Global “Eclipse” Bifurcation in a Twinkling Oscillator

2013 ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Bifurcation Point ◽  
High Frequency ◽  
Global Bifurcation ◽  
Low Frequency ◽  
Negative Stiffness ◽  
Symmetric System ◽  
Ambient Vibrations ◽  
High Frequency Oscillations ◽  
Mass Chain

This work regards the use of cubic springs with intervals of negative stiffness, in other words “snap-through” elements, in order to convert low-frequency ambient vibrations into high-frequency oscillations, referred to as “twinkling”. The focus of this paper is on a global bifurcation of a two-mass chain which, in the symmetric system, involves infinitely many equilibria at the bifurcation point. The structure of this “eclipse” bifurcation is uncovered, and perturbations of the bifurcation are studied. The energies associated with the equilibria are examined.

“Eclipse” Bifurcation in a Twinkling Oscillator

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Bifurcation Point ◽  
High Frequency ◽  
Low Frequency ◽  
Negative Stiffness ◽  
Symmetric System ◽  
Ambient Vibrations ◽  
High Frequency Oscillations ◽  
Mass Chain

This work regards the use of cubic springs with intervals of negative stiffness, in other words, “snap-through” elements, in order to convert low-frequency ambient vibrations into high-frequency oscillations, referred to as “twinkling.” The focus of this paper is on the bifurcation of a two-mass chain that, in the symmetric system, involves infinitely many equilibria at the bifurcation point. The structure of this “eclipse bifurcation” is uncovered, and perturbations of the bifurcation are studied. The energies associated with the equilibria are examined.

Bifurcations in Twinkling Oscillators

2012 ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
High Frequency ◽  
Energy Levels ◽  
Low Frequency ◽  
Degree Of Freedom ◽  
Nonlinear Structure ◽  
High Frequency Oscillations ◽  
Mass Chain ◽  
New Type ◽  
The Masses ◽  
Two Degree Of Freedom

We present the underlying dynamics of snap-through structures that exhibit twinkling. Twinkling occurs when the nonlinear structure is loaded slowly and the masses snap-through, converting the low frequency input to high frequency oscillations. We have studied a nonlinear spring-mass chain loaded by a quasistatic pull. The spring forces are assumed to be cubic with intervals of negative stiffness. Depending on the parameters, the system has equilibria at multiple energy levels. The normal form and the bifurcation behaviors for the single and two degree of freedom systems are studied in detail. A new type of bifurcation, which we refer to as a star bifurcation, has been observed for the symmetric two degree of freedom system, which is of codimension four for the undamped case, and codimension three or two for the damped case, depending on the form of the damping.

scholarly journals Recognition of Emotional States using Multiscale Information Analysis of High Frequency EEG Oscillations

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 609 ◽  
Author(s):  
Gao ◽  
Cui ◽  
Wan ◽  
Gu
Keyword(s):  
Emotion Recognition ◽  
High Frequency ◽  
Low Frequency ◽  
Support Vector ◽  
Discrete Wavelet ◽  
Emotional States ◽  
Circumplex Model ◽  
Information Analysis ◽  
Eeg Signals ◽  
High Frequency Oscillations

Exploring the manifestation of emotion in electroencephalogram (EEG) signals is helpful for improving the accuracy of emotion recognition. This paper introduced the novel features based on the multiscale information analysis (MIA) of EEG signals for distinguishing emotional states in four dimensions based on Russell's circumplex model. The algorithms were applied to extract features on the DEAP database, which included multiscale EEG complexity index in the time domain, and ensemble empirical mode decomposition enhanced energy and fuzzy entropy in the frequency domain. The support vector machine and cross validation method were applied to assess classification accuracy. The classification performance of MIA methods (accuracy = 62.01%, precision = 62.03%, recall/sensitivity = 60.51%, and specificity = 82.80%) was much higher than classical methods (accuracy = 43.98%, precision = 43.81%, recall/sensitivity = 41.86%, and specificity = 70.50%), which extracted features contain similar energy based on a discrete wavelet transform, fractal dimension, and sample entropy. In this study, we found that emotion recognition is more associated with high frequency oscillations (51–100Hz) of EEG signals rather than low frequency oscillations (0.3–49Hz), and the significance of the frontal and temporal regions are higher than other regions. Such information has predictive power and may provide more insights into analyzing the multiscale information of high frequency oscillations in EEG signals.

