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Journal articles on the topic 'Subharmonic mode'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 July 2025

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1

IBADULLAEV, Muhtarhan, Akrom N. TOVBAEV, and Azamat Zh ESENBEKOV. "On the General Theory for Analysis of Subharmonic Oscillations in Three-Phase Ferroresonance Circuits and Systems." Elektrichestvo, no. 12 (2021): 35–44. http://dx.doi.org/10.24160/0013-5380-2021-12-35-44.

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The general theory for analysis of subharmonic oscillations at a frequency of ω/3 in three-phase ferroresonance circuits is presented. The occurrence and existence of ferroresonance oscillations at subharmonic frequencies in power transmission lines and power supply systems is highly undesirable, since they cause overvoltages at various frequencies. At the same time, there is an extensive class of nonlinear electrical circuits in which the excitation of autoparametric oscillations at the frequency of subharmonics forms the basis of phase-discrete frequency converting devices serving as seconda

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2

Monkewitz, Peter A. "Subharmonic resonance, pairing and shredding in the mixing layer." Journal of Fluid Mechanics 188 (March 1988): 223–52. http://dx.doi.org/10.1017/s0022112088000710.

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An instability-wave analysis is presented to describe the spatial evolution of a fundamental mode and its subharmonic on an inviscid parallel mixing layer. It incorporates explicitly the weakly nonlinear interaction between the two modes. The computational finding that the development of the subharmonic, leading eventually to pairing or shredding, crucially depends on its phase relation with the fundamental is fully confirmed. Furthermore it is shown that a critical fundamental amplitude has to be reached before the (spatial) subharmonic becomes phase locked with the fundamental and exhibits a

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3

Panigrahi, P. K., and S. Acharya. "Multi-Modal Forcing of the Turbulent Separated Shear Flow Past a Rib." Journal of Fluids Engineering 126, no. 1 (2004): 22–31. http://dx.doi.org/10.1115/1.1637634.

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Experiments have been conducted to study the development of flow behind a surface mounted rib under different phase controlled excitation. Single mode excitation and multi-mode excitation with different relative phases are studied. The results presented include the coherent and random components of the turbulent energy and shear stresses, the energy exchange with the mean flow and between the modes, and the phase decorrelation of the coherent components. The fundamental-subharmonic excitation does not provide any significant improvements in the shear layer growth over the fundamental excitatio

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4

Yang, Ruixin, Frederic K. Browand, Pierre Coullet, and Patrick Huerre. "A model of defect-induced pairing in mixing layers." Journal of Fluid Mechanics 248 (March 1993): 403–23. http://dx.doi.org/10.1017/s0022112093000825.

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Experiment have shown that the well-known vortex pairing process may take place first in defect regions where the fundamental structure is weakest. A model is introduced here to describe this defect-induced pairing process. The model is constructed in such a way that, in a certain parameter range, a stable fundamental mode and a stable subharmonic mode may coexist. The numerical simulation demonstrates that, when initial conditions consist of a dominant fundamental with one or more defects, the subharmonic component is preferentially generated in the cores of these defects. Moreover, the resul

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5

Eigenwillig, Christoph M., Wolfgang Wieser, Benjamin R. Biedermann, and Robert Huber. "Subharmonic Fourier domain mode locking." Optics Letters 34, no. 6 (2009): 725. http://dx.doi.org/10.1364/ol.34.000725.

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6

Gribanov, Alexey, Mikhail Yakovin, Dmitry Yakovin, and Mikhail Mosin. "Subharmonic mode locking of a Q-switched Nd:YAG laser." Chinese Optics Letters 21, no. 3 (2023): 031406. http://dx.doi.org/10.3788/col202321.031406.

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7

Seya, Keiji, Yasuo Tanaka, and Mine Takeuti. "Nonlinear Two-Mode Coupling Models of Radial Stellar Oscillations." Publications of the Astronomical Society of Japan 42, no. 3 (1990): 405–18. https://doi.org/10.1093/pasj/42.3.405.

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Abstract The two-mode coupling of a stellar model has been studied by using coupled van der Pol oscillators. Numerical studies show subharmonic phase-locking in their coupling oscillations. Period-doubling bifurcation accompanied by beats develops with the changes of a parameter. It is suggested that the observed double-periodic stellar pulsations might be subharmonic phase-locking, and not the superposition of two non-synchronized oscillations.

