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Relation between the oscillation frequency and the coupling strength. ... Capacitive coupled RC-oscillators. ... RC-oscillators... Coupled oscillators... (a) Single RC oscillator and (b) small-signal equivalent circuit. ... Quadrature oscillator... Simulated frequency. ... Van der Pol oscillators... Frequency of oscillation with the oscillators uncoupled and coupled (CX=20fF).
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Typical spontaneous Ca2+ oscillations from the computational study. From top to bottom, the three plots correspond to oscillations in cytoplasmic Ca2+, ER Ca2+, and cytoplasmic IP3. All three variables have the same frequency but different peak times (details are shown in Fig. 4). ... (A) Bifurcation diagram of Ca2+ oscillations as a function of membrane potential. Sustained Ca2+ oscillations occurred in the potential range of −70.0 to −64.9 mV, where the maximum and minimum of Ca2+ oscillations were plotted. The dashed line refers to the unstable steady state. Out of the oscillatory domain, the system evolved into a stable steady state. (B) Frequency of Ca2+ oscillations versus membrane potential. ... Dependence of Ca2+ oscillations on extracellular Ca2+ concentration. Ca2+ oscillations stopped when the extracellular Ca2+ concentration was too low or too high. From 0.1 to 1500 μM, the frequency of Ca2+ oscillations increased with a rise in extracellular Ca2+ concentration. ... Amplitude and frequency of Ca2+ oscillations versus temperature. In the temperature range of 20–37°C, both the amplitude (indicated as an asterisk) and frequency (dotted line) decreased with temperature. ... The occurrence of Ca2+ oscillation depends on the membrane potential. When the membrane potential is −64.9 mV, there is no Ca2+ oscillation. Within −70.0 to −64.9 mV, the frequency and amplitude of Ca2+ oscillations change with the membrane potential.
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(a) Time series for the first chrono-mode of the POD, a1(t), for the three different forcings with vin=0.4m/s (Re=3.1in×103, N=0.02). (b) Power spectra of the chrono-modes a1(t). Frequency peaks are found at fPOD=0.027Hz (FL0). The values of the frequency peaks are in reasonable agreement with the frequencies found for the free surface fluctuations, fTS. ... (a–c) Profiles of the turbulence kinetic energy kturb,2D. (d–f) Profiles of the kinetic energy associated with the large-scale oscillations kosc,2D. The inlet velocity is vin=0.4m/s (Rein=3.1×103, N=0.02). ... Amplitude A and frequency fTS of the free surface oscillation at a monitoring point at x=0.175m for the three different forcings (Rein=3.1×103, N=0.02). Dominant frequency fPOD from the power spectrum of the first chrono mode of the POD. ... Self-sustained oscillations
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Detection of high-frequency repeating impacts in robotic grinding (detailed views). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) ... Impact-cutting map from the speed signal based on the experiment with the bump showing (─) a major regime of 2 impacts/revolution and (…) minor oscillations. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) ... Vibration and rotational frequency in single-pass grinding (overview). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) ... Typical values of ω, ωmax and Δω during a cutting impact from measured rotational frequency in Test (3) at 4500rpm. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) ... Instantaneous angular frequency
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(a) Diffusion signal for different waveforms: square with 90° phase, apodised cosine and apodised trapezoid as a function of oscillation frequency for four different sizes of the restricted compartment; (b) corresponding extracted ADC values. The diffusion signal and ADC for apodised trapezoid and square wave are very similar and are plotted on top of each other. ... Oscillating gradient... (a) Average signal difference between square and sine approximations and the full trapezoidal expressions as a function of α for R=2μm and 10μm. (b) Diffusion signal for R=5μm for the three waveforms with gradient strength G=60mT/m and 200mT/m as a function of oscillation frequency. ... (a) Average signal difference between square and sine approximations and the full trapezoidal expression considering: I – same amplitude, II – same area under the curves, III – same area under the squared curves and IV – same b value per oscillation. (b) Difference between square and sine approximations and the full trapezoidal expressions with SR=200T/m/s as a function of n for all data points with R=5μm. ... Restricted diffusion signal as a function of oscillation frequency for (a) several values of Δ, R=5μm and G=0.1T/m; (b) several gradient strengths, R=5μm and Δ=25ms. In (a) and (b) the filled markers indicate waveforms with integer number of oscillations. Restricted diffusion as a function of (c) gradient strength for several frequencies, R=5μm and Δ=45ms; (d) cylinder radius for several frequencies, G=0.1T/m and Δ=45ms. The markers show the MC simulation and the solid lines are the GPD approximations. The vertical bar separates different scales on the x-axis. ... Square wave oscillations
