Contributors: Yu.P. Emelianova, A.P. Kuznetsov, I.R. Sataev, L.V. Turukina

Date: 2013-02-01

Trajectories on the phase torus. (a) resonant two-frequency regime with winding number w=1:2, (b) three-frequency regime. ...(Color online). Chart of the Lyapunov’s exponents for the system of three coupled phase oscillators (5) for Δ2=1. The color palette is given and decrypted under the picture. The numbers indicate the tongues of the main resonant two-frequency regimes. These regimes are explained in the description of Fig. 5. ...Rotation numbers ν1–2 and ν2–3 versus the frequency detuning Δ1 for the system (11). Values of the parameters are λ1=1.3,λ2=1.9,λ3=1.8,Δ2=1.5 and μ=0.32. ...Subdivision of the chain of four oscillators by clusters for the three types of the phase locked pair of oscillators. Parameters are chosen in such a way that the system of oscillators is near the point of the saddle–node bifurcation. ...Schematic representation of a system of three coupled self-oscillators. ...The problem of growing complexity of the dynamics of the coupled phase oscillators as the number of oscillators in the chain increases is considered. The organization of the parameter space (parameter of the frequency detuning between the second and the first oscillators versus parameter of dissipative coupling) is discussed. The regions of complete synchronization, quasi-periodic regimes of different dimensions and chaos are identified. We discuss transformation of the domains of different dynamics as the number of oscillators grows. We use the method of charts of Lyapunov exponents and modification of the method of the chart of dynamical regimes to visualize two-frequency regimes of different type. Limits of applicability of the quasi-harmonic approximation and the features of the dynamics of the original system which are not described by the approximate phase equations are discussed for the case of three coupled oscillators....Phase oscillators ... The problem of growing complexity of the dynamics of the coupled phase oscillators as the number of oscillators in the chain increases is considered. The organization of the parameter space (parameter of the frequency detuning between the second and the first oscillators versus parameter of dissipative coupling) is discussed. The regions of complete synchronization, quasi-periodic regimes of different dimensions and chaos are identified. We discuss transformation of the domains of different dynamics as the number of oscillators grows. We use the method of charts of Lyapunov exponents and modification of the method of the chart of dynamical regimes to visualize two-frequency regimes of different type. Limits of applicability of the quasi-harmonic approximation and the features of the dynamics of the original system which are not described by the approximate phase equations are discussed for the case of three coupled oscillators.

Contributors: M.R. Qader

Date: 2013-01-01

Driven qubit...The transient scattered radiation due to interaction of a short laser pulse (of rectangular shape) with a qubit is studied through the Haar wavelet window spectrum. Asymmetrical structure in the spectrum is shown due to frequency miss-match of the laser and qubit frequencies and the shift window parameter. ... The transient scattered radiation due to interaction of a short laser pulse (of rectangular shape) with a qubit is studied through the Haar wavelet window spectrum. Asymmetrical structure in the spectrum is shown due to frequency miss-match of the laser and qubit frequencies and the shift window parameter.

Contributors: Václav Tesař

Date: 2014-01-01

Comparison of the oscillation in Fig. 17 and the basic frequency component L in Fig. 23. The replacement of the feedback channel loops by open areas for vortical flow made the feedback paths slightly shorter (and therefore the frequency higher)....Measured oscillation frequency with different feedback tube lengths of the oscillator shown in Fig. 7, plotted as a function of the supplied flow rate. Surprisingly, the frequency is neither proportional to the flow rate (as is usual in the constant Strouhal-number oscillators, e.g., Tesař et al., 2006) – nor constant (as in the oscillators with resonator channel (Tesař et al., 2013)). ...Efficient generation of sub-millimetre microbubbles was recently made possible by pulsating the flow of gas supplied into a parallel-exits aerator, using a fluidic oscillator for the purpose. Without moving parts, it can generate oscillation at high frequency, an important factor due to bubble natural frequency rapidly increasing with the desirable decrease of their size. This paper discusses development of an unusual oscillator – a part of an integral oscillator/aerator unit – capable of generating a particularly high driving frequency, in the kilohertz range, in a layout that promotes a strong third harmonic frequency of the basic oscillation....Fluidic oscillator...Results of measured dependence of oscillation frequency on the supplied flow rate in the layout shown in Figs. 20 and 12. Apart from basic frequency L, the output spectrum exhibited a much higher frequency component H. ...Frequency of generated oscillation plotted as a function of the air flow rate. Similarly as in Fig. 9 this dependence does not the fit the usual (constant Strouhal number) proportionality between frequency and flow rate. ...Basic data on the geometry of the oscillator used in the high-frequency experiments. ...Dependence of bubble natural oscillation frequency on the size – based on the measurements in Tesař (2013b). The line is fitted for constant value of oscillation Weber number We0. ... Efficient generation of sub-millimetre microbubbles was recently made possible by pulsating the flow of gas supplied into a parallel-exits aerator, using a fluidic oscillator for the purpose. Without moving parts, it can generate oscillation at high frequency, an important factor due to bubble natural frequency rapidly increasing with the desirable decrease of their size. This paper discusses development of an unusual oscillator – a part of an integral oscillator/aerator unit – capable of generating a particularly high driving frequency, in the kilohertz range, in a layout that promotes a strong third harmonic frequency of the basic oscillation.

