabi oscillation and Landau-Zener tunneling, proving the coherent dynamics of the qubit. Second, the parametric excitation of nanomechanical motion is studied via experiments with a driven qubit. Degenerate parametric amplification and oscillation are demonstrated, with a new observation of nonlinear dissipation. The squeezing of the back-action noise from the detection amplifier is also observed, up to 4dB. It is the first demonstration using a qubit as an auxiliary system to modify the nanomechanical dynamics, showing a possible route for generation of nanomechanical quantum states. Finally, back-action cooling of nanomechanical motion has been investigated, which is implemented by capacitively coupling a high-Q coplanar waveguide microwave resonator to a nanomechanical resonator. The thermal state with 7.5 mechanical quanta on average is reached, a result that is ultimately limited due to increased bath heating with microwave power. The heating is consistent with a model based on two-level systems resonantly coupled to the nanomechanical mode. This additional heating suggests future efforts to improve coupling and for reducing two-level system density in materials employed to reach the motional ground state via back-action cooling.

Experimental investigations on the proximity effect bridge (a Josephson device) at zero voltage and at finite voltages in the µV range are reported. The phase-super current relation at zero voltage was measured using an asymmetric superconducting quantum interferormeter circuit. The data are in agreement with the Josephson supercurrent-phase relation I_S=I_C sinδ with deviation less than 5% of the critical current I_c. The supercurrent density in the measured bridges reached as high as 50-100 µA/µm^2. Using microcircuitry techniques, proximity effect bridges were strongly coupled to superconducting microstrip resonators. Selfinduced steps in the I-V characteristics of bridges coupled to resonators were observed in the GHz region at voltages (frequencies) corresponding to the expected modes of the resonators. Two types of steps were seen depending on whether the resonator impedance on resonance was much higher or much smaller than the bridge resistance. A simple two fluid model of the bridge-resonator circuit was developed and the size and shape of self-induced steps were calculated for a generalized Josephson oscillator relation I_S = I_c(l-q + q sin∫ 2e/hV dt) where q = 1 corresponds to the original Josephson relation and q = 1/2 represents the phase slip regime. At low critical currents (I_c < 10 µA) and low voltages (V < 3µV) the size and shape of experimentally observed self-induced steps agree with the q = 1 model. At higher voltages and/or critical currents the step size increasingly deviates from the q = 1 model towards q = 1/2. These observations are interpreted to indicate a progressive reduction of the amplitude of the oscillating Josephson supercurrent in proximity effect bridges from I_c towards I_c /2 as the critical current and/or voltage are increased.

A novel Finite Element Method (FEM) is proposed for the analysis of the uncoupled hydrodynamic pressures generated on arch dams due to a steady‐state ground acceleration. In this method the equation governing hydrodynamic pressures and also the prescribed boundary conditions are all transformed from the Cartesian space to a logarithmically condensed cylindrical polar space; in this process the physical configuration of the reservoir‐dam is also mapped into an ‘image’ domain. The transformed governing equation is then solved in the image domain, subject to the transformed boundary conditions, using standard finite elements. Because physical dimensions are logarithmically condensed in the image space, the proposed method is particularly suitable for dealing with large or very large aspect‐ratio reservoir‐dam systems, economically and efficiently.The high degree of accuracy which the proposed method is capable of, and also the simple way in which it can be applied to complex reservoir‐dam shapes, have been demonstrated by means of examples. The method has also been applied to study the uncoupled hydrodynamic pressures on the upstream face of a cylindrical arch dam, generated by a steady‐state vertical ground acceleration.

Many applications require the presence of a dielectric inside a microwave resonator. The paper presents an analysis based on the mode-matching technique of a dielectric-loaded cavity that has a configuration which is more generalised than that first proposed by Amman and Morris. The cavity consists of a wave guide of rectangular cross-section filled with dielectric for part of its length and also for part of its transverse dimension, with movable shorting plungers in the guide beyond both ends of the dielectric. Such a structure supports resonances at frequencies where a particular waveguide mode is above cutoff inside the dielectric, but is below cutoff outside. Frequency tuning is possible via the tunable plungers. Computed results for the resonant frequencies and unloaded Q-factors are presented for anumber of cavity configurations. Close corroboration of the predicted resonance frequency by experiment has been obtained. Furthermore, the performance of a Gunn-effect diode oscillator employing such a dielectric-loaded cutoff waveguide cavity as the frequency stabilising agent is investigated experimentally.

