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The minimum uncertainty and other relations are evaluated in the framework of the coherent states of the damped harmonic oscillator. It is shown that the coherent states of the damped harmonic oscillator are the squeezed coherent states of the simple harmonic oscillator. The unitary operator is also constructed, and this connects coherent states with damped harmonic and simple harmonic oscillators.
An optimum truncation level, N, in a spherical-harmonic analysis of the geomagnetic main field at the core-mantle boundary is determined by harmonic-spline analysis. Specifically, that value of N is found at which the two analyses are closest in a well defined sense and, for that value of N, the 'closeness' of two models is determined. Depending slightly on the definition of closeness, optimum N is found to be either 10 or 11. For those values the two analyses give remarkably similar results, showing that the conveniences of spherical harmonics can be retained with little penalty.
Time harmonic, spherical harmonic and power series expansion of Boltzmann equation
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
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Imperfections and geometry effects in harmonic drive gear reducers cause a cyclic gear error, which at a systems level, results in high frequency torque fluctuations. To address this problem, gear error testing was performed on a wide variety of sizes and types of harmonic drives. It was found that although all harmonic drives exhibit a significant first harmonic, higher harmonics varied greatly with each unit. From life tests, small changes were found in harmonic content, phase shift, and error magnitude (on the order of .008 deg peak-to-peak maximum) occurred for drives with many millions of degrees of output travel. Temperature variations also influenced gear error. Over a spread of approximately 56 C (100 F), the error varied in magnitude approximately 20 percent but changes in a repeatable and predictable manner. Concentricity and parallelness tests of harmonic drive parts resulted in showing alignment influence gear error amplitude. Tests on dedoidaled harmonic drives showed little effect on gear error; surprisingly, in one case for a small drive, gear error actually improved. Electronic compensation of gear error in harmonic drives was shown to be substantially effective for units that are first harmonic dominant.
We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism. We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not corrected for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star. The Oort parameters determined by a straightforward least-squares adjustment in vector spherical harmonics are A=14.0 +/- 1.4, B=13.1 +/- 1.2, K=1.1 +/- 1.8, and C=2.9 +/- 1.4 km s(exp -1) kpc(exp -1). The physical meaning and the implications of these parameters are discussed in the framework of a general linear model of the velocity field. We find a few statistically significant higher degree harmonic terms that do not correspond to any parameters in the classical linear model. One of them, a third-degree electric harmonic, is tentatively explained as the response to a negative linear gradient of rotation velocity with distance from the Galactic plane, which we estimate at approximately -20 km s(exp -1) kpc(exp -1). A similar vertical gradient of rotation velocity has been detected for more distant stars representing the thick disk (z greater than 1 kpc), but here we surmise its existence in the thin disk at z less than 200 pc. The most unexpected and unexplained term within the Ogorodnikov-Milne model is the first-degree magnetic harmonic, representing a rigid rotation of the stellar field about the axis -Y pointing opposite to the direction of rotation. This harmonic comes out with a statistically robust coefficient of 6.2 +/- 0.9 km s(exp -1) kpc(exp -1) and is also present in the velocity field of more distant stars. The ensuing upward vertical motion of stars in the general direction of the Galactic center and the downward motion in the anticenter direction are opposite to the vector field expected from the stationary Galactic warp model.
Simultaneous VLF/ULF observations carried out near Winnipeg, Manitoba show that geomagnetic disturbances control the behavior of harmonics of 60 Hz man-made electric power. The harmonics of 60 Hz detected by the VLF receiver are at multiples of 180 Hz, indicating that they originated from a 3 phase ac power system. Under geomagnetically quiet conditions, only odd harmonics of 70 Hz were detected. In disturbed conditions, both odd and even harmonics were excited. The strength of each harmonic changed concurrently with geomagnetic pulsation (ULF) activity. These findings seem to indicate that a portion of telluric currents shunted into the power line system through the neutrals of the Y-connected transformers give rise to a dc bias to the transformer core materials and that it distorts their hysteresis loops, activating harmonics of 60 Hz power. A mathematical proof is given that a hysteresis loop having a point of symmetry generates odd harmonics only, whereas loops lacking in point-symmetry generally give rise to both odd and even harmonics. A general formula was obtained to calculate the strength of each harmonic based on the shape of the hysteresis loop.
