Hysteresis, Switching and Anomalous Behaviour of a Quartz Tuning Fork in Superfluid 4He

Bradley, D. I.; Fear, M. J.; Fisher, S. N.; Guénault, A. M.; Haley, R. P.; Lawson, C. R.; Pickett, G. R.; Schanen, R.; Tsepelin, V.; Wheatland, L. A.

doi:10.1007/s10909-013-0931-5

Cited by 7 publications

(5 citation statements)

References 15 publications

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“…Figure 2 shows the tip velocity amplitude versus the amplitude of the driving force, which is equal to the dissipative drag force. These results were briefly reported earlier [18]. The points in the figure show the locations of the flow transitions for many sweeps of the driving force.…”

Section: Methodssupporting

confidence: 83%

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Stability of flow and the transition to turbulence around a quartz tuning fork in superfluidHe4at very low temperatures

et al. 2014

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We have studied the transition between pure potential flow and turbulent flow around a quartz tuning fork resonator in superfluid 4 He at millikelvin temperatures. Turbulent flow is identified by an additional drag force on the fork prongs due to the creation of quantized vortices. When driven at a constant driving force amplitude, the transition to turbulence causes an abrupt decrease in the velocity amplitude of the prongs. For a range of driving forces, continuous switching is observed between the two flow states. We have made a statistical study of the switching characteristics and of the lifetimes of the unstable states. We find a characteristic velocity v which separates quasistable turbulent flow at higher velocities and quasistable potential flow at lower velocities. We show that the potential-to-turbulent flow transition is driven by random processes involving remanent vortices pinned to the prongs.

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Section: Methodssupporting

confidence: 83%

“…The two states are easily distinguished by their different force-velocity relationships, which are highly reproducible. However, the transition itself is highly irreproducible and hysteretic [5,18]. Similar behavior has been observed with vibrating wires [14,19,20] and vibrating spheres [13].…”

Section: Introductionsupporting

confidence: 67%

Stability of flow and the transition to turbulence around a quartz tuning fork in superfluidHe4at very low temperatures

et al. 2014

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“…The correct physical picture requires experiments that could visualize the vortices around the sphere or more realistic computer simulations. Hysteresis and switching of the flow have been observed also with vibrating tuning forks and wires [8,9,10] and the significance of remanent vorticity for the critical velocity v * c at breakdown was demonstrated [3,11]. In our work we are relating v * c directly to the intervortex spacing of the remanent vortex density.…”

Section: Discussionmentioning

confidence: 71%

Breakdown of Potential Flow to Turbulence Around a Sphere Oscillating in Superfluid $$^4$$ 4 He Above the Critical Velocity

2015

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The onset of turbulent flow around an oscillating sphere in superfluid 4 He is known to occur at a critical velocity vc ∼ √ κ ω where κ is the circulation quantum and ω is the oscillation frequency. But it is also well known that initially in a first up-sweep of the oscillation amplitude, vc can be considerably exceeded before the transition occurs, thus leading to a strong hysteresis in the velocity sweeps. The velocity amplitude v * c > vc where the transition finally occurs is related to the density L 0 of the remanent vortices in the superfluid. Moreover, at temperatures below ca. 0.5 K and in a small interval of velocity amplitudes between vc and a velocity that is about 2% larger, the flow pattern is found to be unstable, switching intermittently between potential flow and turbulence. From time series recorded at constant temperature and driving force the distribution of the excess velocities ∆v = v * c − vc is obtained and from that the failure rate. Below 0.1 K we also can determine the distribution of the lifetimes of the phases of potential flow. Finally, the frequency dependence of these results is discussed.

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“…Simultaneously, inductance L com compensates capacitance C 0 between the piezoelectric crystal electrodes, which improves the pulling sensitivity. The measurement method is based on the oscillator and the switching part of the circuit, alternatively switching reactances with the digital signal (Q = 1, Q = 0) [1, 2,16,22,31,40,41]. The output frequency f out3 (Equation (22) represents the output oscillator frequency, which is synchronously measured with regard to the switch of the digital signal.…”

Section: Similar Crystal Temperature-frequency Characteristics Compenmentioning

confidence: 99%

“…The stability of the output frequency f out3 is ±0.001 ppm in the temperature range 10-40 • C (Figure 10, cutting angle 0 ) [3,16,18]. Figure 14 shows the switching mode method for the compensation of the crystal's own temperaturefrequency characteristics by two inductances, L ref_com and L x (L ref_com L x ) [1, 2,16,22,31,40,41]. Capacitance C 0 compensation between the piezoelectric crystal's electrodes is achieved by the value of L ref and L x , and by the already explained Equations (13) and (14).…”

Section: Crystal's Temperature-frequency Characteristics Compensationmentioning

confidence: 99%

Detection Principles of Temperature Compensated Oscillators with Reactance Influence on Piezoelectric Resonator

Matko

Milanovič

2020

Sensors

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This review presents various ways of detection of different physical quantities based on the frequency change of oscillators using piezoelectric crystals. These are influenced by the reactance changes modifying their electrical characteristics. Reactance in series, in parallel, or a combination of reactances can impact the electrical crystal substitute model by influencing its resonant oscillation frequency. In this way, various physical quantities near resonance can be detected with great sensitivity through a small change of capacitance or inductance. A piezoelectric crystal impedance circle and the mode of frequency changing around the resonant frequency change are shown. This review also presents the influence of reactance on the piezoelectric crystal, the way in which the capacitance lost among the crystal's electrodes is compensated, and how the mode of oscillators' output frequency is converted to lower frequency range (1-100 kHz). Finally, the review also explains the temperature-frequency compensation of the crystals' characteristics in oscillators that use temperature-frequency pair of crystals and the procedure of the compensation of crystals own temperature characteristics based on the method switching between the active and reference reactance. For the latter, the experimental results of the oscillator's output frequency stability (f out = ±0.002 ppm) at dynamical change of environment temperature (0-50 • C) are shown.

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Hysteresis, Switching and Anomalous Behaviour of a Quartz Tuning Fork in Superfluid 4He

Cited by 7 publications

References 15 publications

Stability of flow and the transition to turbulence around a quartz tuning fork in superfluidHe4at very low temperatures

Stability of flow and the transition to turbulence around a quartz tuning fork in superfluidHe4at very low temperatures

Breakdown of Potential Flow to Turbulence Around a Sphere Oscillating in Superfluid $$^4$$ 4 He Above the Critical Velocity

Detection Principles of Temperature Compensated Oscillators with Reactance Influence on Piezoelectric Resonator

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