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We report detailed experimental measurements and calculations of the amplitude modulation (AM) of a high-frequency de Haas-van Alphen (dHvA) quantum-oscillation waveform, due to magnetic interaction with a low-frequency dHvA oscillation. Experiments were carried out using a pure Au single crystal with $H$ parallel to the 111g direction, at 36.1 kG and 2.0 K. Two new mechanisms by which AM can arise are described in detail: (i) AM can arise in conjunction with the frequency modulation (FM) due to magnetic interaction, through modulation of the Bessel-function arguments which appear in using the field-modulation technique. This FM-AM effect is an unavoidable consequence of using the field-modulation technique in the presence of magnetic interaction. The resulting AM waveforms can be totally different in appearance at different detection harmonics. (ii) AM can also arise via magnetic interaction and phase smearing in an inhomogeneous magnetic field. The observed AM, as a function of a linear magnetic field gradient, is in good qualitative agreement with the prediction of Hornfeldt, Ketterson, and Windmiller. Possible applications of AM effects are briefly discussed.

SUMMARY This paper deals with the theory of asynchronous motors running at variable frequency. Motor characteristics are found by the help of a computer programme where higher harmonics are neglected, but the influence of saturation is considered. It is shown that it is impossible to get optimum performance if the voltage is a function of the frequency only. A regulator which controls the voltage as a function of both frequency and load to keep constant flux gives torque and current characteristics equal to those of a dc-machine. This paper presents two alternatives for such a regulator. Braking methods are discussed and a regulator principle for a four-quadrant drive without current sensing is shown.

The model of the low-level jet over sloping terrain formulated by Holton (1967) is extended to assess the effects of the diurnal variation of eddy viscosity and of higher harmonics of the thermal driving mechanism. A perturbation expansion leads to analytic solutions which are compared to observations in the south central United States. It is suggested that numerical integration of the fully nonlinear equations is necessary to simulate the virtually simultaneous development of the jet throughout the depth of the planetary boundary layer. DOI: 10.1111/j.2153-3490.1974.tb01633.x

In this paper the dynamic interactions between mechanical and reactive modes of machines in a multi-machine power system are investigated. The dynamic interactions are expressed in terms of machine angles, transient voltages, and coefficients which are functions of system parameters and operation conditions. The effect of the dynamic interaction can be examined by the electric torque loci on the A6-Aw phase plane. It is found that the interaction between the mechanical modes of machines has significant effect on stability characterized by the natural mechanical oscillation frequency and damping of individual machines.

The subject of this paper is to make clear the basic characteristics of the AFH. To calculate the characteristics of the AFH with single conduit, the AFH containing a separator and the three-phase AFH, three matrices, namely exact matrix, approximated matrix using the Poiseuille's law and matrix approximated by lumped parameters, are considered. When the input frequency of the AFH is lower than the fundamental characteristic frequency of the conduit, the calculations based upon the approximated matrices induce no important error. The frictional force on the separator caused by the sealing material lowers remarkably the power transmission efficiency of the AFH. With the three-phase AFH, the pressure variation does not become sinusoidal even if the displacement of the input pistons is sinusoidal. In this case a high input frequency can not be taken because some resonance will be induced in the system by a higher harmonics in the pressure wave.

Dielectric and piezoelectric nonlinearities of KH 2 PO 4 below and above the Curie temperature were precisely determined by the harmonic detection method in which the second and third harmonics of the fundamental voltage applied to the crystal were measured. In the ferroelectric region the nonlinearity was closely related to the domain wall motion. Above the Curie temperatrue the result showed that (∂ 2 χ/∂ E 2 ) 0 ∝( T - T c ) -γ with the critical exponent γ of 4.0±0.2.

