Showing papers on "Parametric oscillator published in 2014"
Book•
14 Mar 2014
TL;DR: In this article, the authors present a detailed analysis of the structural dynamics of an active versus passive control system in a single-input, single-output (SISO) spacecraft.
Abstract: Preface to the third edition- Preface to the second edition- Preface to the first edition- 1 Introduction- 11 Active versus passive- 12 Vibration suppression- 13 Smart materials and structures- 14 Control strategies- 141 Feedback- 142 Feedforward- 15 The various steps of the design- 16 Plant description, error and control budget- 17 Readership and Organization of the book- 18 References- 19 Problems- 2 Some concepts in structural dynamics- 21 Introduction- 22 Equation of motion of a discrete system- 23 Vibration modes- 24 Modal decomposition- 241 Structure without rigid body modes- 242 Dynamic flexibility matrix- 243 Structure with rigid body modes- 244 Example- 25 Collocated control system- 251 Transmission zeros and constrained system- 26 Continuous structures- 27 Guyan reduction- 28 Craig-Bampton reduction- 29 References- 210 Problems- 3 Electromagnetic and piezoelectric transducers- 31 Introduction- 32 Voice coil transducer- 321 Proof-mass actuator- 322 Geophone- 33 General electromechanical transducer- 331 Constitutive equations- 332 Self-sensing- 34 Reaction wheels and gyrostabilizers- 35 Smart materials- 36 Piezoelectric transducer- 361 Constitutive relations of a discrete transducer- 362 Interpretation of k2- 363 Admittance of the piezoelectric transducer- 37 References- 38 Problems- 4 Piezoelectric beam, plate and truss- 41 Piezoelectric material- 411 Constitutive relations- 412 Coenergy density function- 42 Hamilton's principle- 43 Piezoelectric beam actuator- 431 Hamilton's principle- 432 Piezoelectric loads- 44 Laminar sensor- 441 Current and charge amplifiers- 442 Distributed sensor output- 443 Charge amplifier dynamics- 45 Spatial modalfilters- 451 Modal actuator- 452 Modal sensor- 46 Active beam with collocated actuator-sensor- 461 Frequency response function- 462 Pole-zero pattern- 463 Modal truncation- 47 Admittance of a beam with a piezoelectric patch- 48 Piezoelectric laminate- 481 Two dimensional constitutive equations- 482 Kirchhoff theory- 483 Stiffness matrix of a multi-layer elastic laminate- 484 Multi-layer laminate with a piezoelectric layer- 485 Equivalent piezoelectric loads- 486 Sensor output- 487 Beam model vs plate model- 488 Additional remarks- 49 Active truss- 491 Open-loop transfer function- 492 Admittance function- 410 Finite element formulation- 411 References- 412 Problems- 5 Passive damping with piezoelectric transducers- 51 Introduction- 52 Resistive shunting- 53 Inductive shunting- 54 Switched shunt- 541 Equivalent damping ratio- 55 References- 56 Problems- 6 Collocated versus non-collocated control- 61 Introduction- 62 Pole-zero flipping- 63 The two-mass problem- 631 Collocated control- 632 Non-collocated control- 64 Notch filter- 65 Effect of pole-zero flipping on the Bode plots- 66 Nearly collocated control system- 67 Non-collocated control systems- 68 The role of damping- 69 References- 610 Problems - 7 Active damping with collocated system- 71 Introduction- 72 Lead control- 73 Direct velocity feedback (DVF)- 74 Positive Position Feedback (PPF)- 75 Integral Force Feedback(IFF)- 76 Duality between the Lead and the IFF controllers- 761 Root-locus of a single mode- 762 Open-loop poles and zeros- 77 Actuator and sensor dynamics- 78 Decentralized control with collocated pairs- 781 Cross talk- 782 Force actuator and displacement sensor- 783 Displacement actuator and force sensor- 79 References- 710 Problems- 8 Vibration isolation- 81 Introduction- 82 Relaxation isolator- 821 Electromagnetic realization- 83 Active isolation- 831 Sky-hook damper- 832 Integral Force Feedback- 84 Flexible body- 841 Free-free beam with isolator- 85 Payload isolation in spacecraft- 851 Interaction isolator/attitude control- 852 Gough-Stewart platform- 86 Six-axis isolator- 861 Relaxation isolator- 862 Integral Force Feedback- 863 Spherical joints, modal spread- 87 Active vs passive- 88 Car suspension- 89 