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(Color online) |A|2 is the probability of finding the spin system in the state |⇓↓〉. It oscillates at the high frequency D (=2.88GHz). The frequency of the beats is χ/2 (=16.7MHz). The amplitude of oscillations is also modulated by an additional cosine wave signal of frequency χ (see text). |C|2 is the probability of finding the spin system in the state |0↓〉. It oscillates at the low frequency χ. It is almost zero in the time interval 90–100ns. The probability of finding spin system in the state |⇑↓〉, |B|2, has the same oscillations than |A|2 but it is anti-phase (see Fig. 3). ... Ideal truth table and schematic representation of a two-qubit CNOT gate irradiated by a sequence of two microwave π/2-pulses of equal width t and a variable waiting time between pulses τ. In the text, x and y are the states of two impurity spins of diamond, namely the spin-12 carried by the P1 center and the spin-1 carried by the NV−1 color center. The symbol ⊕ is the addition modulo 2, or equivalently the XOR operation. ... (Color online) NV−1 Rabi oscillations. Control qubit down: blue, red and green lines correspond, respectively, to the time evolution of |A|2, |B|2 and |C|2, i.e., the probabilities of finding the spin system in the state |⇓↓〉, |⇑↓〉 and |0↓〉. Control qubit up: red, blue and green lines represent, respectively, |A′|2, |B′|2 and |C′|2, i.e., the probabilities of finding the spin system in the state |⇓↑〉, |⇑↑〉 and |0↑〉, i.e., |A′|2=|B|2, |B′|2=|A|2 and |C′|2=|C|2 (see text). Fig. 4 gives details in the interval 60–120ns. They can also be revealed by a zoom in.
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Qubits in solids... Schematic diagram of qubits addressed in a frequency domain. The ions whose 3H4(1)± 3 2–1D2(1) transitions are resonant with a common cavity mode are employed as qubits. ... Basic scheme of the concept of the frequency-domain quantum computer. The atoms are coupled to a single cavity mode. Lasers with frequencies of νk and νl are directed onto the set of atoms and interact with the kth and lth atoms selectively.
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Average PTO power as a function of oscillating frequency for straight (♦: solid line) and bent leg (□: broken line) tines (oscillation angle β=+27°). ... Subsoiler draft signals with time for the control and the range of oscillating frequencies. ... Dominant frequency of draft signal over the oscillating frequency range. ... Proportion of cycle time for cutting and compaction phases versus oscillating frequency (oscillation angle β=+27°). ... Dominant frequency of torque signal over the oscillating frequency range. ... Frequency... Oscillating tine
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Adaptive frequency oscillator... The left plot of this figure represents the evolution of ω(t) when the adaptive Hopf oscillator is coupled to the z variable of the Lorenz attractor. The right plot represents the z variable of the Lorenz attractor. We clearly see that the adaptive Hopf oscillators can correctly learn the pseudo-frequency of the Lorenz attractor. See the text for more details. ... Plots of the frequency of the oscillations of the Van der Pol oscillator according to ω. Here α=50. There are two plots, for the dotted line the oscillator is not coupled and for the plain line the oscillator is coupled to F=sin30t. The strength of coupling is ϵ=2. We clearly see basins of phase-locking, the main one for frequency of oscillations 30. The other major basins appear each 30n (dotted horizontal lines). We also notice small entrainment basins for some frequencies of the form 30pq. For a more detailed discussion of these results refer to the text. ... We show the adaptation of the Van der Pol oscillator to the frequencies of various input signals: (a) a simple sinusoidal input (F=sin(40t)), (b) a sinusoidal input with uniformly distributed noise (F=sin(40t)+uniform noise in [−0.5,0.5]), (c) a square input (F=square(40t)) and (d) a sawtooth input (F=sawtooth(40t)). For each experiment, we set ϵ=0.7 and α=100 and we show three plots. The right one shows the evolution of ω(t). The upper left graph is a plot of the oscillations, x, of the system, at the beginning of the learning. The lower graph shows the oscillations at the end of learning. In both graphs, we also plotted the input signal (dashed). In each experiment, ω converges to ω≃49.4, which corresponds to oscillations with a frequency of 40 rad s−1 like the input and thus the oscillator correctly adapts its frequency to the frequency of the input. ... Frequency spectra of the Van der Pol oscillator, both plotted with ω=10. The left figure is an oscillator with α=10 and on the right the nonlinearity is higher, α=50. On the y-axis we plotted the square root of the power intensity, in order to be able to see smaller frequency components. ... This figure shows the convergence of ω for several initial frequencies. The Van der Pol oscillator is perturbed by F=sin(30t), with coupling ϵ=0.7, α=50. We clearly see that the convergence directly depends on the initial conditions and as expected the different kinds of convergence correspond to the several entrainment basins of Fig. 7.
