Perturbation Waveform Research Articles

Black-hole perturbation theory with post-Newtonian theory: Towards hybrid waveforms for neutron-star binaries

We consider the motion of nonspinning, compact objects orbiting around a Kerr black hole with tidal couplings. The tide-induced quadrupole moment modifies both the orbital energy and outgoing fluxes, so that over the inspiral timescale there is an accumulative shift in the orbital and gravitational wave phase. Previous studies on compact object tidal effects have been carried out in the Post-Newtonian (PN) and Effective-One-Body (EOB) formalisms. In this work, within the black hole perturbation framework, we propose to characterize the tidal influence in the expansion of mass ratios, while higher-order PN corrections are naturally included. For the equatorial and circular orbit, we derive the leading order, frequency dependent tidal phase shift which agrees with the Post-Newtonian result at low frequencies but deviates at high frequencies. We also find that such phase shift has weak dependence ($\le 10\%$) on the spin of the primary black hole. Combining this black hole perturbation waveform with the Post-Newtonian waveform, we propose a frequency-domain, hybrid waveform that shows comparable accuracy as the EOB waveform in characterizing the tidal effects, as calibrated by numerical relativity simulations. Further improvement is expected as the next-leading order in mass ratio and the higher-PN tidal corrections are included. This hybrid approach is also applicable for generating binary black hole waveforms.

Phase Demodulation Based on DCM Algorithm in Φ-OTDR With Self-Interference Balance Detection

A phase demodulation algorithm in phase-sensitive optical time domain reflectometry (φ-OTDR) with self-interference balance detection is proposed. With a simple differentiate-and-cross-multiply (DCM) operation to acquire the perturbation waveform, and a further second-order operation to compensate the amplitude fluctuation of the phase, the phase can be extracted accurately. The self-interference balance detection structure can equivalently achieve the function of dual-pulse detection, but avoid the negative impact of the common-mode noise and the difference between the dual pulses on the demodulation. In experiment, several types of vibrations are retrieved correctly under the condition of single channel and low sampling rate, which demonstrates the validity of this demodulation approach.

Impact of PWM Duty Cycle Jitter on Switching-Mode Power Converter Efficiency

The objective of this paper is to propose an efficiency model to evaluate the impact of the pulse width modulation (PWM) duty cycle jitter on the efficiency of switching-mode power converter. By taking the product of two perturbation terms into consideration, which is ignored in the conventional average small-signal model, the average efficiency model is proposed first. Due to the nonlinear characteristic of the PWM generator, the multifrequency efficiency model is also developed by considering the sideband frequency. Three different perturbation waves are induced to the control loop of the converter to generate the jitter to observe its impact on the efficiency. The mathematical expression of the efficiency drop based on the proposed multifrequency model is derived. The reason of control-to-output gain's magnitude spike on the Bode plot can be explained by the derived equations. Eventually, the methods to reduce the efficiency drop caused by the jitter are suggested. In spite of various perturbation frequencies, amplitudes, and waveforms, the mathematical calculation, the computer simulation, and the hardware measurement of the efficiency drop are consistent which validate the accuracy of the proposed multifrequency efficiency model.

Vortex synchronization in the cylinder wake due to harmonic and non-harmonic perturbations

This paper reports a numerical study of two-dimensional periodically perturbed flow past a cylinder. Both harmonic and non-harmonic perturbation waveforms of the inflow velocity are considered for a maximum instantaneous Reynolds number of 180. Phase portraits of the lift force are employed to identify the dynamical state of the cylinder wake and determine the range of kinematical parameters for which primary synchronization occurs, that is the regime where vortex formation is phase-locked to the subharmonic of the perturbation frequency. The effect of different perturbation waveforms on the synchronization range and on patterns of vortex formation is examined in detail over the normalized amplitude–frequency space. It is shown that systematic shifts of the synchronization range, towards either higher or lower frequencies, can be attained by imposing different perturbation waveforms. As a consequence, in certain regions of the parameter space it is possible to obtain multiple periodic and/or quasi-periodic wake states for waveforms of exactly the same amplitude and frequency. For the range of parameters where synchronization occurs, different vortex patterns are attained in the wake involving the shedding of solitary and binary vortices, or mixtures thereof, which can be controlled by the perturbation waveform. The phenomenology of these patterns, which result from modification of the basic Kármán mode in the unperturbed wake, is discussed and explained in terms of the generation of circulation that is induced by perturbations in the relative velocity. Vortex patterns from cylinders oscillating either in line with or transverse to a free stream are recast in the framework of the relative velocity.