A carbon nanotube (CNT) is a remarkable material and can be thought of as a single-atom thick cylinder of carbon atoms capped of with a semisphere. This is called a single-walled CNT and, depending on how the cylinder is rolled up, CNTs are either semiconducting or metallic. A CNT is made into a mechanical resonator by suspending it between two electrodes. The CNT is driven into motion electrostatically, and the mechanical motion is detected using the current flowing through the CNT. We use the ultraclean fabrication method, which avoids processing on the CNT by first making the electrodes and the trench and only in the final step growing the CNTs. A suspended CNT resonator can be fabricated without defects, thus reducing mechanical damping. In this Thesis, CNTs are studied as electromechanical resonators. An overview is given of the various optical, microscopy, and electrical methods to detect the mechanical motion of CNT resonators, after which the electrical detection methods are compared in detail. Next, it is shown experimentally and theoretically that their mechanical motion couples strongly to single-electron tunneling, as CNTs become quantum dots at cryogenic temperatures. Mechanical modulation of the single-electron average charge leads to spring softening, damping, and a nonlinear restoring force. Because of their high aspect ratio, CNTs can easily be perturbed into the nonlinear regime. To read out their mechanical motion at high frequencies, a novel high-bandwidth readout scheme is developed and discussed.

Nanoelectromechanical systems (NEMS) have proven an excellent test bed for exploring nonlinear dynamics due to short decay times, weak nonlinearities, and large quality factors. In contrast to previous research in nonlinear dynamics involving driven or phase fixed NEMS, where time is referenced by an external source, we describe phenomena classified by phase free phenomena. Here we describe NEMS embedded into feedback oscillators with weak nonlinearities. We make measurements of this mechanical nonlinearity by developing a transduction scheme, the piezoelectric/piezoresistive (PZE/PZR) transduction, which emphasizes the detector dynamic range over absolute sensitivity. Using these measurements, projections on quantum nondemolition schemes involving the mechanical nonlinearity as a detector are made. These measurements also are important for understanding the detection limits of NEMS sensor technology, which uses a mechanical resonator as a frequency reference in a phase locked loop (PLL). This work identifies ways to reduce noise within ‘nonlinear’ feedback oscillators, and these results have implications for sensing systems using nonlinear mechanical resonators embedded in PLLs. Since the mechanical nonlinearity of PZE/PZR resonators can be accurately calibrated, we make predictions for the behavior of these dynamical systems based on the given mechanical and electrical parameters. We show, theoretically, that local isochronicity above critical nonlinear amplitudes can create special operating points in feedback oscillators at which parametric fluctuations may cause less phase noise in the oscillator than in feedback oscillators driven below critical amplitudes. For these predictions, we present data that show quantitative agreement for the amplitude and frequency, and qualitative agreement for the phase noise. Finally, we show synchronization, assisted by nonisochronicity, between two feedback NEMS oscillators. We develop a general theoretical framework for two saturated feedback oscillators which use resonators with nonlinear stiffness. In the limit of small coupling, we show that the system obeys the Adler equation with analytical predictions for the oscillators’ individual amplitudes and net frequency difference. We develop an experiment in which the three important parameters of the system (detuning, nonisochronicity, and coupling) can be tuned, and show data that agrees with the predictions for a large range of coupling. We include data on phase slipping between two oscillators in which the aperiodic frequency difference is clearly observed. Finally, we present data on phase noise in synchronized oscillators.

Is the Burton–Miller formulation really free of fictitious eigenfrequencies?