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8

Friedland, L., J. Fajans, and E. Gilson. "Subharmonic autoresonance of the diocotron mode." Physics of Plasmas 7, no. 5 (2000): 1712–18. http://dx.doi.org/10.1063/1.873989.

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9

GORDEYEV, S. V., and F. O. THOMAS. "Temporal subharmonic amplitude and phase behaviour in a jet shear layer: wavelet analysis and Hamiltonian formulation." Journal of Fluid Mechanics 394 (September 10, 1999): 205–40. http://dx.doi.org/10.1017/s0022112099005650.

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Fourier and wavelet transformation techniques are utilized in a complementary manner in order to characterize temporal aspects of the transition of a planar jet shear layer. The subharmonic is found to exhibit an interesting temporal amplitude and phase variation that has not been previously reported. This takes the form of intermittent π-shifts in subharmonic phase between two fixed phase values. These phase jumps are highly correlated with local minima of the subharmonic amplitude. In contrast, the fundamental amplitude and phase show no such behaviour. The temporal phase behaviour of the su

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10

CHEN, WEN-YAU, and C. F. CHEN. "Effect of gravity modulation on the stability of convection in a vertical slot." Journal of Fluid Mechanics 395 (September 25, 1999): 327–44. http://dx.doi.org/10.1017/s0022112099006011.

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The nature of instability occurring in a differentially heated infinite slot under steady gravity depends only on the Prandtl number of the contained Boussinesq fluid. For fluids with Pr < 12.5, the instability is shear dominated and onsets in a steady convection mode; for fluids with Pr > 12.5, the instability is buoyancy dominated and onsets in an oscillatory mode. In this paper, we examine the effect of gravity modulation on the stability characteristics of convection in an infinite slot with both kinds of fluids, in particular, Pr = 1 and Pr = 25. Using the method of Sinha & Wu (

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11

Wu, Xuesong, and Philip A. Stewart. "Interaction of phase-locked modes: a new mechanism for the rapid growth of three-dimensional disturbances." Journal of Fluid Mechanics 316 (June 10, 1996): 335–72. http://dx.doi.org/10.1017/s0022112096000572.

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In this paper, we have identified a new mechanism which can promote rapid growth of three-dimensional disturbances. The mechanism involves the interaction between a planar mode and an oblique mode, or a pair of oblique modes, which are phase-locked in the sense that they have the same phase speed. This allows a powerful nonlinear interaction to take place within the common critical layer(s). The disturbance is not required to form a subharmonic resonant triad, and hence the mechanism operates under much less restrictive conditions than does subharmonic resonance (although it is somewhat less p

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12

Wundrow, David W., Lennart S. Hultgren, and M. E. Goldstein. "Interaction of oblique instability waves with a nonlinear plane wave." Journal of Fluid Mechanics 264 (April 10, 1994): 343–72. http://dx.doi.org/10.1017/s0022112094000698.

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This paper is concerned with the downstream evolution of a resonant triad of initially non-interacting linear instability waves in a boundary layer with a weak adverse pressure gradient. The triad consists of a two-dimensional fundamental mode and a pair of equal-amplitude oblique modes that form a subharmonic standing wave in the spanwise direction. The growth rates are small and there is a well-defined common critical layer for these waves. As in Goldstein & Lee (1992), the wave interaction takes place entirely within this critical layer and is initially of the parametric-resonance type.

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13

Li, Fei, and Mujeeb R. Malik. "Fundamental and subharmonic secondary instabilities of Görtler vortices." Journal of Fluid Mechanics 297 (August 25, 1995): 77–100. http://dx.doi.org/10.1017/s0022112095003016.

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The nonlinear development of stationary Görtler vortices leads to a highly distorted mean flow field where the streamwise velocity depends strongly not only on the wall-normal but also on the spanwise coordinates. In this paper, the inviscid instability of this flow field is analysed by solving the two-dimensional eigenvalue problem associated with the governing partial differential equation. It is found that the flow field is subject to the fundamental odd and even (with respect to the Görtler vortex) unstable modes. The odd mode, which was also found by Hall & Horseman (1991), is initial

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14

Sheard, G. J., M. C. Thompson, and K. Hourigan. "Subharmonic mechanism of the mode C instability." Physics of Fluids 17, no. 11 (2005): 111702. http://dx.doi.org/10.1063/1.2139682.