The magnitudes of the harmonic fields which are generated when an alternating electric field is applied to a plasma are calculated. The plasma has a density gradient and is immersed in a uniform static magnetic field. The harmonics are very strongly excited near the upper hybrid frequency. A fluid theory is employed to describe the highly non linear behavior near resonance and a kinetic theory is used to find the effect of a finite temperature. It is found that kinetic effects are important if the radius of gyration is comparable in size to the scale length.

In plasmas produced by microwave power the electron density displays a dependence on the magnetic field strength obviously asymmetric with respect to the harmonics of the electron cyclotron frequency. In regions of the magnetic field strength just above the harmonics there are extremely high values of electron density, the density values dropping sharply off towards the other wing of the harmonics.

The analysis of infinite arrays of waveguide apertures on cylinders covered by a dielectric is approached by enforcing the continuity of the EM fields at the air-dielectric and at the dielectric-cylinder interfaces. The continuity of the EM fields at the first interface is enforced by representing the fields in the air and in the dielectric by an orthonormal set of modes LSE and LSM with respect to the radial direction. The matching of the fields at the second interface is performed by resorting to the "eigenexcitation" method [1]. The fields external to the cylinder are represented by a set of space harmonics matching the symmetry of the excitation of the array and the fields in the waveguides by a superposition of normal waveguide modes. The continuity of the fields is approximately enforced by using Galerkin's method. The rigorous analysis of these structures leads to rather involved expressions for the element driving point admittance and for the far fields. An approximate analysis is introduced to simplify the design of these structures for cylinders of large radius. Numerical examples illustrate the good approximation given by the simplified analysis. Numerical results are presented for the case of an array on a cylinder with radius approximately 100\lambda . The array element pattern shows the presence of resonance dips much more pronounced than the notches due to grating lobe phenomena.

Third-order virial equations are used to investigate the oscillations and the stability of the sequence of uniformly rotating compressible Maclaurin spheroids, referred to in an inertial frame. It is seen that in the case of the oscillations belonging to the third harmonics, the frequency spectrum of the Maclaurin sequence referred to in an inertial frame is distinct from the spectrum of the Maclaurin sequence considered stationary in a rotating frame of reference.

The amplitudes and frequencies of the components of the acoustical spectrum of an acoustical wave, generated in a non-viscous liquid filling a cavity, are calculated by solving a boundary value problem. Apart from forced oscillations, the frequencies of the acoustical spectrum are equal to the frequency of the fundamsntal oscillation of the liquid in the cavity and its higher harmonics. If the frequency of the driving acoustical wave coincides with one of these (proper) frequencies, thefractional harmonic components appear. The amplitudes of the component oscillations decrease monotonically as the absolute value of the difference between the frequency of the driving acoustical wave and the frequency of the respective oscillation is increased. The derived relations are compared with the results of some published measurements.

Earlier measurements of absolute frequencies of 12C16O laser lines by heterodyning with second harmonics of a 12C16O2 laser have been extended to 15 more lines by use of the rare isotopes 12C18O2 and 13C16O2. Interband difference frequencies for 20 pairs of 12C16O lines have also been measured by beat frequency techniques. These data together with 1438 other previously reported frequency measurements in the microwave and infrared regions have been analyzed to determine coefficients of a Dunham series E vJ = Σ m,n Y mn (v + 1 2 ) m [J(J + 1)] n for the CO electronic ground state. Transition frequencies predicted from the derived coefficients are substantially more accurate than earlier tabulations, having estimated uncertainties of the order of 2 MHz in the strongest laser bands. The coefficient Y31 has been determined for the first time.

Equipment has been developed which will automatically plot the input impedance curves of the reed‐excited musical instruments as a function of frequency. Sound from a regulated driver unit is passed through a high acoustical impedance into an adapter unit attached to the mouthpiece of the instrument. This impedance is in the form of a capillary of annular cross section, and is designed to have an approximately constant impedance magnitude over the frequency range used. The sound‐pressure amplitude generated in the instrument is measured by means of a microphone whose output is applied to a chart recorder, so that a graph of input impedance versus frequency is obtained. Representative impedance curves were run for selected notes on the clarinet, oboe, bassoon, and saxophone. Input impedance values range from 400 to 1600 cgs acoustic ohms for the various instruments. For the low notes on the clarinet, the resonance frequencies are compressed in relation to the harmonics of the fundamental mode, the higher r...

