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- Non-axisymmetric
**oscillations**... Comparison of axisymmetric**oscillations**and non-axisymmetric**oscillations**observed for**frequencies**40Hz/60Hz and 50Hz respectively, for the same actuation voltage 74Vrms. This figure depicts the existence of a local minimum at 50Hz where non-axisymmetric modes can be observed at lower voltages. ... Number of cycles required for mixing of droplets at different actuation**frequencies**for 115Vrms using non-axisymmetric modes. Below 55Hz, only k=2 mode**oscillations**exist and the number of cycles required for mixing increase with the**frequency**. Beyond 55Hz, other higher**oscillation**modes exist. ... Mixing of droplets of DI water (8μl) and diluted orange food colour droplet (2μl) using non-asymmetric**oscillations**with 115Vrms and**frequencies**(A) 35Hz (mode k=2) and (B) 85Hz (mode k=3). [supplementary videos available]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) ...**Oscillation**patterns (top view) of a 8μl droplet at different voltages and**frequencies**(a) mode k=0 at 35Hz, 74Vrms; (b) mode k=2 at 35Hz, 117Vrms; (c) mode k=3 at 100Hz, 117Vrms. [supplementary videos available]. ... Change in base radius of an drop at different**frequencies**for 35Vrms. Axisymmetric**oscillations**at 35Vrms voltage are found to have a resonance peak at 25Hz (having an average contact angle θa∼113°).Data Types:- Image
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- Coupled
**oscillators**... FRCs of the normalised relative displacement W as a function of the normalised**frequency**, Ω, for γ=2×10−3, ζs=0.046,ζ=0.026 and for different values of the normalised primary resonance of the**oscillator**: (a) ω0=1.4, (b) ω0=1.1, (c) ω0=0.7, (d) ω0=0.5, (e) ω0=0.3, (f) ω0=0.1. Stable solution (blue solid line), unstable solution (red dashed line). Numerical solution by integrating Eqs. (4a) and (4b) for μ=0.001 (black ‘∘’). ... Supplimentary material to “On the interaction of the responses at the resonance**frequencies**of a nonlinear two degrees-of-freedom system”.Data Types:- Image
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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**Data Types:- Image
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- Analytically obtained
**frequency**-response curves defined by Eq. (35) of the**oscillator**governed by Eq. (1) for van der Pol damping, α=4/5, ε=0.2 and different values of F. Numerical results are depicted by dots. The lines and zones related to tr2−4det, tr and det are defined by Eqs. (39) and (40). A backbone curve is plotted as a dashed–dotted line. The mark ‘∗’ stands for the characteristics of free limit cycle**oscillations**. ...**Frequency**-response curves of the**oscillator**governed by Eq. (1) for van der Pol damping, α=3, ε=0.566 and two different values of F. Analytical results from [20] are depicted by a dashed–dotted line, analytical results from this paper by a solid and dotted line and numerical results by dots. The lines and zones related to tr and det are defined by Eqs. (39) and (40). The mark ‘∗’ stands for the characteristics of free limit cycle**oscillations**. ... Period of**oscillations**TexND given by Eq. (7). ...**Frequency**-response curves of the**oscillator**governed by Eq. (1) for linear viscous damping, F=ε=0.1 and for: (a) α=1/4; (b) α=4. Analytical results (49) are depicted by a solid line (stable) and by a dotted line (unstable); a shaded region (instability zone) is bounded by the curves defined by Eq. (53); a backbone curve (48) is shown as a dashed–dotted line; numerical results are depicted by dots. ...**Frequency**-response curveData Types:- Image
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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**Data Types:- Other
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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**Data Types:- Image
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- Center of mass displacement (green curve) and acceleration (blue curve) relative to tail position (red, shown for reference) in L. macrochirus swimming at 1.5BL/s. Surge acceleration shows a double peak