Desynchronization of stochastically synchronized chemical oscillators.

Experimental and theoretical studies are presented on the design of perturbations that enhance desynchronization in populations of oscillators that are synchronized by periodic entrainment. A phase reduction approach is used to determine optimal perturbation timing based upon experimentally measured phase response curves. The effectiveness of the perturbation waveforms is tested experimentally in populations of periodically and stochastically synchronized chemical oscillators. The relevance of the approach to therapeutic methods for disrupting phase coherence in groups of stochastically synchronized neuronal oscillators is discussed.

On multiple alternating steady states induced by periodic spin phase perturbation waveforms

Direct measurement of neural currents by means of MRI can potentially open a high temporal resolution (10-100 ms) window applicable for monitoring dynamics of neuronal activity without loss of the high spatial resolution afforded by MRI. Previously, we have shown that the alternating balanced steady state imaging affords high sensitivity to weak periodic currents owing to its amplification of periodic spin phase perturbations. This technique, however, requires precise synchronization of such perturbations to the radiofrequency pulses. Herein, we extend alternating balanced steady state imaging to multiple balanced alternating steady states for estimation of neural current waveforms. Simulations and phantom experiments show that the off-resonance profile of the multiple alternating steady state signal carries information about the frequency content of driving waveforms. In addition, the method is less sensitive than alternating balanced steady state to precise waveform timing relative to radiofrequency pulses. Thus, multiple alternating steady state technique is potentially applicable to MR imaging of the waveforms of periodic neuronal activity.

ChemInform Abstract: Measurements and Calculations of Oscillations and Phase Relations in the Driven Gas-Phase Combustion of Acetaldehyde

Oscillations in light emission and species concentrations, are measured as periodic perturbations are simultaneously applied to the input rates of acetaldehyde and oxygen in the gas‐phase combustion of acetaldehyde in a continuous‐flow stirred tank reactor for conditions where the autonomous reaction itself is oscillatory. The experimental results are compared with the predictions of a five‐variable thermokinetic model. We measure periodic responses in the fundamental entrainment band (ratio of frequency of perturbation to frequency of response equal to unity) for four different values of phase shift between the acetaldehyde and oxygen perturbation wave forms as we vary the frequency and amplitude of the external periodic perturbations. Outside of the entrainment bands we find quasiperiodic response. We determine the phases of the light emission and six species concentrations, as measured with a mass spectrometer, with respect to the periodic perturbation, the variation of these phases across the fundamental entrainment band for different values of reactant phase shift and for different amplitudes of perturbation, and the effects of the phase shift between the two input perturbations on the light emission response of the system for different frequencies of perturbation. Both the experiments and calculations predict a widening of the entrainment band with an increase in perturbation amplitude, and the same variation in bandwidths for the four values of reactant phase shift studied. The experiments and calculations also predict the same general trends in light phase and species phases (difference between the light emission and species concentrations with respect to the perturbing wave form) as the band is traversed for different amplitudes of perturbation and for different values of reactant phase shift. Some discrepancies in the species phases exist; however, the similarities which exist between the experiments and the calculations provide further substantiation for the model. We find that changing the phase shift between reactant inflows from 0° to 360° produces a sharp change in light phase near 180°, in both the experiments and calculations. In general, we also find that the light emission remains entrained near the total flux minimum of the perturbing wave form, and we attribute this correlation to the net heat loss which arises from the reactant flux through the reactor.

Progress in the development of ELM pace-making with non-axisymmetric magnetic perturbations in NSTX

The application of non-axisymmetric magnetic perturbations has been shown to destabilize edge-localized modes (ELMs) in the National Spherical Torus Experiment. This ELM-triggering effect is used to controllably introduce ELMs into lithium-enhanced ELM-free H-mode discharges, reducing the typical impurity accumulation while maintaining high energy confinement. Recent improvements to the triggering techniques are described. The perturbation waveform has been improved, with large amplitude, short duration perturbations allowing rapid, highly reliable triggering, with reduced braking of toroidal rotation. The rapid triggering allowed the ELM frequency to be increased to over 60 Hz, leading to a reduction in the average ELM size. Combined with improved gas fuelling, this method has resulted in periods of stationary global conditions, although plasma profiles do continue to evolve.

Are age-related impairments in change-in-support balance reactions dependent on the method of balance perturbation?