When a satellite orbit decaying slowly under the action of air drag experiences 15th-order resonance with the Earth's gravitational field, so that the ground track repeats after 15 rev, the orbital inclination suffers appreciable changes due to the perturbations from the harmonics in the geopotential of order 15 and odd degree (15,17,19 …). In this paper the changes in inclination at resonance of 11 satellites at inclinations between 30° and 90° have been analysed to determine values of the geopotential coefficients of order 15 and degree l, C l,15 and S l,15 in the usual notation. The recommended solution, going up to l = 31, is: l 109Cl,15 109Sl,15 15 −21.5 ± 0.9 −8.4 ± 0.9 17 4.4 ± 1.6 9.0 ± 1.5 19 −15.6 ± 2.6 −14.1 ± 2.7 21 10.4 ± 3.0 7.3 ± 3.5 23 22.5 ± 2.8 1.2 ± 4.4 25 −0.9 ± 4.7 −3.8 ± 5.3 27 −11.2 ±3.3 9.1 ± 3.2 29 −20.5 ± 5.4 −1.2 ± 6.1 31 17.7 ± 6.6 −1.0 ± 7.1

Douglaset al. (1973) have estimated tidal parameters from the orbits of GEOS 1 and GEOS 2. Their results, interpreted in terms of Love numbers, are rather dispersive due in part to their neglect of the ocean tides. The ocean tidal corrections are estimated in this paper, but although they do not explain all of the discrepancy they do emphasise the importance of these perturbations on the motion of close Earth satellites. The remaining discrepancies could result in part from the fact that part of the long period tidal perturbations have been absorbed by the zonal harmonics in the Earth's gravity field.

SUMMARY Induction motors fed from a non-sinusoidal voltage source are subjected to augmented losses and parasitic torques, 30th phenomena are due to higher harmonics in the supply source. Parasitic torques can be classified according to the dependence on time. Torques invariable with time are insignificant in magnitude and are not further analysed in the following paper. Time dependant torques have a pulsating character and their integral over a full period equals zero. However, they do cause a fluctuation in the motor speed. Of considerable disadvantage is the fact that their magnitude is not particularly dependent on the load. Therefore, their full import is felt even under no-load operation. Pulsating torques have an unfavourable effect particularly on group drives and during speed control in the low revolution range where it is difficult to introduce various sorts of feedback. Upon clarification of physical phenomena which take place in induction motors fed from pulse-width modulated inverters it is possible to propose improvements in the supply voltage. Such arrangements practically eliminate low-frequency torques which are most dangerous from the point of view of speed fluctuation.

In estimating the pole face loss due to the tooth ripple harmonics, the reaction effect of the rotor eddy current field with the airgap field should be taken into consideration. This reaction effect can be significant, particularly for the recent large synchronous generators.

The paper outlines a general procedure to predict the dynamic response, including resonance of hyperbolic cooling towers to turbulent winds. Pressure spectra on the tower surface were measured in a boundary layer wind tunnel. Simplifying assumptions have led to the description of pressure spectra and response spectra by means of compact formulation. Application to full-scale towers, including Ferrybridge, is examined. It is concluded that the windward and wake regions are not correlated; the quasi-steady response resides mainly in the coupled harmonics m=1, 2, 3; and the resonant response resides mainly in the harmonics m=4, 5, 6. It is also concluded that while the quasi-steady response increases as wind velocity squared, the resonant response increases faster than wind velocity cubed.