Design and Numerical Analysis of an Electrostatic Energy Harvester With Impact for Frequency Up-Conversion

2020 ◽  
Vol 15 (5) ◽  
Author(s):  
R. Lensvelt ◽  
R. H. B. Fey ◽  
R. M. C. Mestrom ◽  
H. Nijmeijer
Keyword(s):  
Power Generation ◽  
High Frequency ◽  
Energy Harvester ◽  
Low Frequency ◽  
Electrostatic Energy ◽  
Computational Time ◽  
Ambient Vibrations ◽  
Frequency Oscillator ◽  
Low Frequency Power ◽  
Frequency Power

Abstract Integration of vibration energy harvesters (VEHs) with small-scale electronic devices may form an attractive alternative for relatively large batteries and can, potentially, increase their lifespan. However, the inherent mismatch between a harvester's high-frequency resonance, typically in the range 100−1000 Hz, relative to the available low-frequency ambient vibrations, typically in the range 10–100 Hz, means that low-frequency power generation in microscale VEHs remains a persistent challenge. In this work, we model a novel electret-based, electrostatic energy harvester (EEH) design. In this design, we combine an out-of-plane gap-closing comb (OPGC) configuration for the low-frequency oscillator with an in-plane overlap comb configuration for the high-frequency oscillator and employ impact for frequency up-conversion. An important design feature is the tunability of the resonance frequency through the electrostatic nonlinearity of the low-frequency oscillator. Impulsive normal forces due to impact are included in numerical simulation of the EEH through Moreau's time-stepping scheme which has, to the best of our knowledge, not been used before in VEH design and analysis. The original scheme is extended with time-step adjustments around impact events to reduce computational time. Using frequency sweeps, we numerically investigate power generation under harmonic, ambient vibrations. Results show improved low-frequency power generation in this EEH compared to a reference EEH. The EEH design shows peak power generation improvement of up to a relative factor 3.2 at low frequencies due to the occurrence of superharmonic resonances.

Observation of Turbulent Waves in a Helium Plasma by Optical Spectroscopy

1975 ◽  
Vol 30 (10) ◽  
pp. 1271-1278
Author(s):  
W. R. Rutgers
Keyword(s):  
Energy Density ◽  
Field Strength ◽  
High Frequency ◽  
Low Frequency ◽  
Turbulent Plasma ◽  
Helium Plasma ◽  
High Frequency Oscillations ◽  
Low Frequency Oscillations ◽  
Frequency Domains ◽  
Turbulent Heating

Abstract From the combined Stark-Zeeman pattern of helium allowed and forbidden optical lines the frequency spectrum, the field strength and the dominant polarization of microfields were determined in a turbulent plasma. Two frequency domains of oscillations were found in a turbulent heating experiment: low-frequency oscillations with dominant polarization perpendicular to the current direction and high-frequency oscillations (f~fpe) with random polarization. The r.m.s. field strength of the oscillations is between 2 kV/cm and 10 kV/cm. The energy density of turbulent microfields amounts to 1‰ of the thermal energy density.

scholarly journals Motoneuron firing patterns underlying fast oscillations in phrenic nerve discharge in the rat

2012 ◽  
Vol 108 (8) ◽  
pp. 2134-2143 ◽  
Author(s):  
Vitaliy Marchenko ◽  
Michael G. Z. Ghali ◽  
Robert F. Rogers
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Medium Frequency ◽  
Adult Rats ◽  
Time Frequency ◽  
High Frequency Oscillations ◽  
Novel Method ◽  
Frequency Coherence ◽  
Fast Oscillations ◽  
First Time

Fast oscillations are ubiquitous throughout the mammalian central nervous system and are especially prominent in respiratory motor outputs, including the phrenic nerves (PhNs). Some investigators have argued for an epiphenomenological basis for PhN high-frequency oscillations because phrenic motoneurons (PhMNs) firing at these same frequencies have never been recorded, although their existence has never been tested systematically. Experiments were performed on 18 paralyzed, unanesthetized, decerebrate adult rats in which whole PhN and individual PhMN activity were recorded. A novel method for evaluating unit-nerve time-frequency coherence was applied to PhMN and PhN recordings. PhMNs were classified according to their maximal firing rate as high, medium, and low frequency, corresponding to the analogous bands in PhN spectra. For the first time, we report the existence of PhMNs firing at rates corresponding to high-frequency oscillations during eupneic motor output. The majority of PhMNs fired only during inspiration, but a small subpopulation possessed tonic activity throughout all phases of respiration. Significant time-varying PhMN-PhN coherence was observed for all PhMN classes. High-frequency, early-recruited units had significantly more consistent onset times than low-frequency, early/middle-recruited and medium-frequency, middle/late-recruited PhMNs. High- and medium-frequency PhMNs had significantly more consistent offset times than low-frequency units. This suggests that startup and termination of PhMNs with higher firing rates are more precisely controlled, which may contribute to the greater PhMN-PhN coherence at the beginning and end of inspiration. Our findings provide evidence that near-synchronous discharge of PhMNs firing at high rates may underlie fast oscillations in PhN discharge.

