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  • Qubit... The oscillation period T0 changes with the temperature T and Coulomb bound potential β. ... The oscillation period T0 changes with the temperature T and electron phonon coupling strength α .
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  • A phase-locking model for entrainment of peripheral oscillators to the cyclin–CDK oscillator. (a) Molecular mechanism of the Cdc14 release oscillator. The mitotic phosphatase Cdc14 is activated upon release from sequestration in the nucleolus. This release is controlled by a negative feedback loop in which Cdc14 release, promoted by the polo kinase Cdc5, activates APC-Cdh1, which then promotes Cdc5 degradation, allowing Cdc14 resequestration. This negative-feedback oscillator is entrained to the cyclin–CDK cycle at multiple points: by cyclin–CDK promotion of CDC5 transcription and Cdc5 kinase activation, and by cyclin–CDK inhibition of Cdh1 activity. (b) Schematic of multiple peripheral oscillators coupled to the CDK oscillator in budding yeast. As described above, coupling entrains such peripheral oscillators to cell cycle progression; peripheral oscillators also feed back on the cyclin–CDK oscillator itself. For example, major genes in the periodic transcription program include most cyclins, CDC20, and CDC5; Cdc14 directly promotes establishment of the low-cyclin–CDK positive feedback loop by activating Cdh1 and Sic1 as well as more indirectly antagonizing cyclin–CDK activity by dephosphorylating cyclin–CDK targets; the centrosome and budding cycles could communicate with the cyclin–CDK cycle via the spindle integrity and morphogenesis checkpoints. (c) Oscillator coupling ensures once-per-cell-cycle occurrence of events. Three hypothetical oscillators are shown: a master cycle in black, a faster peripheral cycle in blue, and a slower peripheral cycle in red. In the absence of phase-locking (top), the oscillators trigger events (colored circles) without a coherent phase relationship. In the presence of oscillator coupling (bottom), the peripheral oscillators are slowed or accelerated within their critical periods to produce a locked phase relationship, with events occurring once and only once within each master cycle. ... Positive and negative feedback loops in the cyclin–CDK oscillator. (a) Inset: a negative feedback loop which can give rise to oscillations. Such an oscillator is thought to form the core of eukaryotic cell cycles, with cyclin–Cyclin Dependent Kinase (cyclin–CDK) acting as activator, Anaphase Promoting Complex-Cdc20 (APC-Cdc20) acting as repressor, and non-linearity in APC-Cdc20 activation preventing the system from settling into a steady state. Below is shown the cyclin–CDK machinery in eukaryotic cell cycles. CDKs, present throughout the cell cycle, require the binding of a cyclin subunit for activity. These cyclin partners can also determine the localization of the complex and its specificity for targets. At the beginning of the cell cycle, cyclin–CDK activity is low, and ramps up over most of the cycle. Early cyclins trigger production of later cyclins and these later cyclins then turn off the earlier cyclins, so that control is passed from one set of cyclin–CDKs to the next. The last set of cyclins to be activated, the G2/M-phase cyclins, initiate mitosis, and also initiate their own destruction by activating the APC-Cdc20 negative feedback loop. APC-Cdc20 targets the G2/M-phase cyclins for destruction, resetting the cell to a low-CDK activity state, ready for the next cycle. (b) Positive feedback is added to the oscillator in multiple ways. Left: a highly conserved but non-essential mechanism consists of ‘handoff’ of cyclin proteolysis from APC-Cdc20 to APC-Cdh1. Cdh1 is a relative of Cdc20 which activates the APC late in mitosis and into the ensuing G1. Cdh1 is inhibited by cyclin–CDK activity, resulting in mutual inhibition (which is logically equivalent to positive feedback). Middle: antagonism between cyclin–CDK and stoichiometric CDK inhibitors (CKIs) results in positive feedback. These loops stabilize high- and low-CDK activity states. Right: a double positive feedback loop comprising CDK-mediated inhibition of the Wee1 kinase (which inhibits CDK) and activation of the Cdc25 phosphatase (which activates CDK by removing the phosphorylation added by Wee1) is proposed to stabilize intermediate CDK activity found in mid-cycle, and an alternative stable state of high mitotic CDK activity.
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  • Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China... (Color online.) Typical density profiles of a rotating two-component dipolar Bose–Einstein condensate in an optical lattice, for contact interactions g=100, and for the rotation frequency Ω=0.6. Here the relative strength between the dipolar and contact interactions of component 1 is fixed to εdd=0.8, (c) and (d) correspond to the total density and density difference of these two components, respectively. The locations of the vortices are marked by crosses (×). ... (Color online.) Typical density profiles of a rotating two-component dipolar Bose–Einstein condensate in an optical lattice, for contact interactions g=100, and for the rotation frequency Ω=0.6. Here the relative strength between the dipolar and contact interactions of component 1 is fixed to εdd=0.3, (c) and (d) correspond to the total density and density difference of these two components, respectively. The locations of the vortices are marked by crosses (×). ... (Color online.) Typical density profiles of a rotating two-component dipolar Bose–Einstein condensate in an optical lattice, for contact interactions g=100, and for a higher rotation frequency Ω=0.9. Here the relative strength between the dipolar and contact interactions of component 1 is fixed to εdd=0.3, (c) and (d) correspond to the total density and density difference of these two components, respectively. The locations of the vortices are marked by crosses (×).
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  • 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.
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  • PES of the qubit system (a) and total dipole surface (b). For both surfaces: −52.8 pm⩽rA1⩽+52.8pm and −37.4pm⩽rE⩽+37.4pm. ... Normal modes included in the quantum dynamical calculation. (a) Coordinates of the qubit modes, (b) coordinates of the non-qubit modes. ... Spectral analysis of the NOT (top) and CNOT (bottom) gate. The solid lines correspond to the spectra of the optimized pulses, the dashed lines to the spectra of the sub pulses. The vertical lines indicate the relevant qubit basis transition frequencies for the quantum gates. ... spectroscopical data of the qubit vibrational modes E and A1 and the non-qubit modes, the δ-deformation mode (E) and the dissociative mode (A1)
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  • Variation of frequency shift due to the amplitude and the rotation rate. ... Conditions for zero frequency shift and zero pressure difference. Broken lines indicate linear fitting lines through the origin. ... Oscillation... Frequency shift
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  • 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)). ... 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.
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  • 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 [14]. ... 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) [14]. 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) [14]. 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) [11]. For clarity, the upper curves are shifted.
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  • (a) The SNR vs noise intensity D for fs=30,15, and 100 Hz, respectively. (b) The mean synaptic input Isyn(t) vs time for fs=30 Hz and D=0.15 and 6, respectively. (c) The SNR for various frequencies for the cases of D=0.5 and 5, respectively, in the case of I0i=0.8 and I1=0.11, and Jij∈[−4,20]. (d) The SNR vs signal frequency for D=0.5 and 5, respectively, for the case of I0i∈[0,1] and I1=0.072. ... Intrinsic oscillations... The 40 Hz oscillation... The frequency sensitivity... The frequency fi and the corresponding height H of the main peak in PSD of Isyn(t) vs (a) A for the case of I0i∈[0,3.5]; (b) M in the case of Jij∈[−5,10]. ... I0i∈[0,2] and Jij∈[−1,10]. (a) The spatiotemporal firing pattern is plotted by recording the firing time tni defined by Xi(tni)>0 and Xi(tni−)frequency fi and the corresponding height H of the main peak in PSD of Isyn(t) for different coupling strength.
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  • 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.
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