Rapid “change-in-support” (stepping or grasping) balance-recovery reactions play a critical role in preventing falls. Studies investigating age-related impairments in these reactions using differing perturbation methods have shown contradictory results. The discrepancies could be due to the different mechanical and sensory stimuli provided by the different perturbation methods, but could also be due to other confounding factors (e.g. differences in perturbation predictability). This study compared two commonly used perturbation methods: weight-drop cable-pulls (CPs) and motor-driven surface-translations (STs). For each perturbation method, effects of aging on the change-in-support reactions were established by comparing 10 young (22–28 years) and 30 older (64–79 years) adults, using large unpredictable multi-directional perturbations similar to those used in previous studies showing age-related differences. Age-related differences in the pattern and spatio-temporal features of the limb movements were examined for stepping and grasping reactions evoked by antero-posterior perturbation of stance, as well as stepping reactions evoked by lateral perturbations delivered while subjects walked “in-place”. Although age-group effects were almost always more pronounced for ST perturbations, the direction of the effect was always the same for both perturbation methods; hence, the perturbation-dependent differences in mechanical and sensory stimuli did not seem to be a critical factor. Perturbation waveform appeared to be a more important factor. For the perturbation methods used here, the ST perturbations were more destabilising than the CP perturbations (leading to a more rapid rise in perturbatory ankle-torque and greater centre-of-mass motion prior to the onset of the postural reaction), and were consequently more effective in revealing age-related deficiencies.

Active control effectiveness and synchronization of wall turbulence under localized imposed unsteadiness

The effect of a spatially localized time-periodic perturbation on the efficiency of suboptimal control of the wall turbulence is analyzed. It is shown that the imposed unsteadiness with a frequency in the median production range doubles the turbulent drag reduction under suboptimal control strategy. It is further observed that the spatially averaged turbulent wall shear is synchronized in time with the imposed perturbation waveform. This is related to the synchronization of the unstable periodic orbits present in the near-wall turbulence in connection with the regeneration cycle of turbulence producing coherent structures.

Experimental observations of longitudinal space-charge waves in intense electron beams

Studies of the dynamics of longitudinal space-charge waves in space-charge dominated beams propagating through a transport channel with a long solenoid are performed at the University of Maryland. In this paper, we report some experimental results on the energy modulations converted from density modulations. By changing the working conditions of the electron gun, pure initial density modulations are generated. Energy perturbation waveforms are measured with a high-resolution energy analyzer. The experimental results are compared with both the linear theory and the simulation results. Good agreements are achieved for the relationship between the energy and current perturbation strengths.

Optimization of the perturbation signal for electrochemical impedance spectroscopy in the time domain

The choice of the perturbation wave form is of crucial importance for reliable electrochemical impedance spectroscopy measurements based on the fast Fourier transformation. Using numerical simulation, arguments and results are presented for the choice and the optimization of a perturbation signal constructed as a superposition of discrete sine waves with selected frequencies. Two possible ways to optimize the perturbation for better noise immunity are described: choosing proper values for the phases of the individual sine waves, minimal perturbation signal amplitudes can be obtained which improve the quality of impedance data by 25%. By introducing response-sensitive amplitudes an improvement in the quality of data by a factor of 4–5 can be reached in the low frequency range. A new technique for single-pulse measurements with continuous perturbations that assures a steady-state response and better accuracy at high capacitive and/or inductive samples is also described.

Measurements and calculations of oscillations and phase relations in the driven gas-phase combustion of acetaldehyde

Oscillations in light emission and species concentrations, are measured as periodic perturbations are simultaneously applied to the input rates of acetaldehyde and oxygen in the gas-phase combustion of acetaldehyde in a continuous-flow stirred tank reactor for conditions where the autonomous reaction itself is oscillatory. The experimental results are compared with the predictions of a five-variable thermokinetic model. We measure periodic responses in the fundamental entrainment band (ratio of frequency of perturbation to frequency of response equal to unity) for four different values of phase shift between the acetaldehyde and oxygen perturbation wave forms as we vary the frequency and amplitude of the external periodic perturbations. Outside of the entrainment bands we find quasiperiodic response. We determine the phases of the light emission and six species concentrations, as measured with a mass spectrometer, with respect to the periodic perturbation, the variation of these phases across the fundamental entrainment band for different values of reactant phase shift and for different amplitudes of perturbation, and the effects of the phase shift between the two input perturbations on the light emission response of the system for different frequencies of perturbation. Both the experiments and calculations predict a widening of the entrainment band with an increase in perturbation amplitude, and the same variation in bandwidths for the four values of reactant phase shift studied. The experiments and calculations also predict the same general trends in light phase and species phases (difference between the light emission and species concentrations with respect to the perturbing wave form) as the band is traversed for different amplitudes of perturbation and for different values of reactant phase shift. Some discrepancies in the species phases exist; however, the similarities which exist between the experiments and the calculations provide further substantiation for the model. We find that changing the phase shift between reactant inflows from 0° to 360° produces a sharp change in light phase near 180°, in both the experiments and calculations. In general, we also find that the light emission remains entrained near the total flux minimum of the perturbing wave form, and we attribute this correlation to the net heat loss which arises from the reactant flux through the reactor.