References- 810 Problems- 9 State space approach- 91 Introduction- 92 State space description- 921 Single degree of freedom oscillator- 922 Flexible structure- 923 Inverted pendulum- 93 System transfer function- 931 Poles and zeros- 94 Pole placement by state feedback- 941 Example: oscillator- 95 Linear Quadratic Regulator- 951 Symmetric root locus- 952 Inverted pendulum- 96 Observer design- 97 Kalman Filter- 971 Inverted pendulum- 98 Reduced order observer- 981 Oscillator- 982 Inverted pendulum- 99 Separation principle- 910 Transfer function of the compensator- 9101 The two-mass problem- 911 References- 912 Problems- 10 Analysis and synthesis in the frequency domain- 101 Gain and phase margins- 102 Nyquist criterion- 1021 Cauchy's principle- 1022 Nyquist stability criterion- 103 Nichols chart- 104 Feedback specification for SISO systems- 1041 Sensitivity- 1042 Tracking error- 1043 Performance specification- 1044 Unstructured uncertainty- 1045 Robust performance and robust stability- 105 Bode gain-phase relationships- 106 The Bode Ideal Cutoff- 107 Non-minimum phase systems- 108 Usual compensators- 1081 System type- 1082 Lead compensator- 1083 PI compensator- 1084 Lag compensator- 1085 PID compensator- 109 Multivariable systems- 1091 Performance specification- 1092 Small gain theorem- 1093 Stability robustness tests- 1094 Residual dynamics- 1010References- 1011Problems- 11 Optimal control- 111 Introduction- 112 Quadratic integral- 113 Deterministic LQR- 114 Stochastic response to a white noise- 1141 Remark- 115 Stochastic LQR- 116 Asymptotic behavior of the closed-loop- 117 Prescribed degree of stability- 118 Gain and phase margins of the LQR- 119 Full state observer- 1191 Covariance of the reconstruction error- 1110Kalman-Bucy Filter (KBF)- 1111Linear Quadratic Gaussian (LQG)- 1112Duality- 1113Spillover- 11131Spillover reduction- 1114Loop Transfer Recovery (LTR)- 1115Integral control with state feedback- 1116Frequency shaping- 11161Frequency-shaped cost functionals- 11162Noise model - 1117References- 1118Problems- 12 Controllability and Observability- 121 Introduction- 1211 Definitions- 122 Controllability and observability matrices- 123 Examples- 1231 Cart with two inverted pendulums- 1232 Double inverted pendulum- 1233 Two dof oscillator- 124 State transformation- 1241 Control canonical form- 1242 Left and right eigenvectors- 1243 Diagonal form- 125 PBH test- 126 Residues- 127 Example- 128 Sensitivity- 129 Controllability and observability Gramians- 1210Internally balanced coordinates- 1211Model reduction- 12111Transfer equivalent realization- 12112Internally balanced realization- 12113Example- 1212References- 1213Problems- 13 Stability- 131 Introduction- 1311 Phase portrait- 132 Linear systems- 1321 Routh-Hurwitz criterion- 133 Lyapunov's direct method- 1331 Introductory example- 1332 Stability theorem- 1333 Asymptotic stability theorem- 1334 Lasalle's theorem- 1335 Geometric interpretation- 1336 Instability theorem- 134 Lyapunov functions for linear systems- 135 Lyapunov's indirect method - 136 An application to controller design- 137 Energy absorbing controls- 138 References- 139 Problems- 14 Applications- 141 Digital implementation- 1411 Sampling, aliasing and prefiltering- 1412 Zero-order hold, computational delay- 1413 Quantization- 1414 Discretization of a continuous controller- 142 Active damping of a truss structure- 1421 Actuator placement- 1422 Implementation, experimental results- 143 Active damping generic interface- 1431 Active damping- 1432 Experiment- 1433 Pointing and position control- 144 Active damping of a plate- 1441 Control design- 145 Active damping of a stiff beam- 1451 System design- 146 The HAC/LAC strategy- 1461 Wide-band position control- 1462 Compensator design- 1463 Results- 147 Vibroacoustics: Volume displacement sensors- 1471 QWSIS sensor- 1472 Discrete array sensor- 1473 Spatial aliasing- 1474 Distributed sensor- 148 References- 149 Problems- 5 Tendon Control of Cable Structures- 151 Introduction- 152 Tendon control of strings and cables- 153 Active damping strategy- 154 Basic Experiment- 155 Linear theory of decentralized active damping- 156 Guyed truss