Dependence of the phase shift α on the two parameters ng and Φe. The qubit is irradiated by microwaves with a frequency of 8.0GHz. The periodic circular structure is due to the variation of the total interferometer-tank impedance caused by transitions from the lower to the upper energy band. The “crater ridges” (solid-line ellipse) correspond to all combinations of the parameters ng and Φe that give the same energy gap (8.0GHz) between the respective states .
... Tank phase shift α dependence on gate parameter ng for different magnetic flux applied to the qubit loop . The data correspond to the flux Φ/Φ0=0.5, 0.53, 0.54, 0.56, 0.57. 0.61, 0.62, 0.65 (from bottom to top). For clarity, the upper curves are shifted.
... Superconducting qubits... Integrated design: Al qubit fabricated in the middle of the Nb coil (left-hand side), and single-Cooper-pair transistor (right-hand side).
... Left-hand side: tank phase shift α dependence on gate parameter ng without microwave power (lowest curve) and with microwave power at different excitation frequencies. The data correspond to the frequency of the microwave ΩMW/2π=8.9, 7.5, 6.0GHz (from top to bottom) . Here the applied external magnetic flux was fixed Φdc=Φ0/2. For clarity, the upper curves are shifted. Right-hand side: energy gap Δ between the ground and upper states of the qubit determined from the experimental data for the case δ=π (Φdc=Φ0/2) . The dots represent the experimental data, the solid line corresponds to the fit (cf. text).
... Calculated dependence of the tank voltage phase shift α on the phase difference δ. The curves correspond to the fixed frequency Ω/2π=7.05GHz with the different amplitude of the excitation (from bottom to top n˜g is: 0.1, 0.2, 0.4) . For clarity, the upper curves are shifted.
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.
... Phase oscillators
Contributors:Sven P. Heinrich, Michael Bach
High-frequencyoscillations... Time–frequency distributions. On the left side, the full 20–1000 Hz range is displayed for three exemplary subjects. The two graphs per subject show the ERG and VEP activity, respectively. The high-frequencyoscillations appear as a distinct area which in most cases is around or above 100 Hz. The flash was given at t=0. Those parts of the time–frequency diagram which would be contaminated by edge effects are displayed in white. Their spread is due to the inevitable frequency-dependent finite time resolution, which also causes the spurious pre-stimulus activity at low frequencies. The white rectangles in the diagrams mark the regions of interest, which are shown enlarged on the right side for all 7 subjects. The arrows link the high-frequency maxima of ERG and VEP. Most subjects produced activity around or above 100 Hz in both VEP and ERG. However, only in one subject (S1) the frequencies matched. Asterisks indicate the significance levels of frequency differences in standard notation, based on a sequential Bonferroni adjustment. No significance value could be obtained for subject S3.
Contributors:Yulia P. Emelianova, Alexander P. Kuznetsov, Ludmila V. Turukina, Igor R. Sataev, Nikolai Yu. Chernyshov
Charts of the Lyapunov exponents for the four dissipatively coupled phase oscillators on the frequency detunings parameter plane (Δ1,Δ3). Values of the parameters are μ=0.4, (а) Δ2=0.4, (b) Δ2=2.4. Resonance conditions in the chain of oscillators are shown by arrows.
... Examples of phase portraits for the system (2). (a) Two-frequency resonance regime of the type 1:3 for Δ1=−1.5, Δ2=1, μ=0.6; (b) three-frequency regime for Δ1=−1, Δ2=1, μ=0.25.
... Chart of the Lyapunov exponents for three coupled van der Pol oscillators on the frequency detunings parameter plane. Numbers correspond to cycle periods in the Poincaré section. Values of the parameters are λ=0.1,μ=0.04.
... Chart of the Lyapunov exponents for three coupled van der Pol oscillators on the frequency detunings parameter plane. Numbers correspond to cycle periods in the Poincaré section. Values of the parameters are λ=1,μ=0.4.
