Contributors: Z.K. Peng, Z.Q. Lang, S.A. Billings, Y. Lu

Date: 2007-11-01

The output frequency response of a nonlinear system. ...The restoring force of a bilinear oscillator. ...The output frequency response of a linear system. ...Bilinear oscillator...The polynomial approximation result for a bilinear oscillator ...Nonlinear output frequency response function...Bilinear oscillator model. ...In this paper, the new concept of nonlinear output frequency response functions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the generalized frequency response functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs. Then, beginning with the demonstration that a bilinear oscillator can be approximated using a polynomial-type nonlinear oscillator, the NOFRFs are used to analyse the energy transfer phenomenon of bilinear oscillators in the frequency domain. The analysis provides insight into how new frequency generation can occur using bilinear oscillators and how the sub-resonances occur for the bilinear oscillators, and reveals that it is the resonant frequencies of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear oscillator model. ... In this paper, the new concept of nonlinear output frequency response functions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the generalized frequency response functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs. Then, beginning with the demonstration that a bilinear oscillator can be approximated using a polynomial-type nonlinear oscillator, the NOFRFs are used to analyse the energy transfer phenomenon of bilinear oscillators in the frequency domain. The analysis provides insight into how new frequency generation can occur using bilinear oscillators and how the sub-resonances occur for the bilinear oscillators, and reveals that it is the resonant frequencies of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear oscillator model.

Contributors: J.C. Cao, X.L. Lei, H.C. Liu

Date: 2003-11-01

We have theoretically investigated spatiotemporal current patterns and self-oscillating characteristics of negative-effective-mass (NEM) p+pp+ diodes. Periodically oscillating current densities are presented as a gray density plot, showing rich patterns with the applied bias and doping concentration as controlling parameters. Such a pattern arises in the NEM p-base with a “N-shaped” velocity–field relation. Two-dimensional applied bias-doping concentration phase diagrams at different lattice temperatures are calculated in order to visualize the effect of lattice temperature on the self-oscillating regions. It is indicated that both the applied bias and the doping concentration strongly influence the patterns and self-oscillating frequencies, which are generally in the terahertz (THz) frequency band. The NEM p+pp+ diode may therefore be used to develop a electrically tunable THz-frequency oscillator....Self-oscillation...Time-periodic self-oscillating current densities for the p+pp+ NEM diodes at T=77 K and doping concentrations Na=7×1016 cm−3 are shown as a density gray plot, where lighter areas correspond to larger amplitudes of the current densities. ...Self-oscillating frequencies of the p+pp+ NEM diodes at T=77 K with four doping concentrations indicated by the arrows in Fig. 2(a): (a) Na=7×1016 cm−3 and (b) Na=4.5×1017 cm−3, respectively. ...Applied bias-doping concentration phase diagrams of current self-oscillations in the p+pp+ NEM diodes at four lattice temperatures: (a) T=77 K, (b) 145 K, (c) 180 K, and (d) 220 K, respectively. Throughout the paper, the p-base length is set to be l=0.3μm, and the doping concentration in the contact p+-region is assumed to be 2×1018 cm−3. ... We have theoretically investigated spatiotemporal current patterns and self-oscillating characteristics of negative-effective-mass (NEM) p+pp+ diodes. Periodically oscillating current densities are presented as a gray density plot, showing rich patterns with the applied bias and doping concentration as controlling parameters. Such a pattern arises in the NEM p-base with a “N-shaped” velocity–field relation. Two-dimensional applied bias-doping concentration phase diagrams at different lattice temperatures are calculated in order to visualize the effect of lattice temperature on the self-oscillating regions. It is indicated that both the applied bias and the doping concentration strongly influence the patterns and self-oscillating frequencies, which are generally in the terahertz (THz) frequency band. The NEM p+pp+ diode may therefore be used to develop a electrically tunable THz-frequency oscillator.