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Summary of resonance frequencies found in all 10 babies (1 and 2 represents first and second run, respectively) ... A screen from our phase analysis program, showing phase analysis performed at four points of the respiratory cycle: top of breath, mid-inspiration, mid-expiration and bottom of breath. Corresponding points from the driving trace and the mouth pressure trace are matched and the phase difference calculated. In this case, the phase difference at the top of breath is 0° at an oscillating frequency of 20 Hz. ... high-frequency oscillation
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Examples of a spike without HFOs (left) and a spike with HFOs (right), as defined with the Analytic Morse wavelet in the time–frequency domain. ... High Frequency Oscillations... Parameter selection for the Analytic Morse Wavelet; top: time–frequency presentation for different values of n (m=40), bottom: raw signal and filtered signal (80–250Hz). Blue lines represent HFO interval marked visually. ... Examples of detection errors. Left: HFO without isolated blob but having oscillation in the raw signal. Right: HFO without visible oscillation in the raw signal but representing an isolated peak. Blue lines show the HFO interval marked by reviewers. ... Time–frequency
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Detection and manipulation of the qubit. (a) Fluorescence image of nanodiamond prepared on the CPW transmission line. NV S1 is circled. The inset is a photo of CPW with 20μm gaps fabricated on a silica glass. (b) CW ODMR spectrum for NV S1. The inset is energy levels of NV center. A 532nm laser is used to excite and initialize the NV center. Fluorescence is collected by a confocal microscope. (c) Rabi oscillation of NV S1. Rabi oscillation period is about 62ns. (d) Hahn echo and CPMG control pulse sequences. πx (πy) implies the direction of microwave magnetic fields parallel to x (y). ... Spectral density of the spin bath. (a) NV S1, (b) NV S2. All values of spectral density S(ω) of the spin bath are extracted from the CPMG data (blue points). Each blue data point represents a specific probed frequency ω=πn/t, in which n is the number of control pulses and t is the specific duration. The red points are the average values at a certain frequency. The mean spectral density is fit to the Lorentzian function (Eq. (3)) (green line). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) ... Characterization of lifetime of NV center spins. (a) Ramsey interference of NV S1 (circle) and NV S2 (diamond). The oscillation in Ramsey signal originates from the beating among different transitions corresponding to the host three 14N nuclear spin states. The oscillation frequency of Ramsey signal is equal to microwave detuning from spin resonance. Solid lines ~exp[−(t/T2⁎)m] fit the experimental data points, where m is a free parameter. (b) Comparison of Hahn echo coherence time T2 of NV S1 (circle) and NV S2 (diamond). The solid lines are fits to ~exp[−(t/T2)p], in which p is a fit parameter.
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Dominant frequencies of 10mm nozzle. ... Condensation regime map by Cho et al. [1] (C–chugging, TC—transitional region from chugging to CO, CO—condensation oscillation, SC—stable condensation, BCO—bubble condensation oscillation, IOC—interfacial oscillation condensation). ... Condensation oscillation... Frequencies at different test conditions—250kgm−2s−1. ... Frequency... Prediction accuracy of simultaneous equations for oscillation frequency. ... Frequencies at different test conditions—300kgm−2s−1.
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Spatial frequencies distributions... Ragged oscillation death... The phase synchronization domains (areas enclosed by the red lines) and the OD regions (black areas) in the parameter space of ε-δω for a ring of coupled Rossler systems with different frequency distributions: (a) G={1,2,3,4,5,6,7,8}, (b) G={1,4,3,6,2,8,5,7}, and (c) G={1,2,3,6,8,4,7,5}. N=8. The ragged OD sates are clear in (b) and (c) within a certain interval of δω indicated by two vertical dashed lines. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... The bifurcation diagram and the largest Lyapunov exponent λ of the coupled Rossler oscillators versus the coupling strength ε with the same spatial arrangement of natural frequencies as in Fig. 1(a)–(c), respectively for δω=0.58. The bifurcation diagram is realized by the soft of XPPAUT [33] where the black dots are fixed points and the red dots are the maximum and minimum values of x1 for the stable periodic solution while the blue dots means the max/min values of x1 for the unstable periodical states. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... The critical curves of OD domain from analysis in N coupled Landau–Stuart oscillators for different N’s: (a) N=2, (b) N=3, and (c)–(e) N=4 for G={1,2,3,4},G={1,2,4,3}, and G={1,3,2,4}, respectively. The ragged OD domain is clear in (d). The numerical results with points within the domains perfectly verify the analytical results. ... The OD regions in the parameter space of ε-δω for a ring of coupled Rossler systems with different frequency distributions: (a) G={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}, (b) G={26,16,25,18,5,14,10,4,6,7,21,12,23,8,1,15,9,29,28,11,2,20,27,30,3,13,17,22,24,19}, and (c) G={19,22,18,13,10,28,7,15,17,8,30,12,26,11,20,9,27,21,25,6,29,1,23,5,3,24,16,14,4,2}. N=30. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. ... Coupled nonidentical oscillators
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Nonlinear oscillator... He’s frequency formulation
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