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15

Sutherland, Bruce R. "Excitation of superharmonics by internal modes in non-uniformly stratified fluid." Journal of Fluid Mechanics 793 (March 16, 2016): 335–52. http://dx.doi.org/10.1017/jfm.2016.108.

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Theory and numerical simulations show that the nonlinear self-interaction of internal modes in non-uniform stratification results in energy being transferred to superharmonic disturbances forced at twice the horizontal wavenumber and frequency of the parent mode. These disturbances are not in themselves a single mode, but a superposition of modes such that the disturbance amplitude is largest where the change in the background buoyancy frequency with depth is largest. Through weakly nonlinear interactions with the parent mode, the disturbances evolve to develop vertical-scale structures that d

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16

Li, Xin-Zheng, Zhan-Guo Bai, Yan Li, and Kun Zhao. "Numerical investigation on oscillatory Turing patterns in a two-layer coupled reaction–diffusion system." Modern Physics Letters B 30, no. 07 (2016): 1650085. http://dx.doi.org/10.1142/s0217984916500858.

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In this paper, various kinds of spontaneous dynamic patterns are investigated based on a two-layer nonlinearly coupled Brusselator model. It is found that, when the Hopf mode or supercritical Turing mode respectively plays major role in the short or long wavelength mode layer, the dynamic patterns appear under the action of nonlinearly coupling interactions in the reaction–diffusion system. The stripe pattern can change its symmetrical structure and form other graphics when influenced by small perturbations sourced from other modes. If two supercritical Turing modes are nonlinearly coupled tog

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17

Zhang, Yinquan, Kun Huang, and Changxing Zhang. "Nonlinear Vibrations of Carbon Nanotubes with Thermal-Electro-Mechanical Coupling." Applied Sciences 13, no. 4 (2023): 2031. http://dx.doi.org/10.3390/app13042031.

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Carbon nanotubes (CNTs) have wide-ranging applications due to their excellent mechanical and electrical properties. However, there is little research on the nonlinear mechanical properties of thermal-electro-mechanical coupling. In this paper, we study the nonlinear vibrations of CNTs by a thermal-electro-mechanical coupling beam theory. The Galerkin method is used to discretize the partial differential equation and obtain two nonlinear ordinary differential equations that describe the first- and second-order mode vibrations. Then, we obtain the approximate analytical solutions of the two equa

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18

Pinault, Jean-Louis. "Glaciers and Paleorecords Tell Us How Atmospheric Circulation Changes and Successive Cooling Periods Occurred in the Fennoscandia during the Holocene." Journal of Marine Science and Engineering 9, no. 8 (2021): 832. http://dx.doi.org/10.3390/jmse9080832.

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Two major climatic phenomena that occurred during the Holocene are interpreted from the resonance in subharmonic modes of long-period Rossby waves winding around the North Atlantic gyre, the so-called gyral Rossby waves (GRWs). These are, on the one hand, the change in atmospheric circulation that occurred in the North Atlantic in the middle Holocene, and, on the other hand, the occurrence of abrupt cooling events more frequently than what is generally accepted. The amplitude of GRWs is deduced by filtering, within bands characteristic of various subharmonic modes, climate records from the Gre

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19

Wang, Xiaohong, Qisong Huang, Bo Zhang, Di Chen, and Quanxue Guan. "Z-domain modeling of peak current mode control for full-bridge DC-DC buck converters." Journal of Power Electronics 21, no. 1 (2020): 27–37. http://dx.doi.org/10.1007/s43236-020-00157-w.

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AbstractTraditional local-averaged state-space modeling for peak current mode (PCM) controls fails to explain the subharmonic oscillation phenomenon when the spectrum is higher than half of the switching frequency. To address this problem, this paper presents a small-signal modeling method in the z-domain, and builds a discrete linear model for the current loop of a full-bridge DC-DC converter. This discrete model is converted into a second-order continuous model that is able to represent the system performance with a wider frequency range. A frequency-domain analysis shows that this model can

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20

Chung, C. A., W. Z. Chien, and Y. H. Hsieh. "Morphological Instabilities in Time Periodic Crystallization." Journal of Mechanics 23, no. 4 (2007): 295–302. http://dx.doi.org/10.1017/s1727719100001349.