Contributors: Niko Bako, Adrijan Baric

Date: 2013-12-01

Oscillator...Block scheme of the oscillator. ...Reference current and the oscillator frequency variations as a function of supply voltage and temperature obtained by simulations. (a) Reference current variation for typical (TT), slow (SS) and fast (FF) process corners with respect to the reference current at room temperature. (b) Frequency variation for typical, slow and fast corners with a supply voltage as a parameter with respect to frequency at room temperature. ...A low-power, 3.82MHz oscillator based on a feedback loop is presented. The oscillator does not need a stable current reference to obtain a stable frequency independent of voltage and temperature variations because of the usage of negative feedback. The frequency variation, in the temperature range from −20°C to 80°C, is±0.6% and it depends only on the temperature coefficient of the resistor R, while the reference current variations are −11%/+25% in the same temperature range. The oscillator power consumption is 5.1μW and the active area is 0.09mm2. The proposed oscillator is implemented in a 0.18μm CMOS process and the simulation results are shown....The oscillator layout. ...Supply voltage compensated frequency...Simulated oscillator output. ...Temperature compensated frequency ... A low-power, 3.82MHz oscillator based on a feedback loop is presented. The oscillator does not need a stable current reference to obtain a stable frequency independent of voltage and temperature variations because of the usage of negative feedback. The frequency variation, in the temperature range from −20°C to 80°C, is±0.6% and it depends only on the temperature coefficient of the resistor R, while the reference current variations are −11%/+25% in the same temperature range. The oscillator power consumption is 5.1μW and the active area is 0.09mm2. The proposed oscillator is implemented in a 0.18μm CMOS process and the simulation results are shown.

Contributors: Weixiong Chen, Quanbin Zhao, Yingchun Wang, Palash Kumar Sen, Daotong Chong, Junjie Yan

Date: 2016-09-01

Submerged steam jet condensation is widely applied in various fields because of its high heat transfer efficiency. Condensation oscillation is a major character of submerged steam turbulent jet, and it significantly affects the design and safe operation of industrial equipment. This study is designed to reveal the mechanism of the low-frequency pressure oscillation of steam turbulent jet condensation and determine its affected region. First, pressure oscillation signals with low frequency are discovered in the downstream flow field through oscillation frequency spectrogram and power analysis. The oscillation frequency is even lower than the first dominant frequency. Moreover, the critical positions, where the low-frequency pressure oscillation signals appear, move downstream gradually with radial distance and water temperature. However, these signals are little affected by the steam mass flux. Then, the regions with low-frequency pressure oscillation occurring are identified experimentally. The affected width of the low-frequency pressure oscillation is similar to the turbulent jet width. Turbulent jet theory and the experiment results collectively indicate that the low-frequency pressure oscillation is generated by turbulent jet vortexes in the jet wake region. Finally, the angular coefficients of the low-frequency affected width are obtained under different water temperatures. Angular coefficients, ranging from 0.2268 to 0.2887, decrease with water temperature under test conditions....Frequency spectrograms distribution along the axial direction (R/D=2). ...Frequency spectrograms of condensation oscillation [21]. ...Frequency spectrograms under radial position of R/D=3.0 and R/D=4.0. ...Half affected width of pressure oscillation. ...Pressure oscillation...Oscillation power axial distribution for low frequency region. ... Submerged steam jet condensation is widely applied in various fields because of its high heat transfer efficiency. Condensation oscillation is a major character of submerged steam turbulent jet, and it significantly affects the design and safe operation of industrial equipment. This study is designed to reveal the mechanism of the low-frequency pressure oscillation of steam turbulent jet condensation and determine its affected region. First, pressure oscillation signals with low frequency are discovered in the downstream flow field through oscillation frequency spectrogram and power analysis. The oscillation frequency is even lower than the first dominant frequency. Moreover, the critical positions, where the low-frequency pressure oscillation signals appear, move downstream gradually with radial distance and water temperature. However, these signals are little affected by the steam mass flux. Then, the regions with low-frequency pressure oscillation occurring are identified experimentally. The affected width of the low-frequency pressure oscillation is similar to the turbulent jet width. Turbulent jet theory and the experiment results collectively indicate that the low-frequency pressure oscillation is generated by turbulent jet vortexes in the jet wake region. Finally, the angular coefficients of the low-frequency affected width are obtained under different water temperatures. Angular coefficients, ranging from 0.2268 to 0.2887, decrease with water temperature under test conditions.