... Chain of van der Pol oscillators... Full synchronization area for the four phase oscillators on the frequency detunings parameter space (Δ1,Δ2,Δ3).
Contributors:Fatema F. Ghasia, Aasef G. Shaikh
(A) Comparison of the frequency of oscillations during oblique, pure horizontal and pure vertical saccades. Number of observations is plotted on y-axis, while x-axis represents bins of oscillationfrequency. Each data point represents the number of observations in a given frequency bin. Black trace suggests oblique saccade, Gray traces with circular symbols are horizontal saccades and triangular symbols represent vertical saccade. Dashed lines depict median oscillationfrequency. (B) Comparison of frequency oblique saccade oscillations with the frequency of orthogonal saccadic oscillations during pure horizontal and vertical saccades. Each data point depicts one subject. Black data points are comparison with pure horizontal saccade, gray data points are comparison with vertical saccade. Dashed gray line is an equality line. (C) Comparison of the amplitude of the sinusoidal modulation of oblique, horizontal, and vertical saccade trajectories. Number of samples is plotted on y-axis, while x-axis represents the amplitude bins. Each data point depicts number of observations in a given bin of the histogram. Black trace shows oblique saccade, Gray trace with circuit symbol is a horizontal saccade and the triangular symbol is a vertical saccade. Dashed lines represent median values.
... An example of horizontal, vertical, and oblique saccade from one healthy subject. The left column depicts horizontal saccade; central column vertical, and right column is oblique saccade. Panels A, B and C illustrate eye position vector plotted along y-axis. Panels D, E and F represent eye velocity vector plotted along y-axis while ordinate in panels G, H and I illustrate eye acceleration. In each panel, x-axis represents corresponding time. Arrows in panels C, F, I show oscillations in oblique saccade trajectory.
Free oscillation response of pendulum mechanism.
... Free oscillation response... Low frequency
Contributors:Lucas C. Monteiro, A.V. Dodonov
We consider the interaction between a single cavity mode and N≫1 identical qubits, assuming that any system parameter can be rapidly modulated in situ by external bias. It is shown that, for the qubits initially in the ground states, three photons can be coherently annihilated in the dispersive regime for harmonic modulation with frequency 3ω0−Ω0, where ω0 (Ω0) is the bare cavity (qubit) frequency. This phenomenon can be called “Anti-dynamical Casimir effect”, since a pair of excitations is destroyed without dissipation due to the external modulation. For the initial vacuum cavity state, three qubit excitations can also be annihilated for the modulation frequency 3Ω0−ω0.
Contributors:Howan Leung, Cannon X.L. Zhu, Danny T.M. Chan, Wai S. Poon, Lin Shi, Vincent C.T. Mok, Lawrence K.S. Wong
High-frequencyoscillations... An example of the implantation schedule (patient #1) demonstrating areas with conventional frequency ictal patterns, ictal high-frequencyoscillations, hyperexcitability, and radiological lesions.
... An example of the implantation schedule (patient #7) demonstrating areas with conventional frequency ictal patterns, ictal high-frequencyoscillations, hyperexcitability, and radiological lesions.
... Summary table for statistical analysis. HFO=high frequencyoscillations, CFIP=conventional frequency ictal patterns.
Contributors:M.E. Leser, S. Acquistapace, A. Cagna, A.V. Makievski, R. Miller
Apparent dilational elasticity modulus as a function of oscillationfrequency 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 oscillationfrequency for an air bubble in pure water.
... Oscillating drops and bubbles... Surface tension and apparent dilational elasticity modulus E as a function of oscillationfrequency for a drop of pure water in air.
... Apparent dilational elasticity modulus as a function of oscillationfrequency for drops of silicon oil (●), paraffin oil (■), amplitude of volume oscillations 2%.
... Limiting frequency... Apparent dilational elasticity modulus as a function of oscillationfrequency for drops of water (♦), water/ethanol 86:14 (■), ethanol (▴), amplitude of volume oscillations 2%.