Summary The basic principle of self-commutated inverters controlled by sinusoidal pulse-duration modulation (also known as sub-harmonic inverters) is explained and illustrated. The current and voltage relationships are demonstrated in a generally valid form by means of equations and diagrams. The case is also dealt with in which the pulse frequency is not a wholenumber multiple of the fundamental frequency, with the result that higher-order oscillations are no longer true harmonics. The best possible methods of control with respect to minimum harmonic content at the lowest inverter switching frequency (= pulse frequency) are dealt with. Special attention is paid to multi-pulse sub-harmonic inverters, of the kind employed successfully in a first experimental locomotive equipped with a 1.5 MW static frequencychanger

Radio signals in the 1.5- to 16-kHz range transmitted from Siple Station, Antarctica (L=4), are used to control wave-particle interactions in the magnetosphere. Observations at the conjugate point show signal growth and triggered emissions including risers, fallers, and hooks. Growth rates of the order of 100 dB/s and total gains up to 30 dB are observed. Triggered emissions may be cut off or have their frequency rate of change altered by Siple pulses. Similar effects occur in association with harmonics from the Canadian power system. The observed temporal growth is predicted by a recently proposed feedback model of cyclotron interaction. Plasma instability theories predicting only spatial growth are not in accord with these observations. Possible applications include study of nonlinear plasma instability phenomena, diagnostic measurements of energetic particles trapped in the magnetosphere, modification of the ionosphere through control of precipitation, and VLF communication through the magnetosphere.

Summary A theoretical framework is given to evaluate the non-linear response of a halfcell when a periodic potential is superimposed on a base potential. Some interesting features of this approach are: o (i) no restriction is placed on the magnitude of the periodic signal; (ii) formally, all the infinite harmonics in the output current can be evaluated; (iii) the time-averaged part of the current (the so called “rectification” component) is also obtained and its identity in form with its d.c. counter part viz. “the bias response”, is established for the case E * =a constant; (iv) the influence of the bias state on the harmonics ( i.e. the time modulation) and the influence of the harmonics on the time averaged part (Fournier polarogram) become explicit; (v) the formalism deduced here is common to several models like those with parallel electron transfers with or without preceding chemical reactions, numerous mass-transport models, any given non-linear dependence of the rates on the overpotential etc. (vi) the applicability of these results are immediate to different input profiles such as (a) the sinusoidal, (b) the square wave, (c) pulse trains of various forms, (d) the triangular ones etc. (vii) the presentation is not restricted to constant “bias” conditions: it is capable of handling all time deependent bias profiles too, provided the latter are sufficiently slowly varying (as compared to the frequency of the periodic part). The computational procedure is briefly sketched. The limitations on our results arise from the assumptions on (i) the absence of adsorption, (ii) the presence of the supporting electrolyte, and (iii) the linear (in the generalized sense) relationship between the interfacial concentrations and the current (faradaic).

Periods of oscillations of sea level in Wellington Harbour, New Zealand (41° 17'S, 174° 52’ E), are calculated by spectral analysis of the residual elevations observed in tide gauge records. These periods are compared with those computed by numerically integrating a one‐dimensional linear momentum equation and the continuity equation. The two main oscillations are the first harmonics along and across the harbour with periods of about 27 and 22 min respectively — the second harmonics were also observed. The quarter wavelength oscillation with forcing at the mouth which was excited by the 1960 Chilean Tsunami has a period of about 160 min.

Several problems in the analysis of shells of revolution are examined for which only the membrane solutions are needed. The significant displacement of truncated shells and domes under snow, wind, and end loads can be obtained for realistic conditions of edge constraint. With a variational method the higher harmonics of prescribed edge displacements are handled without an explicit calculation of the displacement field. The calculation of edge bending stress is trivial. The procedure is particularly well-suited to the calculation of thermal stresses in a shell with constrained edges.