Contributors: Ch. Wunderlich, Ch. Balzer

Date: 2003-01-01

Illustration of a linear ion trap including an axial magnetic field gradient. The static field makes individual ions distinguishable in frequency space by Zeeman-shifting their internal energy levels (solid horizontal lines represent qubit states). In addition, it mediates the coupling between internal and external degrees of freedom when a driving field is applied (dashed horizontal lines stand for vibrational energy levels of the ion string, see text). ...Rabi oscillations on the optical E2 transition S1/2-D5/2 in Ba + . A fit of the data (solid line) yields a Rabi frequency of 71.4 × 2πkHz and a transversal relaxation time of 100 μs (determined by the coherence time of the ir light used to drive the E2 resonance). ...Illustration of the coupled system ‘qubit ⊗ harmonic oscillator’ in a trap with magnetic field gradient. Internal qubit transitions lead to a displacement dz of the ion from its initial equilibrium position and consequently to the excitation of vibrational motion. In the formal description the usual Lamb–Dicke parameter is replaced by a new effective one (see text). ...This chapter discusses quantum measurements and new concepts for experiments with trapped ions. Quantum mechanics is a tremendously successful theory playing a central role in natural sciences even beyond physics, and has been verified in countless experiments, some of which were carried out with very high precision. Quantum theory predicts correlations between two or more quantum systems once an entangled state of these systems has been generated. The chapter introduces experiments with 171Yb+ ions demonstrating the precise manipulation of hyperfine states of single ions essentially free of longitudinal and transverse relaxation. A new concept for ion traps is described that allows for experiments requiring individual addressing of ions and conditional dynamics with several ions even with radiation in the radio frequency (rf) or microwave (mw) regime. It is shown how an additional magnetic field gradient applied to an electrodynamic trap individually shifts ionic qubit resonances making them distinguishable in frequency space. Thus, individual addressing for the purpose of single qubit operations becomes possible using long-wavelength radiation. At the same time, a coupling term between internal and motional states arises even when rf or mw radiation is applied to drive qubit transitions. Thus, conditional quantum dynamics can be carried out in this modified electrodynamic trap and in such a new type of trap all schemes originally devised for optical QIP in ion traps can be applied in the rf or mw regime, too....(a) Relevant energy levels and transitions in 138Ba + . (b) Schematic drawing of major experimental elements. OPO: Optical parametric oscillator; YAG: Nd:YAG laser; LD: laser diode; DSP: Digital signal processing system allows for real time control of experimental parameters; AOM: Acousto-optic modulators used as optical switches and for tuning of laser light; PM: Photo multiplier tube, serves for detection of resonance fluorescence. All lasers are frequency and intensity stabilized (not shown). ...Schematic drawing of the resonances of qubits j and j + 1 with some accompanying sideband resonances. The angular frequency vN corresponds to the Nth axial vibrational mode, and the frequency separation between carrier resonances is denoted by δω. ... This chapter discusses quantum measurements and new concepts for experiments with trapped ions. Quantum mechanics is a tremendously successful theory playing a central role in natural sciences even beyond physics, and has been verified in countless experiments, some of which were carried out with very high precision. Quantum theory predicts correlations between two or more quantum systems once an entangled state of these systems has been generated. The chapter introduces experiments with 171Yb+ ions demonstrating the precise manipulation of hyperfine states of single ions essentially free of longitudinal and transverse relaxation. A new concept for ion traps is described that allows for experiments requiring individual addressing of ions and conditional dynamics with several ions even with radiation in the radio frequency (rf) or microwave (mw) regime. It is shown how an additional magnetic field gradient applied to an electrodynamic trap individually shifts ionic qubit resonances making them distinguishable in frequency space. Thus, individual addressing for the purpose of single qubit operations becomes possible using long-wavelength radiation. At the same time, a coupling term between internal and motional states arises even when rf or mw radiation is applied to drive qubit transitions. Thus, conditional quantum dynamics can be carried out in this modified electrodynamic trap and in such a new type of trap all schemes originally devised for optical QIP in ion traps can be applied in the rf or mw regime, too.