Generation of quasi-stationary magnetic fields by external electromagnetic radiation in a cold magneto-active plasma

1993 ◽  
Vol 49 (1) ◽  
pp. 51-54 ◽  
Author(s):  
Yu. M. Aliev ◽  
B. M. Jovanović ◽  
A. A. Frolov
Keyword(s):  
Electromagnetic Radiation ◽  
High Frequency ◽  
Low Frequency ◽  
Active Plasma ◽  
Method Of Averaging ◽  
Hydrodynamic Equations ◽  
Cold Electron ◽  
Stationary Magnetic Field ◽  
High Frequency Oscillations ◽  
Space Time Evolution

Starting from the hydrodynamic equations for a cold electron fluid, we develop a theory of the ponderomotive effect of the interaction of high-frequency electromagnetic radiation with a magneto-active plasma. Using the method of averaging on high-frequency oscillations, we obtain expressions for the low- frequency nonlinear currents. We also obtain an equation describing the space–time evolution of a quasi-stationary magnetic field in the plasma.

Selective loss of high-frequency oscillations in phrenic and hypoglossal activity in the decerebrate rat during gasping

2006 ◽  
Vol 291 (5) ◽  
pp. R1414-R1429 ◽  
Author(s):  
Vitaliy Marchenko ◽  
Robert F. Rogers
Keyword(s):  
Power Distribution ◽  
High Frequency ◽  
Spectral Characteristics ◽  
Low Frequency ◽  
High Amplitude ◽  
Medial Branch ◽  
Adult Rats ◽  
Time Frequency ◽  
High Frequency Oscillations ◽  
Nerve Recordings

Respiratory motor outputs contain medium-(MFO) and high-frequency oscillations (HFO) that are much faster than the fundamental breathing rhythm. However, the associated changes in power spectral characteristics of the major respiratory outputs in unanesthetized animals during the transition from normal eupneic breathing to hypoxic gasping have not been well characterized. Experiments were performed on nine unanesthetized, chemo- and barodenervated, decerebrate adult rats, in which asphyxia elicited hyperpnea, followed by apnea and gasping. A gated fast Fourier transform (FFT) analysis and a novel time-frequency representation (TFR) analysis were developed and applied to whole phrenic and to medial branch hypoglossal nerve recordings. Our results revealed one MFO and one HFO peak in the phrenic output during eupnea, where HFO was prominent in the first two-thirds of the burst and MFO was prominent in the latter two-thirds of the burst. The hypoglossal activity contained broadband power distribution with several distinct peaks. During gasping, two high-amplitude MFO peaks were present in phrenic activity, and this state was characterized by a conspicuous loss in HFO power. Hypoglossal activity showed a significant reduction in power and a shift in its distribution toward lower frequencies during gasping. TFR analysis of phrenic activity revealed the increasing importance of an initial low-frequency “start-up” burst that grew in relative intensity as hypoxic conditions persisted. Significant changes in MFO and HFO rhythm generation during the transition from eupnea to gasping presumably reflect a reconfiguration of the respiratory network and/or alterations in signal processing by the circuitry associated with the two motor pools.

scholarly journals VIBRATORY SEPARATION OF GRAIN FROM THE EAR: PROBLEMS AND PERSPECTIVES

2020 ◽  
Author(s):  
V.I. Pakhomov ◽  
◽  
S.V. Braginets ◽  
O.N. Bakhchevnikov ◽  
D.V. Rudoy ◽  
...  
Keyword(s):  
High Frequency ◽  
Natural Frequencies ◽  
Low Frequency ◽  
Mechanical Resonance ◽  
High Frequency Oscillations ◽  
Low Frequency Oscillations ◽  
Oscillation Frequencies

The method of vibratory separation of grain from ear is validated in article. It is set that transferring to a stalk with ear low frequency oscillations in the range 18…100 Hz corresponding to natural frequencies of its oscillations are possible to achieve damage of ear or its detachment from a stalk as a result of a resonance. But this interval of oscillation frequencies does not provide separation of grains from ear as does not lead to damage of perular scales. Transmission to ear of high-frequency oscillations in the range 100…14000 Hz matching its natural frequencies of oscillations is perspective for this purpose. The mechanical resonance generate to grain separation owing to break off perular scales from ear can result from such vibratory influence.

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