Contributors: Binbin Qiu, Junjie Yan, Jiping Liu, Daotong Chong, Quanbin Zhao, Xinzhuang Wu

Date: 2014-01-01

Dominant frequency...The first and the second dominant frequencies variation with the steam mass flux. ...The first and the second dominant frequencies variation with the water temperature. ...The dominant frequency regime map. ...Pressure oscillation...Frequency spectrums of pressure oscillation at different water temperatures and steam mass flux. ...Experimental investigations and analysis on the dominant frequency of pressure oscillation for sonic steam jet in subcooled water have been performed. It was found that sometimes there is only one dominant frequency for pressure oscillation, and sometimes there is a second dominant frequency for pressure oscillation. The first dominant frequency had been investigated by many scholars before, but the present study mainly investigated the characteristics of the second dominant frequency. The first dominant frequency is mainly caused by the periodical variation of the steam plume and the second dominant frequency is mainly caused by the generating and rupture of the large steam bubbles. A dominant frequency regime map related to the water temperature and steam mass flux is given. When the water temperature and the steam mass flux are low, there is only one dominant frequency of pressure oscillation. When the water temperature or the steam mass flux is high, the second dominant frequency appears for pressure oscillation. The second dominant frequency decreases with the increasing water temperature and steam mass flux. Meanwhile, the second dominant frequency at high steam mass flux and water temperature is lower than the first dominant frequency at low steam mass flux and water temperature. A dimensionless correlation is proposed to predict the second dominant frequency for sonic steam jet. The predictions agree well with the present experimental data, the discrepancies are within ±20%....The dominant frequencies in different measurement points by Qiu et al. [14]. ... Experimental investigations and analysis on the dominant frequency of pressure oscillation for sonic steam jet in subcooled water have been performed. It was found that sometimes there is only one dominant frequency for pressure oscillation, and sometimes there is a second dominant frequency for pressure oscillation. The first dominant frequency had been investigated by many scholars before, but the present study mainly investigated the characteristics of the second dominant frequency. The first dominant frequency is mainly caused by the periodical variation of the steam plume and the second dominant frequency is mainly caused by the generating and rupture of the large steam bubbles. A dominant frequency regime map related to the water temperature and steam mass flux is given. When the water temperature and the steam mass flux are low, there is only one dominant frequency of pressure oscillation. When the water temperature or the steam mass flux is high, the second dominant frequency appears for pressure oscillation. The second dominant frequency decreases with the increasing water temperature and steam mass flux. Meanwhile, the second dominant frequency at high steam mass flux and water temperature is lower than the first dominant frequency at low steam mass flux and water temperature. A dimensionless correlation is proposed to predict the second dominant frequency for sonic steam jet. The predictions agree well with the present experimental data, the discrepancies are within ±20%.

Contributors: K.M. EL-Naggar

Date: 2009-06-01

Low-frequency oscillations...Undamped swing curve: one oscillation mode. ...Un-damped swing curve with two oscillation modes: f1=0.4, f2=0.5Hz and σ1=−0.025, σ2=+0.037s−1. ...Low-frequency oscillations in the interconnected power systems are observed all around the electrical grids. This paper presents a novel technique for analyzing the low-frequency oscillations in power system networks. The proposed technique is a dynamic estimator based on stochastic estimation theory which is suitable for estimating parameters on-line. The method uses digital set of measurements for power system swings to perform the analysis process digitally. The goal is to estimate the amount of damping in the swing curve as well as the oscillation frequency. The problem is formulated and presented as a stochastic dynamic estimation problem. The proposed technique is used to perform the estimation process. The algorithm tested using different study cases including practical data. Results are evaluated and compared to those obtained using other conventional methods to show the capabilities of the proposed method. ... Low-frequency oscillations in the interconnected power systems are observed all around the electrical grids. This paper presents a novel technique for analyzing the low-frequency oscillations in power system networks. The proposed technique is a dynamic estimator based on stochastic estimation theory which is suitable for estimating parameters on-line. The method uses digital set of measurements for power system swings to perform the analysis process digitally. The goal is to estimate the amount of damping in the swing curve as well as the oscillation frequency. The problem is formulated and presented as a stochastic dynamic estimation problem. The proposed technique is used to perform the estimation process. The algorithm tested using different study cases including practical data. Results are evaluated and compared to those obtained using other conventional methods to show the capabilities of the proposed method.

