Small Phase Lag Research Articles

Some thoughts on the spring-neap cycle of tidal dissipation

The spring-neap cycle of global energy dissipation by ocean tides is calculated with a view to trying to explain an observed anomaly in the tidal fluctuations in the length of day. Calculations are performed in three ways: dissipation by friction linearly proportional to semidiurnal tide velocity, by quadratic friction, and by the torques of the lunar and solar tidal forces on the solar and lunar ocean tides, respectively. All methods give comparable results equivalent to an amplitude of about 0.1 μs change in the length of day with a small phase lag. These are inadequate to explain the observed anomaly of about 3 μs and 0.1 rad phase lag. Further investigations, to determine the generation of a non-equilibrium global MSf wave of equatorial amplitude 0.9 mm by nonlinear interactions in shallow seas using global tide models and observations, are suggested.

Two-tone suppression in cochlear mechanics.

Mechanical responses to one- and two-tone stimuli were recorded from the basilar membrane (BM) in the hook region of the guinea-pig cochlea. The most sensitive or "best" frequencies (BFs) for the sites studied were approximately 25-30 kHz. Two-tone suppression (2TS) of the responses to near BF probe tones was noted using suppressor tones either above or below the BF. Rates of growth of 2TS were highest (approximately 1 dB/dB) when the suppressor tones were presented below the BF. Below-BF suppression thresholds (the suppressor intensities causing approximately 10% reduction in the probe-evoked responses) corresponded to BM displacements of approximately 1-5 nm. Above-BF suppression thresholds corresponded to much smaller displacements at the location studied. Both above- and below-BF suppressor tones changed the phase of the probe tone responses in the same way that increases in the probe tone intensity did (they evoked small phase-lags for below-BF probes, and small phase-leads for near- and above-BF probes). Low-frequency suppressor tones ( < approximately 7 kHz) evoked a frequency- and intensity-dependent mixture of phasic (ac) and tonic (dc) suppression. Peak (ac) suppression was observed around the times of peak BM displacement (not velocity). These findings are discussed in relation to those of other workers.

Force Control of a Semi-Active Damper

SUMMARY Two strategies are investigated for controlling a semi-active damper to track a prescribed force demand signal: (i) ‘open loop’ control, using a model of the damping force versus velocity characteristics; and (ii) force feedback (closed loop) control. The damping characteristics and switching transients of a prototype damper were measured, and used to develop a mathematical model of the dynamics of the damper. The two control strategies were investigated using an idealised (constant velocity) test. Their performance was also simulated and measured under realistic operating conditions using the Hardware-in-the-Loop testing method. Open loop damper control was generally found to give superior performance to force feedback control, due to its smaller phase lag at high frequencies.

The effects of ageing on the pattern electroretinogram and visual evoked potential in humans

We have recorded patterns electroretinograms (PERGs) and visual evoked potentials (VEPs) from 14 elderly subjects (mean age 72 yr) and 12 young subjects (mean age 21 yr) in response to stimulation by high contrast sinusoidal grating patterns of variable spatial frequency (at 9 Hz) and temporal frequency (at 1.7 c/deg). The major effect of ageing on the PERG was an aspecific reduction in amplitude (of about 40%) at most spatial and temporal frequencies, together with a small but systematic phase lag. Control measurements suggest that senile miosis may be responsible for the phase lag, but not for the reduction in amplitude. The effects of ageing on the VEP were more dramatic and depended on the spatial and temporal properties of the stimulus. VEP amplitudes (at 1.7 c/deg) were significantly lower for the aged at low temporal frequencies (below about 6 Hz), but were similar at high temporal frequencies. At 9 Hz, there was no effect of spatial frequency on VEP amplitude. At high temporal frequencies (above 10 Hz), the latencies of VEPs (estimated from the rate at which phase varied with temporal frequency) were similar for old and young (94 and 99 msec respectively). Below 10 Hz, however, the latencies of the old observers was much greater (153 compared with 108 msec). The second-harmonic phase of VEPs of the old but not the young decreased considerably with spatial frequency, by about 1.9π radians (52msec) over the range from 0.5 to 11 c/deg. The selective reduction in amplitude at low temporal frequencies, the longer latencies at low temporal frequencies and the phase lag at high spatial frequencies are consistent with the hypothesis that mechanisms sensitive to high spatial and low temporal frequencies are selectively degraded by ageing.