The objective of this work is the design and the application of various adaptive control concepts to manipulate shear-flows under varying flow conditions, i.e. Reynolds-numbers. A combination of a self-tuning PI-controller, based on an online-estimation of the plant dynamics, and the extremumseeking controller is introduced as an effective control strategy to reduce and/or to increase the reattachment length of a backward-facing step flow. Four loudspeakers are used as actuators driven by a zero-phase sinusoidal voltage signal. The amplitude of the loudspeaker input is calculated by the PI-controller achieving that the measured reattachment length permanently follows its set point. The optimal forcing frequency essentially depending on the Reynolds-number is determined by the extremum-seeking controller. In this work a new adaptive I-controller is introduced as an appropriate approach to control plants, which are characterised by an output saturation. An offline-identification confirms that this flow possesses such a non-linear behaviour. The adaptation law exploits this behaviour guaranteeing a desired tracking dynamics of the closed-loop over a wide range of operating points. A wind tunnel experiment exemplarily demonstrates the use of this controller under moderate variations of the Reynolds-number. For a second flow configuration, the flow within a diffusor, the extremum-seeking controller is employed to adjust the geometry of an acoustic resonator located upstream of the diffusor. The slot width of the resonator and the height of the resonator volume are tuned by the controller. It is shown by experiments that the controller find the optimal geometry of the resonator for several initial values of the sloth width and height. Consequently, the pressure recovery is maximised by the use of the controller. To improve the performance of the closed-loop dynamics an adaptation of the seeking radius and, for fast changes of the Reynolds-number, an adaptation of the controller gain k is necessary. The extremum-seeking controller can also be used to reduce the radiated sound of a turbomachinery. Air injection by valves generates a destructive secondary sound field which is out of phase with the primary sound field caused by a rotor-stator-interaction. The injected air mass is determined by the controller to minimise the overall sound-pressure-level measured downstream of the stator. This work exemplarily shows that the employed adaptive controller and especially the extremumseeking controller are suitable approaches for flow control. Furthermore it is shown that the extremum-seeking controller can be successfully transferred to other flow configurations.

Hydrodynamic and semikinetic treatments of plasma flow along closed geomagnetic field lines are compared. The hydrodynamic treatment is based on a simplified 16‐moment set of transport equations as the equations for the heat flows are not solved; the hear flows are treated heuristically. The semikinetic treatment is based on a particle code. The comparison deals with the distributions of the plasma density, flow velocity, and parallel and perpendicular temperatures as obtained from the two treatments during the various stages of the flow subject to certain assumed boundary conditions. In the kinetic treatment, the appropriate boundary condition is the prescription of the velocity distribution functions for the particles entering the flux tubes at the ionospheric boundaries; those particles leaving the system are determined by the processes occurring in the flux tube. The prescribed distributions are half‐Maxwellian with temperature To and density no. In the hydrodynamic model, the prescribed boundary conditions are placed on density (no), flow velocity (Vo), and temperature (To). We found that results from the hydrodynamic treatment critically depend on Vo; for early stages of the flow this treatment yields results in good agreement with those from the kinetic treatment, when Vo = (kTo/2πm)1/2, which is the average velocity of particles moving in a given direction for a Maxwellian distribution. During this early stage, the flows developing from the conjugate ionospheres show some distinct transitions. For the first hour or so, the flows are highly supersonic and penetrate deep into the opposite hemispheres, and both hydrodynamics and kinetic treatments yield almost similar features. It is found that during this period heat flow effects are negligibly small. When a flow penetrates deep into the opposite hemisphere, the kinetic treatment predicts reflection and setting up of counterstreaming. In contrast, the hydrodynamic treatment yields a shock in the flow. The reasons for this difference in the two treatments is discussed, showing that in view of the relatively warm ions, the coupling of ion beams and the consequent shock formation in the off‐equatorial region are not likely due to the enhancements in the beam temperatures. The counterstreaming in the kinetic treatment and the shock in the hydrodynamic treatment first advance upward to the equator and then downward to the ionospheric boundary from where the flow originated. The transit time for this advancement is found to be about 1 hour for the perspective models. After 2 hours or so, both models predict that the flows from the ionospheric boundaries are generally subsonic with respect to the local ion‐sound speed. At late stages of the flow, when a substantial fraction of ions entering the flux tube begin to return back in the kinetic treatment, the hydrodynamic treatment with the boundary condition Vo = (kTo/2πm)1/2 yields an overrefilling, and the choice of Vo becomes uncertain.

Wave based method for flexural vibration of thin plate with general elastically restrained edges

The possibility, in principle, of determining the content of undissolved water in fuels with high precision using high-quality super-high frequency (SHF) resonance systems (microwave cavity resonator) is substantiated. Results of experimental study of a cylindrical cavity resonator with a thin layer of water on the bottom-end wall are adduced. The proposed method is analyzed using simulation by the finite-element method in the ANSYS system. Results of this research can be of practical use for determining deposited water in jet fuels.