An important factor for many processes in the heat-exchanger systems of electric power plants and chemical engineering equipment is the transfer of heat and mass between a moving or nonmoving medium and surfaces exposed to contact by liquid films, such as condensates. The character of the flow of thin liquid layers and their hydrodynamic structure largely determine the intensity of the processes involved. Numerous studies [1-6] indicate that one of the characteristic stable regimes is the ripple flow of liquid films, which occurs for certain very small Re numbers [i, 2]. In the majority of practical situations [3-6] the characteristics of the ripple surface profile experience a disordered variation. The most effective approach to the analysis of such flows under these conditions is by probabilistic techniques. The presence of harmonics of different intensities and of components of a purely random process are readily discerned through statistical analysis of the parameters of the given flows.

Water temperature residuals, which are taken as the difference between the daily average water temperature (Missouri River, Boonville, Missouri) and the Fourier series regression fit to the data points, are analyzed. A 1-yr record length is used as a base period. The Kolmogorov-Smirnov test is used to determine, for a given number of extracted harmonics, the sample size required to yield a set of normal random variates with mean zero. It is also shown that with only the fundamental harmonic removed, a sample size of at least 180 is required to yield a sample average residual of less than 0.2°F. When the fundamental and higher order harmonics are removed, this sample size is reduced considerably.

A new monolithic structure for solid-state traveling-wave amplifiers is proposed, which promises efficient interaction between a drifting charge carrier stream and a slow electromagnetic wave component. The suggested configuration is potentially suitable for operation in the far-ir frequency regime. A one-dimensional analysis of the interaction between the electromagnetic waveguide mode and the carrier current is presented, including the loss contribution due to the nonsynchronous space harmonics of the electromagnetic mode.

It is proposed that the frequency differences between CO2 laser ines and the harmonics of these differences might be used as intermediate frequencies to bridge the gap between microwave frequency standards and infrared frequencies to simplify absolute measurements of the latter. Tungsten-nickel point-contact diodes would be used as harmonic generators and mixers. The preliminary results of an experimental feasibility study are presented. A description of a novel two-frequency laser, built for this study, is given. It is shown that beat frequencies between differences up to 715 GHz and microwave frequency harmonics up to the twelfth can be observed; interactions with at least the third harmonic of a CO2 frequency difference are possible, producing signals with an S/N of 51 dB in a 2.2-s time constant receiver; attempts to observe a beat between a CO2 frequency and the seventh harmonic of a difference were not successful.

HV DC transmission schemes can have system conditions in which the ac system is in resonance with the ac harmonic filters at particular harmonics of the supply frequency, and these resonances may be excited by transformer magnetizing inrush currents, generating overvoltages at the ac busbars of the HV DC convertor station. In the case of a rectifier station, supplied directly by generators with no local load, these overvoltages may be as high as twice the rated voltage and may exist for many cycles of the supply frequency. This effect is examined in this paper and the results of many thousands of model tests are included.

This paper describes a method of computing harmonics and waveforms in HVdc conversion, taking into account interaction with the ac system, dynamically. The perfbrmance of filters tuned at a nominal frequency is examined when the ac system frequency varies. Computed values of harmonic currents and voltages are presented and the influence of the ac system short circuit ratio is demonstrated. Harmonic magnification can occur due to resonance effects, but the system is harmonically stable.

The general trend of the forces generated by a nonuniform tire and wheel as a function of speed has been available for several years. As a rule it has been found that the first harmonic of the force variation is the greatest single contributory factor in those vehicle shake problems originating at the tire and wheel. The paper shows how the first harmonic varies with speed for a batch of tires, and, in particular, discusses the phase and amplitude relationship between longitudinal force variation and radial force variation with speed; a mathematical analysis is given. Attempts to counteract the high speed nonuniformity forces by using balance weights on the wheel are reported. The relative effect of the tire and the wheel is considered. Also, the application of this work as a vehicle shake diagnostic technique to isolate tire wheel assembly and vehicle effects is discussed.