Temperature Dependence of Photoconductivity Spectra and Phase Lag of p-Type CuGaS2 by Polarized Light Excitation

Photoconductivity spectra and phase lag of the photocurrent for the modulated excitation light are studied between 80 and 340 K on undoped p-type CuGaS2. For the low-resistivity samples, both the intrinsic peak and the extrinsic peak via shallow donor are clearly observed in the polarization-dependent spectra, indicating the selection rule of the uppermost valence bands. For the high-resistivity samples, however, the polarization-dependent behavior of the spectra is greatly reduced due to the mergence of the broadened shallow donor band into the conduction bandtails. On the other hand, a broad peak via deep donor is observed for both types of samples, where almost trap-free hole current with a small phase lag is dominant below 250 K. Above 250 K, there appears a rapid increase in the phase lag, showing the enhancement of the thermal release of trapped holes on a shallow acceptor state.

Vertical eye movement-related secondary vestibular neurons ascending in medial longitudinal fasciculus in cat I. Firing properties and projection pathways

1. The firing characteristics and projection patterns of secondary vestibular nucleus neurons involved in the vertical vestibuloocular pathways were investigated in alert cats. Single-unit recordings were made in the medial longitudinal fasciculus (MLF) near the trochlear nucleus from axons that were monosynaptically activated after electrical stimulation of the vestibular nerve. In a total of 253 identified secondary neurons, 225 discharged in relation to vertical eye movements; 189 of these increased their firing rate for downward eye movements and 36 for upward movements. The activity of the remaining 28 axons was not related to eye movements when the head was still. 2. Virtually all of the secondary neurons with downward on-direction displayed tonic activity that was primarily related to steady eye position during fixation (DPV neurons). The slope of the relationship between firing rate and vertical eye position ranged from 1.2 to 9.1 (spikes/s)/deg with a mean of 3.2 (spikes/s)/deg. The regularity of firing was quantified by calculating the coefficient of variation (CV) of interspike intervals. A comparison of the CV in the population units indicated that DPV neurons could be classified as either regular or irregular neurons. There was a tendency for regular neurons to have higher firing rates and higher correlation coefficients for the rate-position relationships than irregular neurons. 3. During pitch rotation in the light, all the DPV neurons tested increased their firing rate with upward head rotation. Both the phase and the amplitude of the response indicated that DPV neurons discharged not only in relation to eye position but also in relation to head velocity, suggesting that they received monosynaptic input from the posterior semicircular canal. The gain and phase lag of the response relative to head velocity were measured at 0.5 Hz. The range of the gain was 1.1-5.1 (spikes/s)/(deg/s), and that of the phase lag was 18.3-62.4 degrees. There was a tendency for irregular DPV neurons to have a larger gain and smaller phase lag than regular DPV neurons. 4. Ascending and descending projection pathways were determined for 147 DPV axons. Of these, 69 ascended in the contralateral MLF with respect to their soma (crossed-DPV axons), and 78 in the ipsilateral MLF (uncrossed-DPV axons), as revealed by their monosynaptic activation from the contralateral or ipsilateral vestibular nerve. Stimulation of the caudal MLF at the level of the obex evoked direct responses caused by antidromic activation of descending collaterals in approximately 70% (49/69) of the crossed-DPV axons.(ABSTRACT TRUNCATED AT 400 WORDS)

Pursuit eye movement in tracking a target with two sine waves.