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AbstractA linear stability analysis is performed on the interface that forms during directional solidification of a dilute binary alloy in the presence of time-periodic growth rates. The basic state, in which the flat crystal-melt interface advances at a steady rate with an oscillation superimposed, is solved analytically by expanding the governing equations in terms of the assumed-small amplitude of modulation. We find that there is a frequency window of stabilization, in which the Mullins-Sekerka instability can be stabilized synchronously. Outside of the window, large input frequencies may

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21

Nikitopoulos, D. E., and J. T. C. Liu. "Nonlinear binary-mode interactions in a developing mixing layer." Journal of Fluid Mechanics 179 (June 1987): 345–70. http://dx.doi.org/10.1017/s0022112087001563.

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In this paper we present the formulation and results of two-wave interactions in a spatially developing shear layer, directed at understanding and interpreting the physical mechanisms that underlie the results of quantitative observation. Our study confirms the existence of Kelly's mechanism that augments the growth of a subharmonic disturbance by extracting energy from its fundamental or vice versa. This mechanism is shown to be strongest in the region where the fundamental begins to return energy to the mean flow and the two wave modes are of comparable energy levels. It is found that the in

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22

Smith, Gregory D., Charles L. Cox, S. Murray Sherman, and John Rinzel. "Fourier Analysis of Sinusoidally Driven Thalamocortical Relay Neurons and a Minimal Integrate-and-Fire-or-Burst Model." Journal of Neurophysiology 83, no. 1 (2000): 588–610. http://dx.doi.org/10.1152/jn.2000.83.1.588.

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We performed intracellular recordings of relay neurons from the lateral geniculate nucleus of a cat thalamic slice preparation. We measured responses during both tonic and burst firing modes to sinusoidal current injection and performed Fourier analysis on these responses. For comparison, we constructed a minimal “integrate-and-fire-or-burst” (IFB) neuron model that reproduces salient features of the relay cell responses. The IFB model is constrained to quantitatively fit our Fourier analysis of experimental relay neuron responses, including: the temporal tuning of the response in both tonic a

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23

Yang, Wei, Hao Wei, and Liang Zhao. "Parametric Subharmonic Instability of the Semidiurnal Internal Tides at the East China Sea Shelf Slope." Journal of Physical Oceanography 50, no. 4 (2020): 907–20. http://dx.doi.org/10.1175/jpo-d-19-0163.1.

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AbstractOn the basis of measurements from an observing mooring system, the observational evidence of parametric subharmonic instability (PSI) that transfers energy from semidiurnal internal tides (ITs) to the subharmonic waves at the East China Sea continental shelf slope is presented for the first time. Although the mooring station is very close to the energetic semidiurnal IT generation site, about 76% of the observed shear variance is contained in the near-inertial band, which is found to have comparable upward- and downward-propagating energy components. Bispectra and bicoherence estimates

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24

Hoshida, T., Hai-Feng Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya. "Subharmonic hybrid mode-locking of a monolithic semiconductor laser." IEEE Journal of Selected Topics in Quantum Electronics 2, no. 3 (1996): 514–22. http://dx.doi.org/10.1109/2944.571752.

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25

Vodopyanov, K. L. "Ultra-broadband mid-infrared frequency combs produced by optical subharmonic generation." Quantum Electronics 52, no. 4 (2022): 307–12. http://dx.doi.org/10.1070/qel18012.

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Abstract Optical frequency combs have revolutionised accurate frequency and time measurements and have enabled broadband and simultaneously high resolution spectroscopic measurements that were not previously possible. This paper is an overview of the main results of the previously performed work, describing a new approach to extending frequency combs to the mid-infrared ‘molecular signature’ range using a subharmonic generator based on an optical parametric oscillator operating in degenerate mode. Such an instrument acts as an efficient frequency divider that rigorously down-converts and augme

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26

Spalart, Philippe R., and Kyung-Soo Yang. "Numerical study of ribbon-induced transition in Blasius flow." Journal of Fluid Mechanics 178 (May 1987): 345–65. http://dx.doi.org/10.1017/s0022112087001253.

