Frequency Doubling Effect Research Articles

Preliminary studies of an oscillating mercury-droplet electrode

Personnel at the Oak Ridge Y-12 Plant, 3 3 Operated by Martin Marietta Energy Systems, Inc., for the U.S. Department of Energy under Contract DE-AC05-84OR21400. Oak Ridge, Tennessee, have observed and measured the resonance frequencies of eight of the lowest frequency modes of axisymmetric vibration, plus a rocking mode of vibration, for a sessile mercury droplet. This droplet, submerged in a dilute electrolyte solution, was the working electrode within an electrochemical cell. This cell was mounted in the modified cone of a loud speaker. Resonance frequencies were determined by varying the input frequency to the speaker until an optimum mercury-droplet oscillation effect was observed in the current response of the electrochemical cell. Two major types of changes in the current response were observed as input near the resonance frequency caused the mercury-droplet electrode to oscillate. The first effect was that a major current component which oscillated at twice the input frequency developed. This frequency-doubling effect was caused by the periodic variation in the charging and discharging rates as the surface area of the electrical double layer surrounding the mercury droplet expanded and contracted. The second effect was related to the current response due to the electrochemical reduction or oxidation of species in solution. By this process, Faradaic current arising from “microstirring” the electrolyte solution at the surface of the oscillating mercury-droplet electrode caused an appreciable steady-state shift in the baseline of the output current.

Three-wave interaction including frequency doubling effects

A technique is developed in this work to construct asymptotic solutions describing the resonant interaction of shortwaves in weakly nonlinear dispersive media. Also included is the process of generation of multiple harmonics for low dispersion. A calculation of the acoustooptical interaction is performed, including the generation of multiple harmonics of acoustic waves.

On the rank of certain classes of cut-sets and tie-sets of a graph

distributed throughout the plane. This point is relevant to smallintestinal modeling, since only one mode is known to exist in this organ, and thus capacitive coupling appears unlikely as the predominant form of coupling. Resistively coupled oscillators have normally been considered to give a single mode only, and this has been shown to be true for small nonlinearity and small asymmetry. Such a condition appears to exist in the small intestine where waveforms are not highly asymmetrical. Under conditions of high asymmetry a stable antiphase mode has been found which persists down to low coupling values. This mode is equivalent to a ‘stable alternation’ condition noticed by Lewis [lo] in neural modeling. Lewis observed this mode in an electronic model based on Hodgkin-Huxley equations. In this type of electronic model the mode could only be excited for space: mark ratios (i.e., ratio of negative-going period of waveform to its positive-going period) of greater than 3: 1, and similarly in the van der Pol model b had to be greater than 1.0 indicating a high space: mark ratio. For b =0.8 the space: mark ratio was about 3: 1 and stable alternation did not occur. The nonexistence of the mode can be explained by considering the rising portion of the negative section of the waveform (see Fig. 2). For wide pulse widths this portion rises relatively rapidly and the injected current from the adjacent oscillator is sufficient to drive the oscillator into positive pulse generation. Thus the oscillators are forced into inphase entrainment under all conditions. Such a condition does not occur in capacitive coupling since the feedthrough is a differentiated pulse and has equal positive and negative effects. For narrow pulsewidths, however, the feedthrough for resistive coupling is small and occurs during the slowly rising negative period of an oscillator output. In this case insufficient energy is fed through to force the oscillator into its pulse generation phase. The mode stabilizes at 180” because of symmetrical coupling, in that any other phase shift would mean one oscillator having injected energy nearer to the threshold point of pulse generation. This behavior is related to threshold and refractoriness properties of van der Pol and Hodgkin-Huxley oscillations [ 1 I], and has relevance to large-intestinal studies where apparent frequency doubling effects occur. The concept of feedthrough between oscillators explains why antiphase modes are not obtained for inductive coupling under high asymmetry. During the quiescent period of an oscillation, 180” entrainment would mean the injection of the integral of a pulse from the adjacent oscillator. This would not give steady-state conditions and thus the system is always driven to inphase entrainment for which there is no energy transfer between oscillators. For fifth-power van der Pol oscillators the major effect seen from the attraction planes was the increase in likelihood of the double mode as nonlinearity was increased. Greater effects on the relative ease of exciting inphase or antiphase modes would probably have been seen if the size of the zero mode region was reduced, but the values used, however, were representative of conditions existing in the human large intestine [7].

Study of the Shubnikov–de Haas effect in Bi1-XSbX semimetallic alloys

The Shubnikov–de Haas oscillations in Bi1−xSbx semimetallic alloys have been studied over the Sb concentration range 0 ≤ x ≤ 7 at.%. The measurements were carried out at helium temperatures with magnetic fields H of up to 60 kOe in the basal plane of the crystal. The oscillations were Fourier analyzed on a computer to give the dependences on the Sb concentration of the maximum (Smax) and minimum (Smin) cross sections of the electron Fermi surface and of its anisotropy in Bi1−x Sbx alloys. A frequency doubling effect (spin damping) is found; it is shown that the damping angle φd, reckoned from the binary axis in the basal plane, decreases monotonically from the value φd ≈ 2.75° for pure Bi to φd ≈ 0° for the alloy with x ≈ 7 at.% Sb. The correction term to the maximum cross section Smax of the electron Fermi surface resulting from allowance for the movement of the Fermi level in a magnetic field is calculated. The change in the anisotropy of the Fermi surface of Bi1−xSbx alloys is considered within the framework of the Abrikosov–Fal’kovskii model. The angular dependence of the spin splitting Bi1−xSbx alloys is studied.

Stark-PerturbedLαDecay in Flight

The ${\mathrm{L}}_{\ensuremath{\alpha}}$ decay in flight of a 150-keV beam of single-foil-excited hydrogen atoms was tracked with a Geiger-Muller counter transversely viewing successive cylindrical segments of the beam as the counter was moved downstream. An adjustable transverse magnetic field encompassing both the foil and viewing regions produced Stark-induced ${\mathrm{L}}_{\ensuremath{\alpha}}$ intensity oscillations. The experimental fluctuation frequency disagrees with a previously published measurement of Bickel but agrees well with the usual Bethe-Lamb theory of Stark quenching. No frequency doubling effect is found. New information about foil collision dynamics emerges from studying the phase of the fluctuation patterns and the decay rates of the observed radiation. Our conclusion concerning relative ${s}_{\frac{1}{2}}$- and ${p}_{\frac{1}{2}}$- state populations is also in disagreement with the earlier work.

Frequency Doubling in Visual Responses*†

This paper reports an unexpected visual phenomenon. When a wide, photopic stimulus field is sinusoidally modulated in both space and time, over a certain frequency range the apparent spatial frequency of the stimulus is doubled. In its original form, the (deLange) flicker-fusion model which has been accepted by the author and others cannot account for this result. But it can be explained by assuming that there is a second (low-pass) filtering operation which follows the nonlinear (brightness) response of the visual system, rather than preceding it. If this hypothesis is correct, then the frequency-doubling effect is the result of neural mechanisms which are more central than the locus of flicker fusion.