**oscillation**at twice the**frequency**of the tail beat which is absent in the sway data. ... Comparison of COM**oscillation**magnitude for different animals. COM**oscillation**magnitude (peak-to-peak) in each direction was averaged across speeds for terrestrial species to give a single number generally representative of each species. Non-fish data were taken from the literature, and represent COM heave (vertical) motion only since this is the most commonly reported direction of COM**oscillation**, except for the sandfish point which represents sway motion. Fish data (green, red, and blue points) are from the present study and excursions are shown for all three different measured directions: heave, surge, and sway. The linear fit for data on terrestrial animals shown is 1.44x−6.07 (R2=0.88), indicating that COM displacement scales positively with mass, and that larger animals display a larger vertical**oscillation**than would be expected for their size. Fish have significantly lower heave COM**oscillations**than terrestrial animals. The orange point represents lizard sandfish moving in a granular medium and is derived from Ding et al. (2012). ... Two-way ANOVA table to show F-values for speed and species effects on each of the three dimensions of center of mass (COM)**oscillation**. ... Fast Fourier transforms of surge COM acceleration and displacement data for locomotion at 1.5BL/s in (A) L. macrochirus, (B) A. rostrata, and (C) N. chitala. The**frequency**components of the tail beat are shown for comparison in red. At this speed, L. macrochirus uses body and caudal fin undulation and so body undulations are comparable to those of the other species. Grey bars mark the tail beat and double tail beat**frequencies**. Both L. macrochirus and A. rostrata show COM acceleration**frequency**peaks at greater power for double the tail beat**frequency**than for the single beat**frequency**, and significant power for displacement at double the tail beat**frequency**. N. chitala, on the other hand, shows minimal power at double the tail beat**frequency**for acceleration, and negligible power for displacement. ... Speed vs.**frequency**for three species swimming in four swimming modes.**Frequency**had a significant positive relationship (pfrequency was substituted for tail beat**frequency**during labriform propulsion at 0.5BL/s as there was no body undulation at this speed.Data Types:- Image
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- Bistable bilinear
**oscillator**: (a) bilinear restoring force (solid curve) and (b) numerical solution of (1) for γt=0.118, ζt=0.071, and xs=0.0073 (solid curve). ... NL bistable**oscillator**. (a) Bistable**oscillator**composed of a linear**oscillator**and a NL element. (b) The dimensionless restoring force of a bistable**oscillator**for different values of α (α=0, solid curve; α=0.1, dotted curve; α=0.3, dashed curve; α=1, dot-dashed curve) in the case of k˜NL=1 and β=1. (c) Typical response of bistable**oscillator**to harmonic excitation in a highly pre-resonance regime. The displacement (solid curve), potential (dashed curve) and restoring force (dot-dashed curve) are taken from the experimental setup, see Appendix. ... Bistable energy harvester prototype. (a) Close-up on coil and MP, (b) the prototype**oscillator**, and (c) excitation base comprised of a motorized lead screw base. ... (a) Power ratio of a bistable**oscillator**vs. linear**oscillator**as a function of (γ,ζ) for xs=±0.0073. Analytical results represented by 2-dimensional surface; numerical results represented by the contour plot at the bottom of the figure. (b) Power ratio numeric simulation of a wide barrier bistable**oscillator**. The restoring force used on the numerical simulation is extracted from the bistable prototype; (c) the extracted force. The excitation amplitude used is Y=50[mm]. For description of the prototype, see Appendix. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)Data Types:- Image
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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**.Data Types:- Image
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- Bi-stable
**oscillator**...**Frequency**up-conversion... Velocity decomposition. (Right) Fast component shown in a 3D form: projections show the instantaneous**frequency**(IF) vs. time, the envelope vs. time and IF vs. envelope on the far projection. (Left) Velocity components: instantaneous amplitude vs. instantaneous**frequency**. ... Simulated response of a bi-stable energy harvester under constant**frequency**base excitation ω≈0.1ωn () ωn=7Hz, ζ=0.07. Right: nonlinear (bi-stable) potential (––) and force (–––) functions of the system taken from experimental system. ... Fine resolution spectrum of the bi-stable**oscillator**response to pure sine excitation.Data Types:- Image
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