experiment- 157 Micro Precision Interferometer testbed- 158 Free floating truss experiment- 159 Application to cable-stayed bridges- 1510Laboratory experiment- 1511Control of parametric resonance- 1512Large scale experiment- 1513 References- 16 Active Control of Large Telescopes- 161 Introduction- 162 Adaptive optics- 163 Active optics- 1631 Monolithic primary mirror- 1632 Segmented primary mirror- 164 SVD controller- 1641 Loop shaping of the SVD controller- 165 Dynamics of a segmented mirror- 166 Control-structure interaction- 1661 Multiplicative uncertainty- 1662 Additive uncertainty- 1663 Discussion- 167 References- 17 Semi-active control- 171 Introduction- 172 Magneto-rheological fluids- 173 MR devices- 174 Semi-active suspension- 1741 Semi-active devices- 175 Narrow-band disturbance- 1751 Quarter-car semi-active suspension- 176 References- 177 Problems- Bibliography- Index
647 citations
TL;DR: In this paper, a lumped-element Josephson parametric amplifier with strong coupling to the environment is presented, which allows for frequency dependent variation of the external impedance at a given frequency.
Abstract: We present a lumped-element Josephson parametric amplifier designed to operate with strong coupling to the environment. In this regime, we observe broadband frequency dependent amplification with multi-peaked gain profiles. We account for this behavior using the “pumpistor” model which allows for frequency dependent variation of the external impedance. Using this understanding, we demonstrate control over the complexity of gain profiles through added variation in the environment impedance at a given frequency. With strong coupling to a suitable external impedance, we observe a significant increase in dynamic range, and large amplification bandwidth up to 700 MHz giving near quantum-limited performance.
171 citations
TL;DR: In this paper, the authors discuss the control of the dynamic range of Josephson parametric amplifiers by using Josephson junction arrays and derive useful design criteria, which may find broad application in the development of a practical parametric amplifier.
Abstract: One of the central challenges in the development of parametric amplifiers is the control of the dynamic range relative to its gain and bandwidth, which typically limits quantum limited amplification to signals which contain only a few photons per inverse bandwidth. Here, we discuss the control of the dynamic range of Josephson parametric amplifiers by using Josephson junction arrays. We discuss gain, bandwidth, noise, and dynamic range properties of both a transmission line and a lumped element based parametric amplifier. Based on these investigations we derive useful design criteria, which may find broad application in the development of practical parametric amplifiers.
149 citations
TL;DR: In this article, a high-gain quantum-limited microwave parametric amplifier based on a superconducting lumped LC resonator with the inductor L including an array of eight quantum interference devices (SQUIDs) was developed and measured.
Abstract: We have developed and measured a high-gain quantum-limited microwave parametric amplifier based on a superconducting lumped LC resonator with the inductor L including an array of eight superconducting quantum interference devices (SQUIDs). This amplifier is parametrically pumped by modulating the flux threading the SQUIDs at twice the resonator frequency. Around 5 GHz, a maximum gain of 31 dB, a product amplitude gain x bandwidth above 60 MHz, and a 1 dB compression point of -123 dBm at 20 dB gain are obtained in the nondegenerate mode of operation. Phase-sensitive amplification-deamplification is also measured in the degenerate mode and yields a maximum gain of 37 dB. The compression point obtained is 18 dB above what would be obtained with a single SQUID of the same inductance, due to the smaller nonlinearity of the SQUID array.
100 citations
TL;DR: In this article, the authors explored a new paradigm through the employment of parametric resonance, which is not limited due to linear damping, therefore, the power output can potentially build up to higher levels.