Contributors: Uwe Starossek

Date: 2015-01-01

Free oscillation response of pendulum mechanism. ...Free oscillation response...Low frequency...A pendulum mechanism is presented whose natural frequency of oscillation is distinctly lower than that of a conventional pendulum of comparable size. Furthermore, its natural frequency is approximately proportional to its amplitude of oscillation. The mechanism can thus be tuned to extremely low frequencies by using small amplitudes. The undamped free oscillation response of the mechanism is studied. The derivation of the equation of motion is outlined for both large and, after neglecting higher order terms, small displacements. In both cases, a second-order nonlinear differential equation results. When higher order terms are neglected, the equation of motion is of simple form and can be solved symbolically in terms of a Jacobi elliptic function. Based on this solution, a closed-form expression for the natural frequency is derived and the characteristics of the free oscillation response are discussed. ... A pendulum mechanism is presented whose natural frequency of oscillation is distinctly lower than that of a conventional pendulum of comparable size. Furthermore, its natural frequency is approximately proportional to its amplitude of oscillation. The mechanism can thus be tuned to extremely low frequencies by using small amplitudes. The undamped free oscillation response of the mechanism is studied. The derivation of the equation of motion is outlined for both large and, after neglecting higher order terms, small displacements. In both cases, a second-order nonlinear differential equation results. When higher order terms are neglected, the equation of motion is of simple form and can be solved symbolically in terms of a Jacobi elliptic function. Based on this solution, a closed-form expression for the natural frequency is derived and the characteristics of the free oscillation response are discussed.

Contributors: Howan Leung, Cannon X.L. Zhu, Danny T.M. Chan, Wai S. Poon, Lin Shi, Vincent C.T. Mok, Lawrence K.S. Wong

Date: 2015-01-01

High-frequency oscillations...An example of the implantation schedule (patient #1) demonstrating areas with conventional frequency ictal patterns, ictal high-frequency oscillations, hyperexcitability, and radiological lesions. ...An example of the implantation schedule (patient #7) demonstrating areas with conventional frequency ictal patterns, ictal high-frequency oscillations, hyperexcitability, and radiological lesions. ...High-frequency oscillations (HFOs, 80–500Hz) from intracranial electroencephalography (EEG) may represent a biomarker of epileptogenicity for epilepsy. We explored the relationship between ictal HFOs and hyperexcitability with a view to improving surgical outcome....Summary table for statistical analysis. HFO=high frequency oscillations, CFIP=conventional frequency ictal patterns. ... High-frequency oscillations (HFOs, 80–500Hz) from intracranial electroencephalography (EEG) may represent a biomarker of epileptogenicity for epilepsy. We explored the relationship between ictal HFOs and hyperexcitability with a view to improving surgical outcome.