Contributors: Ting Wang, Xiaoguang Wang, Zhe Sun

Date: 2007-09-15

We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L>3, the concurrences and negativities display oscillatory behaviors, and the oscillations of the ground-state and the first-excited-state entanglements are out of phase or in phase....The thermal concurrences between qubits 1 and 2 in the 2–6-qubit spin-half open Heisenberg chains. ... We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L>3, the concurrences and negativities display oscillatory behaviors, and the oscillations of the ground-state and the first-excited-state entanglements are out of phase or in phase.

Contributors: V.J. Law

Date: 2008-02-19

Frequency pulling...Oscillator phase noise...Spectral density of switching frequency as a function flowing afterglow interaction (free space and surface material at 8mm from DBD nozzle). Data acquisition resolution=1Hz. ...Passive radio spectroscopy is employed to examine plasma process instabilities generated by the interaction between the power source oscillator and the plasma load. A fixed frequency of 13.56MHz and a 170–180kHz Flyback transformer are considered. The carrier frequencies are interrogated using a resolution bandwidth that constitutes ∼1/7000–1/580 of the target oscillator frequencies with a sweep time of less than 0.06s across the phase noise disturbance. Within these spectrum analyzer measurement parameters, oscillator phase noise (1/fn=1–3, discrete spurs and raised noise floor) is shown to be linked to plasma load mismatch and periodic instabilities. In the case of the Flyback circuit, it is found that the oscillator frequency pulling and modulation are linked to the plasma reactance. These results indicate that oscillator phase noise can be used as a non-invasive plasma process metrology tool....A typical fixed frequency output from a radio frequency generator coupled to a non-linear plasma load. Oscillator signal, phase noise, ±spurs, and the noise floor. ...Trace of 2N0335 transistor switching frequency and damped oscillation. Data acquisition resolution=0.05μs. ... Passive radio spectroscopy is employed to examine plasma process instabilities generated by the interaction between the power source oscillator and the plasma load. A fixed frequency of 13.56MHz and a 170–180kHz Flyback transformer are considered. The carrier frequencies are interrogated using a resolution bandwidth that constitutes ∼1/7000–1/580 of the target oscillator frequencies with a sweep time of less than 0.06s across the phase noise disturbance. Within these spectrum analyzer measurement parameters, oscillator phase noise (1/fn=1–3, discrete spurs and raised noise floor) is shown to be linked to plasma load mismatch and periodic instabilities. In the case of the Flyback circuit, it is found that the oscillator frequency pulling and modulation are linked to the plasma reactance. These results indicate that oscillator phase noise can be used as a non-invasive plasma process metrology tool.