Abstract: In the arena of vibration energy harvesting, the key technical challenges continue to be low power density and narrow operational frequency bandwidth. While the convention has relied upon the activation of the fundamental mode of resonance through direct excitation, this article explores a new paradigm through the employment of parametric resonance. Unlike the former, oscillatory amplitude growth is not limited due to linear damping. Therefore, the power output can potentially build up to higher levels. Additionally, it is the onset of non-linearity that eventually limits parametric resonance; hence, this approach can also potentially broaden the operating frequency range. Theoretical prediction and numerical modelling have suggested an order higher in oscillatory amplitude growth. An experimental macro-sized electromagnetic prototype (practical volume of ~1800 cm3) when driven into parametric resonance, has demonstrated around 50% increase in half power band and an order of magnitude higher peak power density normalised against input acceleration squared (293 mW cm23 m22 s4 with 171.5 mW at 0.57 m s22) in contrast to the same prototype directly driven at fundamental resonance (36.5 mW cm23 m22 s4 with 27.75 mW at 0.65 m s22). This figure suggests promising potentials while comparing with current state-of-the-art macro-sized counterparts, such as Perpetuum’s PMG-17 (119 mW cm23 m22 s4).
64 citations
TL;DR: KTiOPO₄ (KTP) crystal is used as the nonlinear medium in a surface-emitted terahertz-wave parametric oscillator for the first time and the maximum output of the THz wave is 336 nJ.
Abstract: KTiOPO4 (KTP) crystal is used as the nonlinear medium in a surface-emitted terahertz-wave parametric oscillator for the first time. The oscillating Stokes beam propagates along the x axis of the KTP crystal, the pumping beam propagates with a small incident angle θext to the x axis, and the polarizations of the pumping beam, the Stokes beam, and the THz wave are along the z axis. When θext is changed from 1.250° to 6.000°, the THz wave is intermittently tuned from 3.17 to 3.44 THz, from 4.19 to 5.19 THz, and from 5.55 to 6.13 THz. The maximum output of the THz wave is 336 nJ, obtained at 5.72 THz with a pumping energy of 80 mJ. The two frequency gaps, from 3.44 to 4.19 THz and from 5.19 to 5.55 THz, are located in the vicinities of the A1 modes of 134 and 178.7 cm−1, which are strongly infrared absorbing.
64 citations
TL;DR: In this article, the integration of auto-parametric resonance, as a form of resonant amplification of the base excitation, to further minimise this activation criterion and realize the profitable regions of parametric resonance at even lower input acceleration levels.
Abstract: Parametric resonance, as a resonant amplification phenomenon, is a superior mechanical amplifier than direct resonance and has already been demonstrated to possess the potential to offer over an order of magnitude higher power output for vibration energy harvesting than the conventional direct excitation. However, unlike directly excited systems, parametric resonance has a minimum threshold amplitude that must be attained prior to its activation. The authors have previously presented the addition of initial spring designs to minimise this threshold, through non-resonant direct amplification of the base excitation that is subsequently fed into the parametric resonator. This paper explores the integration of auto-parametric resonance, as a form of resonant amplification of the base excitation, to further minimise this activation criterion and realise the profitable regions of parametric resonance at even lower input acceleration levels. Numerical and experimental results have demonstrated in excess of an order of magnitude reduction in the initiation threshold amplitude for an auto-parametric resonator (∼0.6 ms−2) as well as several folds lower for a parametric resonator with a non-resonant base amplifier (∼4.0 ms−2), as oppose to a sole parametric resonator without any threshold reduction mechanisms (10's ms−2). Therefore, the superior power performance of parametric resonance over direct resonance has been activated and demonstrated at much lower input levels.
63 citations
TL;DR: Mid-infrared (3-5 μm) pulses with high energy are produced using nonlinear conversion in a ZnGeP(2)-based master oscillator-power amplifier, pumped by a Q-switched cryogenic Ho:YLF oscillator.
Abstract: Haakestad, Magnus Willum; Fonnum, Helge; Lippert, Espen.
Mid-infrared source with 0.2 J pulse energy based on nonlinear conversion of Q-switched pulses in ZnGeP2. Optics Express 2014 ;Volum 22.(7) s. 8556-8564
60 citations
TL;DR: An experimental scheme based on parametric feedback control of the oscillator, which stabilizes the amplified quadrature while leaving the orthogonal one unaffected, allows the technique to surpass the -3 dB limit in the noise reduction, associated with parametric resonance.