It has been reported that, when subjects track a moving target comprising two sine waves, the tracking lag for the faster sine wave component is much smaller than that for the slower one. To understand this phenomenon further, this study examined frequency characteristics of the human tracking response and pursuit eye movement in response to the target with two sine waves of equal amplitude. Analysis indicates that, while the tracking response has very large phase lag for the slower sine wave component and very small phase lag for the faster one, the pursuit eye movement has a conspicuously large phase lead for the slower component and very small phase lag for the faster one. It is suggested that the lack of synchrony of the pursuit eye movement with slower component of the target may be associated with the inferiority of the slower component to the faster one in tracking lag.

Organization of leg movements in preterm infants.

This study describes and establishes baseline data of early movement in preterm infants using a sensitive and quantitative measurement system, kinematic analysis. Subjects were 10 infants born at 34 to 36 weeks gestational age. Spontaneous leg movements were videotaped, and a 10-second segment was digitized to provide kinematic data. The same infants were tested at 3 days and again at 40 weeks postgestational age. Data obtained were compared to evaluate changes with age. Results showed that all infants had organized movement as determined by high interjoint correlations and small phase lags. Movement durations were restricted at 550 and 765 msec for flexion and extension, respectively. Amplitude, velocity, pause durations, and joint angles differed among infants. Infant leg movements are highly organized synergies not disrupted by postnatal events. Differences in movements are attributed to dynamic interaction of elements in the motor control system in real and developmental time. Similar studies on high-risk or sick preterm infants may provide clues to early detection of neuromuscular dysfunction.

Frequency characteristics of the smooth pursuit component in tracking eye movements.

Frequency responses of the human eye tracking system vary remarkably according to the motion of the visual target. In general, periodic (predictable) target motion yields a higher gain and a smaller phase lag in comparison with random (unpredictable) target motion. This paper deals with the question of which of the saccadic and smooth pursuit systems causes this variability. Two kinds of target motions, sine (predictable) and Gaussian random (unpredictable) waves, were presented to the subject with either of two instructions: to fixate on the target or to fixate on the target and do mental arithmetic simultaneously. Recorded eye movements were separated into their saccadic and smooth components, and the respective frequency characteristics were analysed. The result shows that the large phase lag in non-predictive tracking is mainly due to the saccadic system. At low frequencies, the smooth component reveals a rather large phase lead in non-predictive tracking but not in predictive tracking. We also descri...

Photoelectric transducer for measuring the length and diameter of elastic vessels

This photoelectric transducer was developed to measure diameter and length variations in arterial segments in vitro and in elastic tubes. Its construction is simple, its nonlinearity small and its sensitivity adequate. The cut-off frequency is 300 Hz and its small phase lag changes linearly with frequency.

Active and passive smooth eye movements: Effects of stimulus size and location

We measured active smooth pursuit eye movements and passive smooth eye movements in the open-loop condition as subjects viewed moving stimuli of different sizes and at various retinal loci. Active movements have high gain and relatively large phase lag. Passive movements have lower gain and smaller phase lag, and occur with either foveal or eccentric stimuli. They appear to be similar or identical to optokinetic movements. Although different, active and passive movements show a similar increase in amplitude and phase lag as the size of the stimulus was increased. From these findings we suggest that: (1) The stimuli for the active movements are target position and velocity; (2) the stimulus for passive movements is target velocity; (3) the active response to target velocity is related, in part, to the passive response and thus is related to optokinesis.

A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems

We consider a one-parameter family of Noumerov-type methods for the integration of second order periodic initial-value problems: y″ = f( t, y), y( t 0) = y 0, y′( t 0) = y′ 0. By applying these methods to the test equation: y″ + λ 2 y = 0, we determine the parameter of the family so that the phase-lag (frequency distortion) for the method is minimal. The resulting method has a very small phase-lag of size 1 12096 λ 6h 6 ( h is the step-size); interestingly, this method also possesses an interval of periodicity of size 2.71. Noumerov's method has a phase-lag of size 1 480 λ 4h 4 and an interval of periodicity of size 2.449. The superiority of our method over Noumerov's method is illustrated by two examples.