A study was made of nonequtlibrium mixing of ultrashort laser pulses. The theory was developed for the Gaussian and Lorentzian distributions of the original waves; the latter case was analyzed in detail. Nonequilibrium generation (by a cascade method) of the third harmonic of a laser emitting locked longitudinal modes was observed experimentally. It was predicted theoretically and confirmed experimentally that the width of the spectrum of the harmonic frequency reached saturation under nonequilibrium mixing conditions. The measured spectra of the second and third harmonics generated under quasistatic conditions and the ratio of their widths indicated that the spectrum of a train of ultrashort laser pulses was Lorentzian. Calculations were also made of the characteristic parameters of the nonequilibrium generation of sum frequencies in KDP and CaCO3 crystals.

The most common approach to the study of plasma nonlinearities is by a form of perturbation theory which first studies the linearized equations, then evaluates effects of nonlinearities in terms of these linear solutions. Such an approach is probably justifiable for the effect of weak nonlinearities, but will almost certainly miss features that are exclusively nonlinear in nature (i.e. effects which cannot be described by modifying linear theory, or effects which are present only when e.g. a source of disturbances in a plasma reaches a certain threshold amplitude). It is the object of this paper to investigate one possible such nonlinear effect.

Waves of small but finite amplitude in shallow water can occur as periodic wave trains of permanent shape in two known forms, either as Stokes waves for the shorter wavelengths or as cnoidal waves for the longer wavelengths. Calculations are made here of the periodic wave trains of permanent shape which span uniformly the range of increasing wavelength from Stokes waves to cnoidal waves and beyond. The present investigation is concerned with the stability of such permanent waves to periodic disturbances of greater or equal wavelength travelling in the same direction. The waves are found to be stable to infinitesimal and to small but finite disturbances of wavelength greater than the fundamental, the margin of stability decreasing either as the fundamental wave becomes more nonlinear (i.e. contains more harmonics), or as the wavelength of the periodic disturbance becomes large compared with the fundamental wavelength. The decreasing margin of stability is associated with an increasing loss of spatial periodicity of the wave train, to the extent that small but finite disturbances can cause a form of interaction between consecutive crests of the disturbed wave train. In such a case, a small but finite disturbance of wavelength n times the fundamental wavelength converts the wave train into n interacting wave trains. The amplitude of the disturbance subharmonic is then nearly periodic, the time scale being the time taken for repetitions of the pattern of interactions. When the disturbance is of the same wavelength as the permanent wave, the wave is found to be neutrally stable both to infinitesimal and to small but finite disturbances.

Cosmos 359 rocket 1970-65D, was launched on 22 August 1970 into an orbit inclined at 51·2° to the Equator, with an initial perigee height of 209 km: it decayed on 6 October 1971 after a lifetime of 410 days. The orbit has been determined at 42 epochs during the lifetime, using the RAE orbit refinement program, PROP, with over 2600 observations. Observations from the Hewitt cameras at Malvern and Edinburgh were available for 10 of the 42 orbits. Ten values of density scale height, at heights between 185 and 261 km, have been determined from analysis of the variations in perigee height. Upper-atmosphere zonal winds and 15th-order harmonics in the geopotential have been evaluated from the changes in orbital inclination. The average atmospheric rotation rate, for heights near 220 km, is found to be 1·04 rev/day; but there are striking departures from the average, with well-established values of 1·30, 0·75, 1·35 and 0·95 over four successive 75-day intervals. The changes in inclination at the 15th-order resonance in November 1970 give values of lumped 15th-order harmonics, which will provide equations for evaluating coefficients of order 15 and even degree (16,18,…) and also show that useful results on the geopotential can be obtained from satellites with perigee as low as 200 km.

This paper develops steady-state time harmonic expressions for synchronous motors. Using these expressions, the current harmonics and waveforms for motors supplied by variable-frequency solid-state power converters can be predicted. Such waveforms are particularly useful in the design of inverter commutation circuits. The models include the effects of saliency and dampers. Experimental results are included to confirm the analysis and show its limitations.