Transient reversal of the stretch reflex in human arm muscles

1. Load perturbation responses can violate the law of reciprocal innervation between antagonist muscles under particular conditions. Thus flexor and extensor muscles of wrist and elbow joints are reflexly coactivated by the impact of a ball on the hand during a catching task. The aim of this study was to determine whether reflex coactivation can be preset within the central nervous system (CNS) or whether it is entirely due to the peripheral stimulus. To this end, we studied the behavior of stretch reflex responses of arm muscles evoked by torque motor perturbations applied before and during the catching task. 2. Subjects were instructed to catch a ball dropped from 1.6 m. A torque motor delivered perturbations to the elbow joint, resulting in angular motion at both elbow and wrist joints because of their dynamic mechanical coupling. Two series of experiments were performed that differed in the perturbation waveform. In the first series, a single torque pulse could be randomly applied at different times during the task. The corresponding responses were recovered by subtracting the average of the unperturbed trials from the averages of perturbed trials. In the second series of experiments, a train of pseudorandom pulses was applied continuously during each trial. The time-varying impulse responses were computed at 20-ms intervals by cross-correlation methods. 3. The pattern of the short-latency electromyographic responses evoked by either single pulses or pseudorandom perturbations obeyed the law of reciprocal innervation of antagonist muscles under basal conditions. However, the pattern of the responses evoked by the same perturbations around the time of ball impact on the hand consisted of a substantial coactivation of both stretched and shortening muscles. Reflex coactivation resulted from response patterns that differed at different joints. At the elbow, reflex coactivation resulted from a transient reversal of the direction of the short-latency responses of flexor muscles, with little changes of the responses of extensor muscles. At the wrist, instead, reflex coactivation resulted from simultaneous changes in the response waveform of both flexor and extensor muscles. 4. The peripheral conditions associated with the applied perturbations were constant before the time of ball impact. Thus, because the changes of the stretch reflex responses began before that time, they must have been generated within the CNS. It is here hypothesized that the reversal of the reflex responses is centrally gated by switching from the pathways of reciprocal inhibition to those of coactivation of antagonist alpha-motoneurons.(ABSTRACT TRUNCATED AT 400 WORDS)

Chapter 26 A system identification approach to balance testing

By modelling the posture control system as a linear transfer function cascaded with a saturation-like nonlinearity, the problem of quantifying relative stability was reduced to a linear system identification problem. The relative stability of different individuals was quantified in terms of the nominal ‘saturation amplitude’ (SA), the transient perturbation amplitude at which the resulting COP displacement would saturate (or equal the length of) the BOS. To ensure subject safety and to minimize anticipatory adaptations, the transient response was determined indirectly. A small-amplitude pseudorandom perturbation was applied and the results used to identify the linear component of the cascade model. The linear transfer function was then used to predict the large-amplitude transient response, thereby allowing the saturation amplitude to be estimated. Three system identification methods were used: cross spectral, least squares and maximum likelihood. In order to approximate the kinematics and sensory input of typical falling situations, the test perturbation was selected to be an anterior-posterior acceleration of the platform on which the subject stood, with a visual field that moved with the platform. The perturbation waveform, power spectrum, bandwidth, duration and amplitude were selected to meet requirements for persistent excitation, accurate identification, stationarity and subject safety and tolerance. Pilot experiments were performed to aid in the selection of the perturbation parameters. Testing of 64 young and elderly normal adults has shown the balance test to be a sensitive measure of the deterioration in postural control known to occur in normal ageing. Depending on the system identification method used, the balance test has been able to identify up to three of five patients with peripheral vestibular lesions and five of five elderly subjects with a history of falling, at a false positive rate of 25%. Comparison of the model predictions with direct measurements of transient response has indicated that the model may overestimate the response to large transient perturbations; however, the transient test results may have been confounded by adaptive effects. The balance test results have shown no significant correlation with measures of spontaneous postural sway, except in normal young adults.