BACKGROUND: Newer contrast agents as well as tissue harmonic imaging enhance left ventricular (LV) endocardial border delineation, and therefore, improve LV wall-motion analysis. Interpretation of dobutamine stress echocardiography is observer-dependent and requires experience. This study was performed to evaluate whether these new imaging modalities would improve endocardial visualization and enhance accuracy and efficiency of the inexperienced reader interpreting dobutamine stress echocardiography. METHODS AND RESULTS: Twenty-nine consecutive patients with known or suspected coronary artery disease underwent dobutamine stress echocardiography. Both fundamental (2.5 MHZ) and harmonic (1.7 and 3.5 MHZ) mode images were obtained in four standard views at rest and at peak stress during a standard dobutamine infusion stress protocol. Following the noncontrast images, Optison was administered intravenously in bolus (0.5-3.0 ml), and fundamental and harmonic images were obtained. The dobutamine echocardiography studies were reviewed by one experienced and one inexperienced echocardiographer. LV segments were graded for image quality and function. Time for interpretation also was recorded. Contrast with harmonic imaging improved the diagnostic concordance of the novice reader to the expert reader by 7.1%, 7.5%, and 12.6% (P < 0.001) as compared with harmonic imaging, fundamental imaging, and fundamental imaging with contrast, respectively. For the novice reader, reading time was reduced by 47%, 55%, and 58% (P < 0.005) as compared with the time needed for fundamental, fundamental contrast, and harmonic modes, respectively. With harmonic imaging, the image quality score was 4.6% higher (P < 0.001) than for fundamental imaging. Image quality scores were not significantly different for noncontrast and contrast images. CONCLUSION: Harmonic imaging with contrast significantly improves the accuracy and efficiency of the novice dobutamine stress echocardiography reader. The use of harmonic imaging reduces the frequency of nondiagnostic wall segments.
The magnitude of discrete frequency sound radiated by a rotating blade is strongly influenced by the presence of a nonuniform distribution of aerodynamic forces over the rotor disk. An analytical development and experimental results are provided for a technique by which harmonic blade loads are derived from acoustic measurements. The technique relates, on a one-to-one basis, the discrete frequency sound harmonic amplitudes measured at a point on the axis of rotation to the blade-load harmonic amplitudes. This technique was applied to acoustic data from two helicopter types and from a series of test results using the NASA-Langley Research Center rotor test facility. The inferred blade-load harmonics for the cases considered tended to follow an inverse power law relationship with harmonic blade-load number. Empirical curve fits to the data showed the harmonic fall-off rate to be in the range of 6 to 9 db per octave of harmonic order. These empirical relationships were subsequently used as input data in a compatible far field rotational noise prediction model. A comparison between predicted and measured off-axis sound harmonic levels is provided for the experimental cases considered.
Since torque in harmonic drives is transmitted by a pure couple, harmonic drives do not generate radial forces and therefore can be instrumented with torque sensors without interference from radial forces. The installation of torque sensors on the stationary component of harmonic drives (the Flexipline cup in this research work) produce backdrivability needed for robotic and telerobotic compliant maneuvers. Backdrivability of a harmonic drive, when used as torque increaser, means that the output shaft can be rotated via finite amount of torque. A high ratio harmonic drive is non-backdrivable because its output shaft cannot be turned by applying a torque on it. This article first develops the dynamic behavior of a harmonic drive, in particular the non-backdrivability, in terms of a sensitivity transfer function. The instrumentation of the harmonic drive with torque sensor is then described. This leads to a description of the control architecture which allows modulation of the sensitivity transfer function within the limits established by the closed-loop stability. A set of experiments on an active hand controller, powered by a DC motor coupled to an instrumented harmonic drive, is given to exhibit this method's limitations.
Harmonic imaging is a new ultrasonographic technique that is designed to improve image quality by exploiting the spontaneous generation of higher frequencies as ultrasound propagates through tissue. We studied 51 difficult-to-image patients with blinded side-by-side cineloop evaluation of endocardial border definition by harmonic versus fundamental imaging. In addition, quantitative intensities from cavity versus wall were compared for harmonic versus fundamental imaging. Harmonic imaging improved left ventricular endocardial border delineation over fundamental imaging (superior: harmonic = 71.1%, fundamental = 18.7%; similar: 10.2%; P <.001). Quantitative analysis of 100 wall/cavity combinations demonstrated brighter wall segments and more strikingly darker cavities during harmonic imaging (cavity intensity on a 0 to 255 scale: fundamental = 15.6 +/- 8.6; harmonic = 6.0 +/- 5.3; P <.0001), which led to enhanced contrast between the wall and cavity (1.89 versus 1.19, P <.0001). Harmonic imaging reduces side-lobe artifacts, resulting in a darker cavity and brighter walls, thereby improving image contrast and endocardial delineation.