The adaptive tracking of slowly varying processes with coloured-noise disturbances

An adaptive tracking technique is developed to estimate the output of a slowly varying process which is corrupted by a coloured noise disturbance. There are two estimators in the adaptive tracker. The primary estimator and the vernier estimator is simply a low-pass filter or its equivalent. The vernier estimator is self-tuning and is adaptive to the varying disturbances. Since the process contains unknown parameters, the usual Kalman filter can not be used. A conventional low-pass filter might be employed but it would give a significant phase lag in this situation. The adaptive tracker has a small phase lag and has particular advantages over the conventional low-pass filter when the frequency of the coloured noise disturbance is varying.

Influence of panting frequency on thoracic gas volume measurements in chronic obstructive pulmonary disease.

Frequency dependence of thoracic gas volume (Vtg) and phase angles between volume and mouth pressure signals were evaluated in 10 normal subjects and in 31 patients with bronchitis, who panted sequentially at 0.8 Hz and 2.5 Hz during the same occlusion. A slight negative frequency dependence of Vtg (-1.2 +/- 0.9%/Hz, -m +/- SD), accompanied by a very small phase lag of volume with respect to pressure variations (-1.5 +/- 0.9 degrees at 2.5 Hz) was found in normal subjects. In contrast, patients with bronchitis exhibited a mild positive frequency dependence of Vtg (+ 0.5 +/- 1.7%/Hz and + 0.8 +/- 2.3%/Hz in subjects with normal and increased airway resistance, respectively), whereas the volume signal slightly led the pressure signal at 2.5 Hz. Both the frequency dependence and the phase difference increased when the subjects with the largest airway resistance did not support their cheeks during the panting maneuvers. The data confirm previous indirect evidence that Vtg is, in most instances, accurately measured by Boyle's law in mild and moderate chronic airway obstruction.

Low‐frequency current and temperature variability from Gulf Stream frontal eddies and atmospheric forcing along the southeast U.S. outer continental shelf

Low‐frequency current and temperature time series from the outer shelf between Cape Canaveral, Florida, and Cape Romain, South Carolina, are compared with shipboard hydrographic data, satellite VHRR, coastal and buoy winds, and coastal sea level during the period from February to June 1980. Low‐frequency current and temperature variability along the shelf break was primarily produced by cyclonic, cold core Gulf Stream frontal eddies. These disturbances traveled to the north at speeds of 50 to 70 cm s−1 with periods of 5 to 9 days throughout the experiment and produced cold cyclonic perturbations of the northward mean flow and temperature fields over an along‐shelf coherence scale of 100 km. Frontal eddies appear to be an important mechanism in the observed eastward transport of northward momentum and heat along the shelf edge. They also appear to play a key role in the transfer of eddy kinetic and potential energy back to the mean flow, which suggests an upstream formation region and shear‐induced dissipation. Upwelling velocities of about 10−2 cm s−1 in the cold core provide the major source of new nutrients to the outer shelf. Subtidal flow variability at the 40‐m isobath was a mixed response to Gulf Stream and wind forcing. Barotropic along‐shelf current oscillations were coherent with the local winds and coastal sea level at periods of 3–4 and 10–12 days over along‐shelf scales of 400 km with small phase lags, suggesting a nearly simultaneous frictional equilibrium response to coherent wind‐induced sea level slopes.

Compensatory head and eye movements in the frog and their contribution to stabilization of gaze