Contributors: Satoshi Takahashi, Michio Hori

Date: 2005-08-21

Time series of the lefties in the model with large reproductive susceptibility c. The thin line is the frequency of species x's lefty, xL. The bold line is the frequency of the lefty of species y, yL. Frequencies of the morphs oscillate. While lefty of species x, xL, increases, that of species y, yL, decreases. The reproductive susceptibility c=5. Other parameters and initial values are same to those of Fig. 2. ...Time series of the model with its susceptibility c large. Horizontal axis is time. Vertical axis is fraction of species x, (xL+xR), or species y, (yL+yR). Each curve in the graphs is labeled by x or y. Species x increases with time, while species y decreases in (a), (b), (c), and (f). Lefty–righty frequency in each species oscillates, which affects the coexistence of two competing species (c=5,Ty=6) (a) Tx=4; (b) Tx=5.2; (c) Tx=5.8; (d) Tx=6.2; (e) Tx=7; (f) Tx=9. Other parameter values are same to those in Fig. 2. ...Time series of the lefties in the model with small reproductive susceptibility c. Frequencies of the morphs in each species do not oscillate and tend to a point in the continuum of the equilibria. The thin line is the frequency of species x's lefty, xL. The bold line is the frequency of the lefty of species y, yL. Parameter values are: b=0.75,c=0.5,Tx=4,Ty=6. Initial values are xL(t)=0.2,xR(t)=0.1(-Tx⩽t⩽0),yL(t)=0.6,yR(t)=0.1(-Ty⩽t⩽0). ...Scale-eating cichlids in Lake Tanganyika exhibit genetically determined lateral asymmetry, especially in their mouth-opening. Frequencies of the morphs oscillate due to strong frequency-dependent selection caused by the switching of prey's attention, and its delayed effect by their growth period. Two scale-eaters coexist in similar densities at south shore of the lake, with their morph frequencies oscillating in phase. We investigated the effect of the oscillation in morph frequencies to the coexistence of competing species. If the difference of two species’ growth period is large, the oscillation facilitates the coexistence of the two species, while small difference of growth periods hinders their coexistence. In the latter case, the species with shorter growth period drives the other species to the extinction....Frequency-dependent selection...Oscillation...Frequency of the righty morph in P. microlepis (thin line) and P. straeleni (bold line). The data are plotted for years ’88, ’90, ’92, ’93, ’94 (P. microlepis only), and ’95. ... Scale-eating cichlids in Lake Tanganyika exhibit genetically determined lateral asymmetry, especially in their mouth-opening. Frequencies of the morphs oscillate due to strong frequency-dependent selection caused by the switching of prey's attention, and its delayed effect by their growth period. Two scale-eaters coexist in similar densities at south shore of the lake, with their morph frequencies oscillating in phase. We investigated the effect of the oscillation in morph frequencies to the coexistence of competing species. If the difference of two species’ growth period is large, the oscillation facilitates the coexistence of the two species, while small difference of growth periods hinders their coexistence. In the latter case, the species with shorter growth period drives the other species to the extinction.

Contributors: Hans G. Mayr, Kenneth H. Schatten

Date: 2012-01-01

(a) Altitude variation of eddy diffusivity/viscosity, K, which dissipates the oscillation (Mayr et al., 1997). (b) Eddy viscosity time constant versus altitude; periods around 2 years define the QBO oscillation. ...(a) Meridional wind, V, oscillations, at 4° latitude, with periods of about 2 months, generated only with meridional GW propagating north/south. (b) Snapshots are shown of normalized meridional winds, and the associated momentum source produces sharp peaks near vertical wind shears, similar to Fig. 3 (Mayr et al., 2003). ...Shown are equatorial zonal winds, U, plotted versus altitude and time (a), and the corresponding oscillation periods (b), computed without the influence of time dependent solar heating. A constant gravity wave (GW) flux provides the energy for the momentum source that generates the QBO-like oscillation below 35km (Mayr et al., 1998). ...(a) A familiar example of a nonlinear oscillator (NLO) is the mechanical clock, where the escapement mechanism produces the impulse/nonlinearity that generates the oscillation without external time dependent source. Illustrated are the impulse sequence and broadband frequency sequence, which produce the pendulum oscillation with resonance frequency. Examples of linear oscillators (LO) are: (b) the electric circuit of the radio tuner, which filters out a single frequency (right panel) from the received broadband wave spectrum (left panel); and (c) gravity wave oscillations with resonance maxima, which are generated by an external time dependent energy source (Mayr and Volland, 1976). ...Seasonal variations of westward propagating 12-h (semidiurnal) tidal oscillations for m=1 meridional winds at 100km, applying a running window of 3 days. Generated with (a) and without (b) solar excitation of the diurnal tides, the oscillations, at times, have comparable amplitudes (Talaat and Mayr, 2011). ...We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Earth's atmosphere, foremost the quasi-biennial oscillation (QBO). These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has a particular form, of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental frequency of the internal oscillation, which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation....Intra-seasonal bimonthly oscillation...Wave-driven quasi-biennial oscillation ... We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Earth's atmosphere, foremost the quasi-biennial oscillation (QBO). These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has a particular form, of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental frequency of the internal oscillation, which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.