Abstract: We report the confinement of an optomechanical micro-oscillator in a squeezed thermal state, obtained by parametric modulation of the optical spring. We propose and implement an experimental scheme based on parametric feedback control of the oscillator, which stabilizes the amplified quadrature while leaving the orthogonal one unaffected. This technique allows us to surpass the ?3??dB limit in the noise reduction, associated with parametric resonance, with a best experimental result of ?7.4??dB . While the present experiment is in the classical regime, in a moderately cooled system our technique may allow squeezing of a macroscopic mechanical oscillator below the zero-point motion.
57 citations
TL;DR: In this paper, a comparison between the Reduced Order Model (ROM) method and the Method of Multiple Scales (MMS) for both small and large amplitudes is reported for parametric resonance of microelectromechanical cantilever resonators under soft damping, and soft alternating current (AC) electrostatic actuation to include fringing effect.
Abstract: This paper deals with parametric resonance of microelectromechanical (MEMS) cantilever resonators under soft damping, and soft alternating current (AC) electrostatic actuation to include fringing effect. A comparison between the Reduced Order Model (ROM) method and the Method of Multiple Scales (MMS) for both small and large amplitudes is reported. The actuation is parametric non-linear. It includes non-linear terms with periodic coefficients. The AC frequency is near resonator׳s natural frequency. The amplitude frequency response is investigated using ROM. Damping, voltage, and fringe effects on the response are also reported. It is showed that five terms ROM accurately predicts the behavior of the resonator at all amplitudes, while MMS is accurate only for small amplitudes.
52 citations
TL;DR: In this paper, a time-domain nonlinear numerical model is presented for describing the dynamic stability of point absorbers, where pressure of the incident wave is integrated over the instantaneous wetted surface to obtain the nonlinear Froude-Krylov excitation force and the non linear hydrostatic restoring forces, while first order diffraction-radiation forces are computed by a linear potential flow formulation.
TL;DR: In this article, two distinct design routes have been explored, namely an intrinsically lower threshold through a pendulum-lever configuration and amplification of base excitation fed into the parametric resonator through a cantilever-initial-spring configuration.
Abstract: A vibration energy harvester designed to access parametric resonance can potentially outperform the conventional direct resonant approach in terms of power output achievable given the same drive acceleration. Although linear damping does not limit the resonant growth of parametric resonance, a damping dependent initiation threshold amplitude exists and limits its onset. Design approaches have been explored in this paper to passively overcome this limitation in order to practically realize and exploit the potential advantages. Two distinct design routes have been explored, namely an intrinsically lower threshold through a pendulum-lever configuration and amplification of base excitation fed into the parametric resonator through a cantilever-initial-spring configuration. Experimental results of the parametric resonant harvesters with these additional enabling designs demonstrated an initiation threshold up to an order of magnitude lower than otherwise, while attaining a much higher power peak than direct resonance.
TL;DR: In this paper, the authors investigated the non-linear dynamic responses of a top-tensioned riser under combined parametric and external vortex excitations, and the effects of key design parameters on the dynamic properties of a TTR under combined excitation were discussed.
TL;DR: In this article, the conditions under which a multimode nanomechanical resonator, operated as a purely mechanical parametric oscillator, can be driven into highly nonclassical states were investigated.
Abstract: We investigate theoretically the conditions under which a multimode nanomechanical resonator, operated as a purely mechanical parametric oscillator, can be driven into highly nonclassical states. We find that when the device can be cooled to near its ground state, and certain mode matching conditions are satisfied, it is possible to prepare distinct resonator modes in quantum entangled states that violate Bell inequalities with homodyne quadrature measurements. We analyze the parameter regimes for such Bell inequality violations, and while experimentally challenging, we believe that the realization of such states lies within reach. This is a re-imagining of a quintessential quantum optics experiment by using phonons that represent tangible mechanical vibrations.
TL;DR: The implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies are discussed.
