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The method of multiple scales is used to derive a nonlinear Schroedinger equation for the temporal and spatial modulation of the amplitudes and the phases of waves propagating in a hard-walled circular duct. This equation is used to show that monochromatic waves are stable and to determine the amplitude dependance of the cutoff frequencies.
The method of multiple scales is used to derive a nonlinear Schroedinger equation for the temporal and spatial modulation of the amplitudes and the phases of waves propagating in a hard-walled circular duct. This equation is used to show that monochromatic waves are stable and to determine the amplitude dependance of the cut off frequencies.
Adiabatic demagnetization (ADRF) can be achieved in a dipolar coupled nuclear spin system in solids by applying a string of short RF pulses and gradually modulating the pulse amplitudes or pulse angles. This letter reports an adiabatic inverse polarization effect in solids and a rotary spin echo phenomenon observed in liquids when the pulse angle is gradually changed across integral multiples of pi during a string of RF pulses. The RF pulse sequence used is illustrated along with the NMR signal from a CaF2 single crystal as observed between the RF pulses and the rotary spin echo signal observed in liquid C6F6 for n = 2. The observed effects are explained qualitatively on the basis of average Hamiltonian theory.
The linear stability of three-dimensional incompressible, isothermal, nonparallel boundary-layer flows has been investigated. The method of multiple scales is used to derive the partial-differential equations that describe the spatial modulations of the amplitude, phase and wavenumber of a disturbance. Group velocities are used to determine the disturbance growth direction. The envelope method is used to calculate the logarithmic amplitude growth rate N. The theory is applied to the flows over a swept-back tapered wing with boundary-layer suction. Results of such analysis for the X-21 wing are discussed. It is found that the nonparallel effects for this wing is substantial.
During a 60-day period in the summer of 1982, a joint observing project between the High Altitude Observatory and the University of Hawaii was undertaken to collect a set of solar photospheric, chromospheric, and coronal data. From these data, the relationships between quantities recognized to be related to solar activity are specified. The amplitude of rotational modulation of the diagnostic parameters derived for the full disk was approximately equal to the modulation observed over an entire solar cycle. Those integrated solar data have been used as diagnostics of generalized stellar activity. A relationship between the Ca II line K flux and total inferred coronal mass of the sun existed during this observation period, and this fact leads to the hypothesis that ca II flux modulation in other stars may be used to infer stellar coronal conditions.
Highlights of recent Stanford University VLF research in the Antarctic include new observations of wave-induced particle precipitation and controlled experiments on nonlinear wave growth phenomena. Higher-than-expected levels of burst precipitation have been discovered inside the plasmasphere, near L = 2, using subionospheric signal perturbations called 'Trimpi events'. Studies of burst precipitation have been extended to the region poleward of the plasmapause using the Siple transmitter signal as a waveguide probe. Experiments on the 'coherent wave instability', using the amplitude and frequency modulation capability of the new Siple transmitter, have produced exciting new results. Examples are: (1) better definition of the power threshold for the stimulation of temporal wave growth, (2) generation of strong sidebands by unamplified 'beat' waves and (3) generation of chorus-like elements within a band of simulated hiss. Using a new digital processing technique developed at Stanford, new features of the phase behavior of growing waves have been found. Opportunities for extending these experiments are discussed.
A new type of dual wavelength He-Ne laser is described in which the output power at each of the two wavelengths is modulated with equal amplitude and opposite phase to each other. This laser source can greatly simplify the setup and improve the sensitivity of the differential absorption measurements for the methane detection, as verified by a preliminary experiment. A simple scheme to measure the concentration of methane is also proposed.
Over the past decade considerable strides were made in explicating the antecedant conditions necessary for the elicitation, and the modulation of the amplitude and latency, of a number of components of the event-related brain potential (ERP). The focus of this report is on P300. The degree to which the psychophysiological measures contribute to issues in two real-world domains (communication devices for the motor impaired and the assessment of mental workload of aircraft pilots) are examined.