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The early three-dimensional stages of transition in the Blasius boundary layer are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and low-amplitude three-dimensional random disturbances are introduced. Rapid amplification of the three-dimensional components is observed and leads to transition. For intermediate amplitudes of the two-dimensional wave the breakdown is of subharmonic type, and the dominant spanwise wavenumber increases with the amplitude. For high amplitudes the energy of the fundamental mode is comparable to the energy of the

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Qiu, Zhan, Wenhao Xu, Jiaxin Yuan, and Fuxin Wang. "Secondary resonances in aeroelastic response of oscillating airfoil under dynamic stall." Journal of Vibration and Control 24, no. 23 (2018): 5665–80. http://dx.doi.org/10.1177/1077546318764191.

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To clarify the mechanism of the complex aeroelastic responses of flexible blades of helicopter rotors under dynamic stall, experiments on a 2D aeroelastic system are performed. In the spectra of the response from experiment results, special frequency components are found. Then, a numerical method based on the same aeroelastic model is introduced. Here, the flow field is solved using a zonal solver based on vorticity dynamics. When changing a system’s natural frequency, the same extra frequency components in the response spectra are found when particular ratios of natural and forcing frequencie

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Sun, Oliver M., and Robert Pinkel. "Subharmonic Energy Transfer from the Semidiurnal Internal Tide to Near-Diurnal Motions over Kaena Ridge, Hawaii." Journal of Physical Oceanography 43, no. 4 (2013): 766–89. http://dx.doi.org/10.1175/jpo-d-12-0141.1.

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Abstract Nonlinear energy transfers from the semidiurnal internal tide to high-mode, near-diurnal motions are documented near Kaena Ridge, Hawaii, an energetic generation site for the baroclinic tide. Data were collected aboard the Research Floating Instrument Platform (FLIP) over a 35-day period during the fall of 2002, as part of the Hawaii Ocean Mixing Experiment (HOME) Nearfield program. Energy transfer terms for a PSI resonant interaction at midlatitude are identified and compared to those for near-inertial PSI close to the M2 critical latitude. Bispectral techniques are used to demonstra

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29

Jurman, L. A., S. E. Deutsch, and M. J. Mccready. "Interfacial mode interactions in horizontal gas—liquid flows." Journal of Fluid Mechanics 238 (May 1992): 187–219. http://dx.doi.org/10.1017/s002211209200168x.

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The behaviour of shear-generated interfacial waves in a cocurrent gas-liquid flow in a small rectangular channel is studied experimentally at conditions close to neutral stability. It is found that the linearly most unstable mode, which typically has a frequency of 8–10 Hz and a wavelength 1–4 cm, grows initially — followed immediately by the first overtone. Measurements of the bicoherence spectrum indicate that the overtone and fundamental are coherent in phase, which suggests that energy is transferred from the fundamental to the linearly stable first overtone. This energy transfer mechanism

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30

Pelekasis, Nikolaos A., and John A. Tsamopoulos. "Bjerknes forces between two bubbles. Part 2. Response to an oscillatory pressure field." Journal of Fluid Mechanics 254 (September 1993): 501–27. http://dx.doi.org/10.1017/s002211209300223x.

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The motion of two gas bubbles in response to an oscillatory disturbance in the ambient pressure is studied. It is shown that the relative motion of bubbles of unequal size depends on the frequency of the disturbance. If this frequency is between the two natural frequencies for volume oscillations of the individual bubbles, the two bubbles are seen to move away from each other; otherwise attractive forces prevail. Bubbles of equal size can only attract each other, irrespective of the oscillation frequency. When the Bond number, Bo (based on the average acceleration) lies above a critical region

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31

Sivaramakrishnan, Sudarshan, and Herbert G. Winful. "Subharmonic anti-phase dynamics in coupled mode-locked semiconductor lasers." Optics Letters 42, no. 23 (2017): 4905. http://dx.doi.org/10.1364/ol.42.004905.

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32

SHEARD, G. J., M. C. THOMPSON, K. HOURIGAN, and T. LEWEKE. "The evolution of a subharmonic mode in a vortex street." Journal of Fluid Mechanics 534 (June 21, 2005): 23–38. http://dx.doi.org/10.1017/s0022112005004313.

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Hilali, M'F, G. Dewel, and P. Borckmans. "Subharmonic and strong resonances through coupling with a zero mode." Physics Letters A 217, no. 4-5 (1996): 263–68. http://dx.doi.org/10.1016/0375-9601(96)00344-1.