Abstract: High frequency large scanning angle electrostatically actuated microelectromechanical systems (MEMS) mirrors are used in a variety of applications involving fast optical scanning. A 1-D parametrically resonant torsional micromirror for use in biomedical imaging is analyzed here with respect to operation by duty-cycled square waves. Duty-cycled square wave excitation can have significant advantages for practical mirror regulation and/or control. The mirror's nonlinear dynamics under such excitation is analyzed in a Hill's equation form. This form is used to predict stability regions (the voltage-frequency relationship) of parametric resonance behavior over large scanning angles using iterative approximations for nonlinear capacitance behavior of the mirror. Numerical simulations are also performed to obtain the mirror's frequency response over several voltages for various duty cycles. Frequency sweeps, stability results, and duty cycle trends from both analytical and simulation methods are compared with experimental results. Both analytical models and simulations show good agreement with experimental results over the range of duty cycled excitations tested. This paper discusses the implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies.
TL;DR: In this article, a novel Josephson parametric amplifier based on a flux-tunable quarter-wavelength resonator was proposed, and it was shown that the added noise can be less than 0.5 added photons.
Abstract: We characterize a novel Josephson parametric amplifier based on a flux-tunable quarter-wavelength resonator. The fundamental resonance frequency is ~1GHz, but we use higher modes of the resonator for our measurements. An on-chip tuning line allows for magnetic flux pumping of the amplifier. We investigate and compare degenerate parametric amplification, involving a single mode, and nondegenerate parametric amplification, using a pair of modes. We show that we reach quantum-limited noise performance in both cases, and we show that the added noise can be less than 0.5 added photons in the case of low gain.
TL;DR: In this article, the frequency domain analysis of the smooth and discontinuous (SD) oscillator subjected to harmonic excitation is carried out, where the multi-harmonic balance method (MHBM) in combination with arc length continuation is used to obtain the periodic solutions.
TL;DR: In this paper, the authors developed linearized models to describe the parametrically flux-pumped SQUID in terms of an impedance, which can be seen as a result of a negative resistance of the pumpistor.
Abstract: A Superconducting QUantum Interference Device (SQUID) modulated by a fast oscillating magnetic flux can be used as a parametric amplifier, providing gain with very little added noise. Here, we develop linearized models to describe the parametrically flux-pumped SQUID in terms of an impedance. An unpumped SQUID acts as an inductance, the Josephson inductance, whereas a flux-pumped SQUID develops an additional, parallel element which we have coined the “pumpistor.” Parametric gain can be understood as a result of a negative resistance of the pumpistor. In the degenerate case, the gain is sensitive to the relative phase between the pump and signal. In the nondegenerate case, gain is independent of this phase. We develop our models first for degenerate parametric pumping in the three-wave and four-wave cases, where the pump frequency is either twice or equal to the signal frequency, respectively. We then derive expressions for the nondegenerate case where the pump frequency is not a multiple of the signal frequency, for which it becomes necessary to consider idler tones that occur. For the nondegenerate three-wave case, we present an intuitive picture for a parametric amplifier containing a flux-pumped SQUID where current at the signal frequency depends upon the load impedance at an idler frequency. This understanding provides insight and readily testable predictions of circuits containing flux-pumped SQUIDs.
TL;DR: In this paper, a parametric resonance of a truncated conical shell rotating at periodically varying angular speed is studied based upon the Love-s thin shell theory and generalized differential quadrature (GDQ) method.
TL;DR: In this paper, the authors consider the evolution of linear fluctuations around highly symmetric though inhomogeneous backgrounds and demonstrate that a large degree of asymmetry develops over time from tiny fluctuations superposed upon planar and SO(2,1) symmetric backgrounds.
Abstract: This is the first paper in a series where we study collisions of nucleated bubbles taking into account the effects of small initial (quantum) fluctuations in a fully 3+1-dimensional setting. In this paper, we consider the evolution of linear fluctuations around highly symmetric though inhomogeneous backgrounds. We demonstrate that a large degree of asymmetry develops over time from tiny fluctuations superposed upon planar and SO(2,1) symmetric backgrounds. These fluctuations arise from zero-point vacuum oscillations, so excluding them by enforcing a spatial symmetry is inconsistent in a quantum treatment. We consider the limit of two colliding planar walls, with fluctuation mode functions characterized by the wavenumber transverse to the collision direction and a longitudinal shape along the collision direction $x$, which we solve for. Initially, the fluctuations obey a linear wave equation with a time- and space-dependent mass $m_{eff}(x,t)$. When the walls collide multiple times, $m_{eff}$ oscillates in time. We use Floquet theory to study the fluctuations and generalize techniques familiar from preheating to the case with many coupled degrees of freedom. This inhomogeneous case has bands of unstable transverse wavenumbers $k_\perp$ with exponentially growing mode functions. From the detailed spatial structure of the mode functions in $x$, we identify both broad and narrow parametric resonance generalizations of the homogeneous $m_{eff}(t)$ case of preheating. The unstable $k_\perp$ modes are longitudinally localized, yet can be described as quasiparticles in the Bogoliubov sense. We define an effective occupation number to show they are created in bursts for the case of well-defined collisions in the background. The transverse-longitudinal coupling accompanying nonlinearity radically breaks this localized particle description, with nonseparable 3D modes arising.