CCD time-resolved V and B differential light curves are presented for the dwarf novae AR And, FS Aur, TT Boo, UZ Boo, AF Cam, AL Com, AW Gem, X Leo, RZ Leo, CW Mon, SW UMa, and TW Vir. The time-series observations ranged from 2 to 6 hours and have accuracies of 0.025 mag or better for the majority of the runs. Except for AR And, X Leo, CW Mon, and TW Vir, the periods are below the cataclysmic-variable period gap (about 2 hours), and the systems are potential SU UMa stars. Photometric periods for five of the stars are the first such determinations, while those for the other seven generally confirm previous spectroscopic or photometric observations. In several cases, the photometric modulations are large amplitude (up to 0.5 mag). The results on AL Com and SW UMa indicate they may be magnetic variables.
The low-mass X-ray binary GX 9+9 (4U 1728-16) was observed during September 13-19, 1977, and March 11-17, 1978, with the HEAO A-1 instrument in scanning mode. An algorithm for detecting periodicities in the resulting light curves has been applied; it is based on the Scargle periodogram and takes into account the non-Gaussian nature of the intrinsic source variability. A 4.19 + or - 0.02 hr periodic modulation is detected in the September 1977 data. The folded light curve shows sinusoidal modulation with an amplitude of 3.8 percent. This amplitude is comparable to the 4.6 percent residual intrinsic source variability at all phases of the light curve. The 4.19 hr period is interpreted as the binary period of the system. The lack of eclipses and the sinusoidal light curve imply that the binary system is viewed at a low inclination angle of less than about 63 deg. Light curves of this type may be relatively common among low-mass X-ray binaries, but are difficult to detect without the long observations and high sensitivity possible with HEAO A-1.
Fifty-seven observations of the solar analogue Alpha Centauri A made by the IUE over a 3-year interval have been examined for variability. It is found that the UV continuum flux of this star in the 1715- to 1915-A range varies by as much as 19 percent. However, nearly all of this range in variability can occur within one stellar rotation period. Consequently, if Alpha Cen A undergoes a stellar activity cycle similar to that of the sun, the results indicate that the amplitude of this modulation is small, contrary to recently proposed empirical (theoretical) models of solar activity.
The status of the Joint University Program is given. Brief synopsis of some areas of research follow. The study of spectrum efficient methods for transmitting weather information to aircraft has resulted in definition of an improved amplitude and phase modulation process which permits reutilization of voice channels for both voice and data. The system is being implemented for testing. Multisensor navigation systems introduce increased flexibility and performance for aviation, at the expense of increased complexity. Insuring a high level of system reliability and integrity requires that faults not only be detected, but also isolated to specific elements, so that the remaining capabilities of the system may be used with confidence. An algorithm was developed. The JUP has served as a vehicle for reporting work accomplished in evoked potential vision tracking experiments to determine the engineering parameters of this input and control method. Application of GPS in an interferometric mode permits accurate measurement of differential motion; aircraft attitude may be determined using GPS only, with multiple antennas.
The magnitude and nature of residuals expected in the times of pulsar arrival (TOA) of the millisecond pulsar PSR 1257 + 12 as a function of the observational time span is estimated so that an observing progam may be planned to optimize the detection of a perturbation signature of a possible planetary system. The numerical and analytic procedures for evaluating the residuals are described. Calculations results are given in which a recognizable signature is shown to be a modulation of the amplitude of the TOA residual differences as a function of both epoch and observational interval. A supplementary approach involving intensive closely spaced observations over selected time intervals to find the time of a particular zero crossing of the TOA residuals is also discussed.