The reported investigation constitutes an extension of studies conducted by Ashour-Abdalla and Kennel (1975, 1976, 1978) with respect to a basic plasma model of Young et al. (1973). The model involves a combination of a cold Maxwellian background plasma, a hot plasma, and a 'loss cone' type of free energy source. Previous results on the first cyclotron harmonic bands are extended to multiharmonics. The significance of the obtained relations is discussed and tentative conclusions are presented. Given that the spatial growth rates of the convective modes are comparable, and that simultaneous nonconvective instability (NCI) is possible, it is concluded that multiharmonic emissions ought to be a common feature of the magnetospheric electrostatic wave observations. Since the volume of parameter space for which the first harmonic is NCI, and the volume for which the convective first harmonic mode has significant spatial growth rates, exceed those for the higher harmonics, first harmonic waves should be the most commonly observed and the higher harmonics should usually be accompanied by the first harmonic.
When the ISIS 1 satellite passes through the auroral kilometric radiation (AKR) source region the sounder receiver often detects harmonic bands of radiation associated with the fundamental AKR band. These harmonic components were earlier attributed to a nonlinear instrumental response to the strong wide-band bursty AKR fundamental signal. Evidence is here presented that indicates that these harmonics are of natural origin, namely: (1) all the harmonic signals are sometimes observed to have nearly the same bandwidth, (2) when the fundamental signal has two components the harmonic signal sometimes corresponds to the weaker rather than the stronger component, (3) a weak harmonic can be observed to be associated with a weak fundamental, and (4) a 'harmonic' signal can be observed when there is no fundamental.
This paper demonstrates the use of resonant-tunneling diodes as varistors for harmonic multiplication. It is shown that efficient odd-harmonic conversion is possible and that even harmonics do not appear because of the antisymmetry of the current-voltage (I-V) curve. It is also shown that, with the proper choice of resonant-tunneling structure and pump amplitude, most of the harmonic output power can be confined to a single odd-harmonic frequency. Fifth-harmonic multiplication was demonstrated with an output at 21.75 GHz and a power conversion efficiency of 0.5 percent, and a fifth-harmonic efficiency of 2.7 percent was achieved in a circuit simulation using an improved I-V curve.
The Mars Reconnaissance Orbiter (MRO) spacecraft has three two-axis gimbal assemblies that support and move the High Gain Antenna and two solar array wings. The gimbal assemblies are required to move almost continuously throughout the mission's seven-year lifetime, requiring a large number of output revolutions for each actuator in the gimbal assemblies. The actuator for each of the six axes consists of a two-phase brushless dc motor with a direct drive to the wave generator of a size-32 cup-type harmonic gear. During life testing of an actuator assembly, the harmonic gear teeth failed completely, leaving the size-32 harmonic gear with a maximum output torque capability less than 10% of its design capability. The investigation that followed the failure revealed limitations of the heritage material choices that were made for the harmonic gear components that had passed similar life requirements on several previous programs. Additionally, the methods used to increase the stiffness of a standard harmonic gear component set, while accepted practice for harmonic gears, is limited in its range. The stiffness of harmonic gear assemblies can be increased up to a maximum stiffness point that, if exceeded, compromises the reliability of the gear components for long life applications.
Power spectra of magnetic pulsations observed at synchronous orbit by the ATS 6 satellite often show several spectral peaks simultaneously. Such pulsations, called harmonic events because of the nearly constant separation between successive peaks, are continuously observed in the dayside in the Pc 3-4 frequency range (6.6-100 mHz). The harmonic events are seen clearly only in the east-west magnetic field component. The spectral peaks are regularly spaced with a typical minimum separation of 14 mHz in the morning gradually decreasing to 10 mHz in the afternoon. In the dynamic spectra of harmonic events, the fundamental mode is usually absent. In addition, the relative amplitudes of the higher harmonics depend on the magnetic latitude. These observed features can be explained by a standing Alfven wave consisting of many discrete harmonic frequencies. A statistical analysis of power spectra demonstrates that at least 10-30% of Pc 3 pulsations can be classified as harmonic events. For a selected event on August 7, 1975, the plasma mass density at the synchronous orbit is estimated to be 3-8 hydrogen mass/cu cm.
Harmonically related Pc 3-4 pulsations (7-100 mHz) are observed simultaneously by the three geosynchronous satellites ATS 6, SMS 1, and SMS 2, which are separated 20 deg from one another. At a given instant the frequency of the same harmonic is different from one spacecraft to another and each spacecraft observes a decrease in the fundamental frequency as it moves from morning (15 mHz) to afternoon (10 mHz). This frequency behavior is explained in terms of standing Alfven waves, for which the frequency is determined by the local magnetic field and plasma density. Occurrence of harmonic Pc 3-4 waves only during daytime hours (0400-2000 LT) and their frequency characteristics suggest a broadband energy source located on the dayside. Possible azimuthal wave number m and azimuthal phase velocity V(phi) of the second through fourth harmonics are determined from an unusual interval during which identical harmonic frequencies were observed at SMS 1 and ATS 6. Under the assumption of tailward propagation of constant-phase fronts at the same velocity for all these harmonics, V(phi) of about 1700 km/s is obtained.