TL;DR: In this article, an amplifier based on intrinsic negative resistance of a selectively damped Josephson junction was proposed to achieve low-noise amplification at microwave frequencies, which is the goal of the quantum limit.
Abstract: Low-noise amplification at microwave frequencies has become increasingly important for the research related to superconducting qubits and nanoelectromechanical systems. The fundamental limit of added noise by a phase-preserving amplifier is the standard quantum limit, often expressed as noise temperature $$T_q=\hbar \omega /2k_B$$
. Towards the goal of the quantum limit, we have developed an amplifier based on intrinsic negative resistance of a selectively damped Josephson junction. Here we present measurement results on previously proposed wide-band microwave amplification and discuss the challenges for improvements on the existing designs. We have also studied flux-pumped metamaterial-based parametric amplifiers, whose operating frequency can be widely tuned by external DC-flux, and demonstrate operation at $$2\omega $$
pumping, in contrast to the typical metamaterial amplifiers pumped via signal lines at $$\omega $$
.
TL;DR: In this article, a reliability analysis was used to investigate the parametric instability of a top tensioned riser (TTR) operating under irregular sea conditions, where the authors derived the Hill equation of a TTR operating under real sea conditions and the corresponding stochastic external excitation was obtained using the Pierson-Moskowitz wave spectrum.
Abstract: A reliability analysis was used to investigate the parametric instability of a top tensioned riser (TTR) operating under irregular sea conditions. In practical applications, the parametric instability evaluation of a riser is a very difficult task, owing to uncertainty of various parameters such as the environmental conditions of the load, the structural geometric parameters, and material properties. Considering the uncertainties of these parameters, it is vital to adopt a probabilistic approach in evaluating the instability. In this work, the Hill equation of a TTR operating under real sea conditions is first derived, and the corresponding stochastic external excitation is obtained using the Pierson–Moskowitz wave spectrum. The effects of various random variables on the parametric instability are studied by a sensitivity analysis. A surrogate model is used to construct the response surface for assessing the reliability of the parametric instability of the riser. The distribution regularity of parametrically unstable cases is examined using the contour of the parametrically excited responses. The effect of three significant uncertain factors on the probability of the parametric stability is investigated using the surrogate model. The proposed approach is demonstrated to be efficient for evaluating the reliability of the parametric instability of a TTR.
TL;DR: In this paper, the authors consider a simple dynamic model of the vibrating screen operating in the parametric resonance (PR) mode, which is characterized by larger values of the amplitude and by insensitivity to damping in a rather wide range.
TL;DR: In this article, the authors demonstrate parametric resonance in Bose-Einstein condensates (BECs) with attractive two-body interaction in a harmonic trap under parametric excitation by periodic modulation of the s-wave scattering length.
Abstract: We demonstrate parametric resonance in Bose-Einstein condensates (BECs) with attractive two-body interaction in a harmonic trap under parametric excitation by periodic modulation of the s-wave scattering length. We obtain nonlinear equations of motion for the widths of the condensate using a Gaussian variational ansatz for the Gross-Pitaevskii condensate wave function. We conduct both linear and nonlinear stability analyses for the equations of motion and find qualitative agreement, thus concluding that the stability of two equilibrium widths of a BEC might be inverted by parametric excitation.
TL;DR: In this paper, a design for a MEMS parametric amplifier modulated by the Casimir force is presented, which allows for the implementation of a very sensitive voltage measuring technique, where the amplitude of a high quality factor resonator includes a tenth power dependency on an applied DC voltage.
