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Shape **oscillations**... PSDs of a2 the different fluids at (a) Re=639 and (b) Re=418. In (a), the green solid line denotes f=107Hz, the natural **frequency** of n=2 mode **oscillation** for water droplet and the green dashed line denotes f=90Hz, the natural **frequency** of n=2 mode **oscillation** for glycerol droplet. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
... Sequence of consecutive snapshots (5ms apart) of the **oscillating** droplets. The scale bar in the first image represents 1mm.
... Power spectral density of the instantaneous velocity measured at the wake of the **oscillating** droplets for water and glycerol at two different Reynolds numbers.

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Various biological processes regulated by cytosolic Ca2+ **oscillations**.
... Calcium **oscillations**... Cartoon illustrating the main mechanisms involved in the generation of cytosolic Ca2+ **oscillations**. Cytosolic Ca2+ **oscillations** are generated through the concerted action of cellular mechanisms that increase (red) and decrease (blue) the concentration of Ca2+ in the cytoplasm. Oscillatory signals are initiated by stimuli that trigger entry of external Ca2+ through receptor (R) or voltage (ΔV) gated Ca2+ channels in the plasma membrane or by activation of receptors (R) that stimulate PLC and InsP3-mediated Ca2+-release from the ER/SR. When the cytosolic level of Ca2+ increases, Ca2+ itself stimulates InsP3Rs and/or RyRs to release further Ca2+ into the cytoplasm. During this phase, Ca2+ buffers bind Ca2+ which contributes to the decrease in the cytosolic concentration of free Ca2+. When the Ca2+ concentration reaches high levels, the plasma membrane Ca2+-ATPase (PMCA) and Na+/Ca2+-exchanger (NCX) extrude Ca2+ to the outside, whereas the ER/SR Ca2+-ATPase (SERCA) pumps Ca2+ back into the ER/SR.

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Vortex structures and corresponding vortex shedding **frequency** for different inlet flows. (a) and (b): uniform; (c) and (d): St0/St=0.5 and Re′=25; (e) and (f): St0/St=0.75 and Re′=50; (g) and (h): St0/St=1.25 and Re′=100.
... **Oscillating** flow... Correlation between the time-average lift coefficient ratio 〈Cl〉/〈Cl0〉 and the **frequency** ratio of the **oscillating** inlet flow St0/St.
... Correlation between the maximum lift coefficient ratio ClMax/〈Cl0〉 and the **oscillating** Reynolds number Re′.
... Correlations between (a) the gradient of the maximum lift coefficient calculated by Eq. (22) and the **frequency** of the inlet **oscillating** flow St0/St; (b) the gradient of the maximum lift coefficient calculated by Eq. (25) and the **oscillating** Reynolds number Re′.
... Correlations between the average drag coefficient ratio 〈Cd〉/〈Cd0〉−1 and (a) the **frequency** ratio St0/St; (b) the **oscillating** Reynolds number Re′.

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High **frequency** **oscillations**

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The proposed **oscillator** circuits reported in [10].
... Variation of the **frequency** of **oscillation** of the circuit of Fig. 1(b) with R1 (R2=10kΩ, R3=1kΩ, C1=C2=1nFandR0=10kΩ).
... Sinusoidal **oscillators**... Variation of the **frequency** of **oscillation** of the circuit of Fig. 1(a) with R0 (R2=10kΩ, R3=1kΩ, C1=C2=1nFandR1=10kΩ).
... Variation of the **frequency** of **oscillation** of the circuit of Fig. 1(a) with R1 (R2=10kΩ, R3=1kΩ, C1=C2=1nFandR0=10kΩ).

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Jump-up **frequencies** of the Duffing **oscillator** as a function of the non-dimensional parameter α, which governs the degree of nonlinearity. A negative value of α denotes a softening system and a positive value of α denotes a hardening system; solid line—Eq. (12); ○, numerical integration ζ=0.02; ×, numerical integration ζ=0.05; (a) and (b) denote the **frequencies** at which a jump will occur for the threshold value of |α| for ζ=0.02 and 0.05, respectively.
... Normalised jump-up and jump-down **frequencies** and the normalised response amplitudes at these **frequencies** calculated using the harmonic balance method
... Jump-down **frequencies** of the Duffing **oscillator** as a function of the ratio of non-dimensional parameters α and ζ2, which governs the degree of nonlinearity and damping, respectively. A negative value of α/ζ2 denotes a softening system and a positive value of α/ζ2 denotes a hardening system; solid line—Eq. (9) ○, numerical integration ζ=0.02; ×, numerical integration ζ=0.05; (a) and (b) denote the **frequencies** at which a jump will occur for the threshold value of |α| for ζ=0.02 and 0.05, respectively.
... **Frequency** response curves for the Duffing **oscillator**. The dashed lines denote unstable solutions. The crosses denote the responses at the jump-up **frequencies** and the circles denote the maximum values of the response, which occur approximately at the jump-down **frequencies**. Expressions for the jump-up and jump-down **frequencies**, and the response amplitudes at these **frequencies** are given in Table 1. For all the simulations ζ=0.02; for the softening systems α=0.9αm and 1.1αm where αm=-4/3ζ2, and for the hardening system α=−5αm. Note that there is no jump-down **frequency**, when α=1.1αm.
... Non-dimensional maximum amplitude of the Duffing **oscillator**, which occurs approximately at the jump-down **frequency** as a function of the non-dimensional parameter α, which governs the degree of nonlinearity. A negative value of α denotes a softening system and a positive value of α denotes a hardening system; solid line—Eq. (8) with ζ=0.02; dashed line---Eq. (8) with ζ=0.05; ○, numerical integration ζ=0.02; ×, numerical integration ζ=0.05; (a) and (b) denote the threshold value of |α| for ζ=0.02 and 0.05, respectively.

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Parametric **oscillator**... Diagram of the optical parametric **oscillator** modeled in this paper. The reflectivity of mirrors can be changed to meet demands of users.

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Effects of the dimensionless **frequency** of the lid velocity on stream function at central point of cavity (X=0.5 and Y=−0.1443) for Re=100, Gr=5×105.
... Periodic movement of minimum local Nusselt number point on the **oscillating** lid, at W=0.863, Re=100, and Gr=5×105.
... **Frequency** spectrum of the periodic flow field for various dimensionless **frequencies** of lid velocity at Re=100 and Gr=5×105. (a) Constant–velocity lid, (b)W=0.2 and (c) W=0.5.
... Periodic flow and temperature fields in one **oscillating** lid period, at Re=100 and Gr=5×105. (a) Constant–velocity lid, (b) W=0.1 (τpw=62.83) and (c) W=0.863 (τpw=7.28).
... Lid **oscillation**... Maximum and minimum stream functions and Nusselt numbers reached in a period of flow **oscillation** as functions of the dimensionless **frequency** of lid velocity, at Re=100 and Gr=5×105.

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Heat flux, Reynolds number and **oscillating** **frequency** ranges
... Variation of Nusselt number with Reynolds number for different **oscillating** **frequencies**.
... **Oscillating** flow... Variation of exergy loss with Reynolds number at **oscillating** **frequencies** (a) f=0 Hz and (b) f=20 Hz along tube length.
... Oscillatory **frequency**... Variation of Exergy loss with Reynolds Number at different **oscillating** **frequencies**.
... Local Nusselt number versus tube length for different **oscillating** **frequencies** at (a) Re=5000, (b) Re=20,000.

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