Contributors: Olivier Audouin, Jacques Bodin

Date: 2007-02-20

Extensive slug-test experiments have been performed at the Hydrogeological Experimental Site (HES) of Poitiers in France, made up of moderately fractured limestones. All data are publicly available through the “H+” database, developed within the scope of the ERO program (French Environmental Research Observatory, http://hplus.ore.fr). Slug-test responses with high-frequency (>0.12Hz) oscillations have been consistently observed in wells equipped with multiple concentric casing. These oscillations are interpreted as the result of inertia-induced fluctuations of the water level in the annular space between the inner and outer casing. In certain cases, these high-frequency oscillations overlap with lower frequency (oscillations, which leads to complex responses that cannot be interpreted using conventional models. Slug-test data have been processed in the Fourier-frequency domain, in order to remove the high-frequency component by a signal-filtering method. The corrected signals have been interpreted with the model of [McElwee, C.D., Zenner, M., 1998. A nonlinear model for analysis of slug-test data. Water Resour. Res. 34 (1), 55–66.], which accounts for the inertia of the water-column above the well screen, non-linear head losses in the well, and neglects the aquifer storage (quasi-steady-state approximation). Hydraulic conductivity values interpreted from dual-frequency slug-tests compare well to those interpreted from “standard” overdamped or underdamped slug-test responses....Frequency spectrum of the slug-test response in HES well M05, for an initial head displacement H0=0.2m (slug-test reference=STM5_02). ...Filtering of high-frequency oscillations: example of processing of the slug test STM5_02 (HES well M05, initial head displacement H0=0.2m). ...High-frequency oscillations...Filter shape in the frequency domain for ρ=0.9. ...Interpretation of high-frequency oscillations: inertia-induced water level fluctuations in the annular space between the inner PVC casing and the outer steel casing. ...Typical slug-test responses in HES wells. (a) “Standard” overdamped response; (b) “standard” underdamped response with low-frequency oscillations; (c) overdamped response with high-frequency oscillations; (d) underdamped response with dual-frequency oscillations. ... Extensive slug-test experiments have been performed at the Hydrogeological Experimental Site (HES) of Poitiers in France, made up of moderately fractured limestones. All data are publicly available through the “H+” database, developed within the scope of the ERO program (French Environmental Research Observatory, http://hplus.ore.fr). Slug-test responses with high-frequency (>0.12Hz) oscillations have been consistently observed in wells equipped with multiple concentric casing. These oscillations are interpreted as the result of inertia-induced fluctuations of the water level in the annular space between the inner and outer casing. In certain cases, these high-frequency oscillations overlap with lower frequency (<0.05Hz) oscillations, which leads to complex responses that cannot be interpreted using conventional models. Slug-test data have been processed in the Fourier-frequency domain, in order to remove the high-frequency component by a signal-filtering method. The corrected signals have been interpreted with the model of [McElwee, C.D., Zenner, M., 1998. A nonlinear model for analysis of slug-test data. Water Resour. Res. 34 (1), 55–66.], which accounts for the inertia of the water-column above the well screen, non-linear head losses in the well, and neglects the aquifer storage (quasi-steady-state approximation). Hydraulic conductivity values interpreted from dual-frequency slug-tests compare well to those interpreted from “standard” overdamped or underdamped slug-test responses.

Contributors: M.E. Leser, S. Acquistapace, A. Cagna, A.V. Makievski, R. Miller

Date: 2005-07-01

Apparent dilational elasticity modulus as a function of oscillation frequency for drops of water (♦), water/ethanol 86:14 (■), ethanol (▴), amplitude of volume oscillations 8%. ...Surface tension and apparent dilational elasticity modulus E as a function of oscillation frequency for an air bubble in pure water. ...Oscillating drops and bubbles...Surface tension and apparent dilational elasticity modulus E as a function of oscillation frequency for a drop of pure water in air. ...Apparent dilational elasticity modulus as a function of oscillation frequency for drops of silicon oil (●), paraffin oil (■), amplitude of volume oscillations 2%. ...Limiting frequency...To determine the dilational rheology of surface layers, the profile analysis tensiometry can be used with oscillating drops or bubbles. The methodology limits for these oscillations depend on the liquids’ properties, such as density, viscosity and surface tension. For the most frequently studied water/air interface, the maximum oscillation frequency is of the order of 1Hz, although much higher frequencies are technically feasible by the existing profile analysis tensiometers. For f>1Hz, deviations of the drops/bubbles from the Laplacian shape mimic non-zero dilational elasticities for the pure water/air and ethanol/air interface. For liquids of higher viscosity, the critical frequency is much lower....Apparent dilational elasticity modulus as a function of oscillation frequency for drops of water (♦), water/ethanol 86:14 (■), ethanol (▴), amplitude of volume oscillations 2%. ... To determine the dilational rheology of surface layers, the profile analysis tensiometry can be used with oscillating drops or bubbles. The methodology limits for these oscillations depend on the liquids’ properties, such as density, viscosity and surface tension. For the most frequently studied water/air interface, the maximum oscillation frequency is of the order of 1Hz, although much higher frequencies are technically feasible by the existing profile analysis tensiometers. For f>1Hz, deviations of the drops/bubbles from the Laplacian shape mimic non-zero dilational elasticities for the pure water/air and ethanol/air interface. For liquids of higher viscosity, the critical frequency is much lower.