Abstract: In this paper, we discuss a design for a MEMS parametric amplifier modulated by the Casimir force. We present the theory for such a device and show that it allows for the implementation of a very sensitive voltage measuring technique, where the amplitude of a high quality factor resonator includes a tenth power dependency on an applied DC voltage. This approach opens up a new and powerful measuring modality, applicable to other measurement types.
TL;DR: In this paper, an unusual oscillator was developed for sub-millimetre microbubbles, capable of generating a particularly high driving frequency in the kilohertz range, in a layout that promotes a strong third harmonic frequency of the basic oscillation.
Abstract: Efficient generation of sub-millimetre microbubbles was recently made possible by pulsating the flow of gas supplied into a parallel-exits aerator, using a fluidic oscillator for the purpose. Without moving parts, it can generate oscillation at high frequency, an important factor due to bubble natural frequency rapidly increasing with the desirable decrease of their size. This paper discusses development of an unusual oscillator – a part of an integral oscillator/aerator unit – capable of generating a particularly high driving frequency, in the kilohertz range, in a layout that promotes a strong third harmonic frequency of the basic oscillation.
TL;DR: In this paper, a phase sensitive scheme based on four-wave mixing followed by a polarizer was proposed to achieve an ideal binary step-like phase transfer function at nonlinear phase shifts as low as 0.3 radians by significantly increasing the parametric de-amplification component.
Abstract: We propose and demonstrate a new phase sensitive scheme based on four-wave mixing followed by a polarizer to achieve an ideal binary step-like phase transfer function at nonlinear phase shifts as low as 0.3 radians by significantly increasing the parametric de-amplification component. Phase-sensitive operation is obtained by polarization mixing the phase-locked and orthogonally-polarized signal and idler, which is generated in a degenerate dual-pump vector parametric amplifier.
TL;DR: In this article, a design for a MEMS parametric amplifier modulated by the Casimir force is presented, which allows for the implementation of a very sensitive voltage measuring technique, where the amplitude of a high quality factor resonator includes a tenth power dependency on an applied DC voltage.
Abstract: In this paper, we discuss a design for a MEMS parametric amplifier modulated by the Casimir force. We present the theory for such a device and show that it allows for the implementation of a very sensitive voltage measuring technique, where the amplitude of a high quality factor resonator includes a tenth power dependency on an applied DC voltage. This approach opens up a new and powerful measuring modality, applicable to other measurement types.
TL;DR: A MgO:LiNbO₃ slab configuration for the surface-emitted terahertz-wave parametric oscillator (TPO) is presented, and the intensity distributions of the THz wave beams were measured, and they were unsymmetrical in the horizontal direction while symmetry in the vertical direction.
Abstract: A MgO:LiNbO3 slab configuration for the surface-emitted terahertz-wave parametric oscillator (TPO) is presented. The pump and the oscillating Stokes beams were totally reflected at the slab surface and propagated zigzaggedly in the slab MgO:LiNbO3 crystal. Up to five terahertz beams were emitted perpendicularly to the surface of the crystal. The total output energy of the five THz-wave beams was 3.56 times as large as that obtained from the conventional surface-emitted TPO at the same experimental conditions. The intensity distributions of the THz wave beams were measured, and they were unsymmetrical in the horizontal direction while symmetrical in the vertical direction.
TL;DR: In this article, the authors investigate theoretically a system consisting of a one-dimensional Bose-Einstein condensate trapped inside the optical lattice of an optical cavity, and they show that using the nonlinear effect of atomic collisions, how one can manipulate and control the state of the Bogoliubov mode and produce squeezed states.
Abstract: In this paper, we investigate theoretically a system consisting of a one-dimensional Bose–Einstein condensate trapped inside the optical lattice of an optical cavity. In the weak-interaction regime and under the Bogoliubov approximation, the wave function of the Bose–Einstein condensate can be described by a classical field (condensate mode) having some quantum fluctuations (the Bogoliubov mode) about the mean value. Such a system behaves as a so-called atomic parametric amplifier, similar to an optical parametric amplifier, where the condensate and the Bogoliubov modes play, respectively, the roles of the pump field and the signal mode in the degenerate parametric amplifier and the s-wave scattering frequency of atom–atom interaction plays the role of the nonlinear gain parameter. We show that using the nonlinear effect of atomic collisions, how one can manipulate and control the state of the Bogoliubov mode and produce squeezed states.