The Joint University Program (JUP) offers students, faculty, and staff of the Avionics Engineering Center the opportunity to conduct basic research relating to the safety and efficiency of the National Airspace System. During the 1993-1994 year research was continued in a variety of GPS-related technologies and also in a hybrid data uplink system. (1) Processing techniques developed for the GPS attitude determination have been applied to centimeter-level kinematic GPS aircraft positioning for flight reference systems and aircraft autoland and taxiing operations. This resulted in the first real-time kinematic GPS autoland. (2) The fault detection and isolation (FDI) algorithm developed under the Joint University Program has been fully adopted by RTCA Special Committee 159 as the baseline algorithm for sole-means navigation of GPS integrated with GLONASS, LORAN-C, or baro-altimeter. (3) A Satellite Coverage Research Analysis Model (SCRAM) has been developed which provides outage areas, outage dynamics, and availability information for satellite-based navigation systems. RTCA Special Committee 159 has adopted this model for use in their work. (4) A basic receiver structure has been simulated and tested for use with the hybrid data uplink. This uplink utilizes the phase of an existing AM carrier to transmit digital data, thus both amplitude and phase modulation are applied, resulting in a hybrid carrier. The receiver simulation is directly applicable to real-time implementation as a result of the development platform.
Resonances or near resonances are ubiquitous among the excited nonradial pulsation modes of variable stars and they must play an important role in determining their pulsational behavior. Here in a first step at nonlinear asteroseismology, we explore some of the consequences of resonances by means of the amplitude equation formalism. We show how parity and angular momentum constraints can be used to eliminate many of the possible nonlinear resonant couplings between modes (and multiplets of modes), and how the amplitude equations can thus be simplified. Even when we may not be able, nor wish, to make an ab initio computation of the values of the coupling coefficients, it is still possible to obtain constraints on the nature of the excited modes if a resonance between observed frequencies can be identified. Resonances can cause nonlinear frequency locking of modes. This means that the observed frequencies appear in exact resonance even though the linear frequencies are only approximately in resonance. The nonlinear frequency lock, when it occurs, it does so over a range of departures from linear resonance, and it is accompanied by constant pulsation amplitudes. The locked, nonlinear frequencies can differ noticeably from their nonresonant counterparts which are usually used in seismology. This is particularly true for multiplets of modes split by rotation. Beyond the regime of the frequency lock, amplitude and frequency modulations can appear in the pulsations. Far from the resonance condition one recovers the regime of steady pulsations with nonresonant frequencies for which the seismological studies, as they are presently carried out, are justified (provided furthermore, of course, that nonlinear frequency shifts are negligible). Success in identifying a resonance in an observed power spectrum depends on the quality of the data. While keeping this limitation in mind, ew discuss the possible existence of peculiar resonances the pulsations specific variable white dwarfs and delta Scuti stars.
Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.
This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.
A method of polarimetric imaging, now undergoing development, involves the use of two photoelastic modulators in series, driven at equal amplitude but at different frequencies. The net effect on a beam of light is to cause (1) the direction of its polarization to rotate at the average of two excitation frequencies and (2) the amplitude of its polarization to be modulated at the beat frequency (the difference between the two excitation frequencies). The resulting modulated optical light beam is made to pass through a polarizing filter and is detected at the beat frequency, which can be chosen to equal the frame rate of an electronic camera or the rate of sampling the outputs of photodetectors in an array. The method was conceived to satisfy a need to perform highly accurate polarimetric imaging, without cross-talk between polarization channels, at frame rates of the order of tens of hertz. The use of electro-optical modulators is necessitated by a need to obtain accuracy greater than that attainable by use of static polarizing filters over separate fixed detectors. For imaging, photoelastic modulators are preferable to such other electrio-optical modulators as Kerr cells and Pockels cells in that photoelastic modulators operate at lower voltages, have greater angular acceptances, and are easier to use. Prior to the conception of the present method, polarimetric imaging at frame rates of tens of hertz using photoelastic modulators was not possible because the resonance frequencies of photoelastic modulators usually lie in the range from about 20 to about 100 kHz.