Compensatory head movements, recorded in unrestrained frogs, were compared to compensatory eye movements recorded from animals that had their head fixed. Movements were evoked by oscillating the animal in the dark (vestibular stimulation) or in the light in front of an earth-fixed, patterned visual background (combined stimulation) or by rotating vertical black and white bars (optokinetic stimulation) around the stationary animal. Oscillations occurred in the horizontal plane at frequencies between 0.025 and 0.5 Hz. Gain and phase values of head and eye movements, relative to stimulus movements were calculated. Evoked eye movements were limited in amplitude to +/- 3-6 degrees, increasing with the size of the animal. Head movements were limited to +/- 30-40 degrees. Resetting fast-phases of both head and eyes were very rarely observed during sinusoidal stimulation and no eye movements were recorded in the absence of intended head movements. Vestibularly evoked head movements exhibited a frequency-dependent threshold that was not observed for vestibulo-ocular responses. Above threshold, the gain of evoked head responses increased and reached a frequency-dependent plateau at which the system behaved approximately linearly. Within the linear range, gain of vestibularly evoked responses increased with frequency (from 0.04 at 0.025 Hz to 0.75 at 0.5 Hz) and phase lead decreased (from about 80 degrees to 0 degrees). Vestibularly evoked eye movements similarly increased in gain from 0.05 to 0.56 and decreased in phase lead from about 56 degrees to 10 degrees over the same frequency range. Optokinetically evoked head and eye movements had their highest gains (about 0.8 and 0.5) at low constant velocities (less than or equal to 1-4 degrees/S) or frequencies (less than or equal to 0.025 Hz). At higher constant velocities or frequencies the gain dropped. The phase lag increased from close to zero (at 0.025 Hz) to about 60 degrees for the head and to about 20 degrees for the eye movements (at 0.25 Hz). These phase lags are explained by reaction times of the evoked movements of about 600 ms (head) and 200 ms (eyes). Combined stimulation evoked compensatory head movements with gain and phase values that were frequency-independent in the linear range. Head movements compensated for about 80-90% of the imposed gaze shift with a small phase lag (0-10 degrees). Evoked eye movements were found to be large enough in amplitude and fast enough in time to enable a frog to stabilize its gaze exclusively with slow phase compensatory movements for a large variety of frequency and amplitude combinations. The two motor systems controlling movements of the head and the eye are matched in such a way that the non-linearities of the evoked eye movements can compensate for the non-linearities of the evoked head movements.

Circadian organization of food intake and meal patterns in the rat

The temporal distribution of food intake and of the two parameters, meal size and meal frequency, was determined in rats exposed to light-dark (LD) cycles and to constant illumination (LL). All three measures displayed characteristic multimodal circadian patterns that entrained to the LD cycle and free-ran in LL. Under both conditions, the circadian rhythm of meal size showed a small phase lag relative to the meal frequency rhythm. Lighting condition had no effect on total daily food intake, or on mean meal size and frequency. However, exposure to LL resulted in an attenuation of the rhythms, accompanied by an increase in postprandial correlations. The results indicate that circadian rhythms of food intake are attributable to circadian oscillations in both meal parameters, and suggest a competitive relationship between circadian rhythms and the metabolic controls underlying the rat's meal pattern.

Wave reflections in the solar atmosphere

The small phase-lag between velocities observed at different chromospheric levels is interpreted as being due to acoustic waves reflected by the very hot atmospheric layers of the chromosphere-corona transition zone. We consider first an isothermal slab, then a realistic solar atmospheric model and calculate weighting functions for velocities in Ca ii lines. It is shown that taking into account these functions and integrating over horizontal wave numbers leads to a good agreement with previous observations (Mein, 1977) in the case of 8498 and 8542 Ca ii lines. For the K line, the less good agreement shows that magnetoacoustic waves become important in the upper chromospheric layers.

Novel generalized differential integrator with controlled phase lead

A new active compensation method for the differential integrator is given. The proposed integrator has a phase lead which is controlled by a single resistor. The circuit realizes a novel phase lead inverting (noninverting) integrator by shorting one of the two input ports to ground. A differential integrator with a very small phase lag which includes the compensated Miller [1] and the compensated balanced time constant [2] integrators as special cases is also given.

On the Effect of Bottom Friction on Barotropic Motion Over the Continental Shelf

Abstract Observations of the velocity fields over the continental shelf and slope off Oregon and off Peru have shown that there is a phase difference in the onshore-offshore direction, with the velocity fluctuations nearshore leading those offshore in time. It is shown here that the effects of bottom Ekman layer friction and cross-shelf depth variation combine to result in such a phase lag in a model for forced or free long barotropic continental shelf waves. The model also shows that bottom friction results in a smaller phase lag between the alongshore components of velocity and wind stress than that predicted by a frictionless model, a feature found in the observations off Oregon.