Contributors: R. Zelmann, F. Mari, J. Jacobs, M. Zijlmans, F. Dubeau, J. Gotman

Date: 2012-01-01

Diagram of the MNI detector. (A) baseline detector. (B) HFOs detection in channels with baseline. (C) HFOs detection in channels with continuous high frequency activity. If more than 5s/min of baselines are found, HFOs are detected with respect to the baseline segments (B). If less than 5s/min of baseline were detected, HFOs are detected with respect to the entire EEG segment in an iterative way (C). WE: wavelet entropy; Rxx: autocorrelation; th: Threshold. ...High frequency oscillations...Histogram of peak frequencies of FRs not occurring with ripples. Out of the 7994 PosAnd HFOs, 554 corresponded to FR that did not co-occur with a visually marked ripple. The peak frequencies of these events included not only the 250–500Hz band but also the 80–250Hz band. All these events were visually marked as FR using a high-pass filter at 250Hz. Two examples are presented. Top: FR with a peak frequency at 150Hz; Bottom: FR with a peak at 265Hz. The unfiltered EEG, the filtered EEG above 80Hz and the filtered EEG above 250Hz are shown. The oscillations become visible only when filtering above 250Hz. ...High frequency oscillations (HFOs) are a biomarker of epileptogenicity. Visual marking of HFOs is highly time-consuming and inevitably subjective, making automatic detection necessary. We compare four existing detectors on the same dataset. ... High frequency oscillations (HFOs) are a biomarker of epileptogenicity. Visual marking of HFOs is highly time-consuming and inevitably subjective, making automatic detection necessary. We compare four existing detectors on the same dataset.

Contributors: Gülnur Birol, Abdel-Qader M Zamamiri, Martin A. Hjortsø

Date: 2000-07-01

Frequency spectra (a), (b) and (c) correspond to the frequency spectra of signals in Fig. 6 (a), (b) and (c), respectively. By construction, frequency spectrum in (a) is equal to the sum of the spectra in (b) and (c). ...Period and amplitude of oscillation versus average dilution rate (h−1) calculated by FFT analysis in intervals of 512 data points of the filtered data shown in Fig. 4. ...Frequency spectra of the exhaust CO2 signal shown in Fig. 1: (a) through (d) correspond to regions 1 through 4 of Fig. 1, respectively; (e) shows the frequency spectrum of the overall signal. ...Autonomous oscillations...Calculated periods of oscillations, in minutes, obtained by FFT analysis of various signals ...Measurements of state variables from oscillating chemostat cultures of Saccharomyces cerevisiae were analyzed by Fourier transformation. Of the signals tested, carbon dioxide and oxygen in the exit gas stream and dissolved oxygen in the medium, all gave identical results. Analysis of data from reactors operated at fixed conditions showed that after oscillations start, they pass through an extended transient lasting several days, before the oscillation period becomes constant. Under transient operating conditions, Fourier analysis revealed expected qualitative trends in the change of oscillation period with dilution rate....Filtered CO2 signal of the ramp experiment shown in Fig. 3. The filtered signal was obtained by subtracting moving signal averages from the original signal and represents the oscillating part of the signal. ... Measurements of state variables from oscillating chemostat cultures of Saccharomyces cerevisiae were analyzed by Fourier transformation. Of the signals tested, carbon dioxide and oxygen in the exit gas stream and dissolved oxygen in the medium, all gave identical results. Analysis of data from reactors operated at fixed conditions showed that after oscillations start, they pass through an extended transient lasting several days, before the oscillation period becomes constant. Under transient operating conditions, Fourier analysis revealed expected qualitative trends in the change of oscillation period with dilution rate.