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Oscillation detection in a single electrode with weak alpha. The electrode was selected from the same subject as in Figs. 2 and 4. (A) The 256-electrode array with the selected electrode highlighted in yellow. (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) Oscillations detected across all frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes -closed condition (red) and eyes-open condition (black) that oscillations were detected at each frequency. (E) The raw signal from the chosen electrode, with detected oscillations at the peak alpha frequency (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E, to show the spindle-like appearance of the alpha oscillation. ... Temporal independence of two alpha components. (A) An 8-s epoch from the alpha component shown in Fig. 2, with detected alpha-frequency oscillations highlighted in red. (B) The same time segment as in A, from the alpha component in Fig. 6. Note the alpha oscillation is maximal in B when the oscillation is at a minimum in A, demonstrating why these were extracted as temporally independent components. ... Lateralized alpha component. From the same subject as Figs. 2 and 4–5. (A) The spline-interpolated scalp distribution of an alpha component extracted by ICA. Color scale denotes electrode weight (unitless). (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) Oscillations detected across all frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that oscillations were detected at each frequency. (E) The time-domain representation of the chosen component, with detected oscillations at the peak alpha frequency (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E. ... Oscillation detection in an ICA alpha component. (A) The spline-interpolated scalp distribution of an alpha component extracted by ICA. Color scale denotes electrode weight (unitless). (B) Background wavelet power spectrum mean and standard deviation (blue) and the linear regression fit to the background (green). (C) Oscillations detected across all frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that oscillations were detected at each frequency. (E) The time-domain representation of the chosen component, with detected oscillations at the peak alpha frequency (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E, to show the spindle-like appearance of the alpha oscillation. ... Oscillation... Oscillation detection in a single electrode with strong alpha. The electrode was selected from the same subject as in Fig. 2. (A) The 256-electrode array with the selected electrode highlighted in yellow. (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) Oscillations detected across all frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that oscillations were detected at each frequency. (E) The raw signal from the chosen electrode, with detected oscillations at the peak alpha frequency (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E to show the spindle-like appearance of the alpha oscillation.
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Cross-frequency coupling... Simulation results. Coupling portraits for simulated data for (A) clean (SNR=20dB) and (B) noisy cases (SNR=−10dB). PAC was generated to be at 60–80Hz (amplitude frequency) and 15Hz (phase frequency). The simulated signal contained also oscillations (at 20, 25, 30, 40 and 100Hz) having no coupling relation. These portraits show the mean PAC estimates over 100 repetitions for each method. Only methods robust enough were presented: direct PAC estimate, GLM with spurious term removed, MI with statistics and raw MI without statistics (ordered from left to right). Notice that the first two methods yield very similar outputs identifying PAC correctly and they are robust to both non-coupled oscillations and noise. ... Oscillations
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Flow forces acting on an oscillating cylinder. ... Dimensionless (a) amplitude (A*=A/D) and (b) frequency (f*=fos/fna) of the crossflow oscillations versus the reduced velocity for a curved cylinder in the convex configuration (■) and a vertical cylinder (○). ... Flow visualizations in the wake of a curved cylinder for the fixed (a) convex and (b) concave configurations, and free-to-oscillate (c) convex and (d) concave configurations. Flow is from left to right. ... Dimensionless (a) amplitude (A*=A/D) and (b) frequency (f*=fos/fna) of the crossflow oscillations versus the reduced velocity for a curved cylinder in the concave configuration (▲) and a vertical cylinder (○).
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In this figure we report as a function of optical depth the computed frequencies, center of mass (γ0), amplitudes and phases derived from the fit of velocities for each of the selected lines. Meaning of the symbols is: circles (red) carbon lines, stars (magenta) silicon lines, triangles (blues) oxygen lines and boxes (green) nitrogen lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) ... Pulsations, oscillations, and stellar seismology
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Numerical validation of the FRCs shown in the corresponding plots of Fig. 4. Stable FRC solution (blue solid line), unstable FRC solution (red dashed line), numerical solution (black circles). In (e) and (f) the approximate analytical expression for the FRC fails to predict the response, which is not harmonic (NH) in a small frequency range around 1. Approximate expressions for the jump frequencies given in Table 3 are shown as vertical dashed lines. (a) Region I, (b) Region II′, (c) Region IIIb, (d) Region IIIa′, (e) Region IV and (f) Region V. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) ... Approximate expressions for the jump-up and jump-down frequencies together with their regions of applicability. ... Three-dimensional plots illustrating the relationship between the bifurcation curves and the FRCs, for ω0=0.3 and different combinations of ζ and γ: ζ=0.002 and (a) γ=2×10−9, (b) γ=2×10−6, (c) γ=2×10−5; ζ=0.02 and (d) γ=5×10−4, (e) γ=4×10−3 and (f) γ=2×10−2. On the Ω−γ plane, γ1 is indicated by the upper thin solid line, γ2 by the lower one. On the Ω−W plane, the FRC is plotted with the stable solution (blue solid line) and the unstable solution (red dashed line). The intersections between the Ω−W plane containing the FRC and the bifurcation curves on the Ω−γ plane indicate the expected values for the jump frequencies. (a) Region I, (b) Region II′, (c) Region IIIb, (d) Region IIIa′, (e) Region IV and (f) Region V. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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