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YOUNG, W. R., Y. K. TSANG, and N. J. BALMFORTH. "Near-inertial parametric subharmonic instability." Journal of Fluid Mechanics 607 (June 30, 2008): 25–49. http://dx.doi.org/10.1017/s0022112008001742.

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New analytic estimates of the rate at which parametric subharmonic instability (PSI) transfers energy to high-vertical-wavenumber near-inertial oscillations are presented. These results are obtained by a heuristic argument which provides insight into the physical mechanism of PSI, and also by a systematic application of the method of multiple time scales to the Boussinesq equations linearized about a ‘pump wave’ whose frequency is close to twice the inertial frequency. The multiple-scale approach yields an amplitude equation describing how the 2f0-pump energizes a vertical continuum of near-in

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VUKASINOVIC, BOJAN, MARC K. SMITH, and ARI GLEZER. "Dynamics of a sessile drop in forced vibration." Journal of Fluid Mechanics 587 (August 31, 2007): 395–423. http://dx.doi.org/10.1017/s0022112007007379.

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The interfacial dynamics of a sessile water drop was investigated experimentally. The low-viscosity drop was forced by an underlying diaphragm driven vertically by a piezoelectric actuator. This high-frequency forcing produced very low diaphragm displacements, even at high acceleration amplitudes. As the driving amplitude was increased from zero, the drop exhibited several transitions to states of increasing spatio-temporal complexity. The first state of the forced drop consisted of harmonic axisymmetric standing waves that were present for even the smallest diaphragm motion. Wave modes up to

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Sivasubramanian, Jayahar, and Hermann F. Fasel. "Numerical investigation of the development of three-dimensional wavepackets in a sharp cone boundary layer at Mach 6." Journal of Fluid Mechanics 756 (September 3, 2014): 600–649. http://dx.doi.org/10.1017/jfm.2014.434.

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AbstractDirect numerical simulations were performed to investigate wavepackets in a sharp cone boundary layer at Mach 6. In order to understand the natural transition process in hypersonic cone boundary layers, the flow was forced by a short-duration (localized) pulse. The pulse disturbance developed into a three-dimensional wavepacket, which consisted of a wide range of disturbance frequencies and wavenumbers. First, the linear development of the wavepacket was studied by forcing the flow with a low-amplitude pulse (0.001 % of the free-stream velocity). The dominant waves within the resulting

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Chen, Shih-Chung, Chao-Lin Kuo, Chia-Hung Lin, Chih-Hung Hsu, and Chien-Kuo Tsui. "Applications of Fuzzy Sliding Mode Control for a Gyroscope System." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/931285.

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The study proposed the application of the fuzzy sliding mode for a gyroscope system status control. The state response analysis of the gyroscope system revealed highly nonlinear and chaotic subharmonic motions of2Tduring state formation. The current study discussed the use of tracking control on the sliding mode control and fuzzy sliding mode control of a gyroscope control system. Consequently, the gyroscope system drives from chaotic motion to periodic motion. The numerical simulation results confirm that the proposed controller provides good system stability and convergence without chatterin

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STAN, NICOLETA, LIGIA MUNTEANU, and VETURIA CHIROIU. "On the dynamics of sonic composites." Romanian Journal of Technical Sciences - Applied Mechanics 69, no. 2-3 (2024): 127–38. https://doi.org/10.59277/rjts-am.2024.2-3.02.

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The paper is concerned with the full band-gaps size and the localized modes around interfaces in a multilayer film. The film consists of alternating layers of piezoelectric ceramics and epoxy resin following a triadic Cantor sequence. The Cantor structure is characterized by anharmonic coupling between the extended-mode (phonon) and the localized-mode (fracton) vibration regimes, and by extremely low thresholds for subharmonic generation of ultrasonic waves, as compared to the corresponding homogeneous and periodical ones. The dynamic optimization tracks the enhancing of full band-gaps for bot

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Chang, You Min, Junsu Lee, and Ju Han Lee. "A Q-switched, mode-locked fiber laser employing subharmonic cavity modulation." Optics Express 19, no. 27 (2011): 26627. http://dx.doi.org/10.1364/oe.19.026627.

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40

Popov, V., E. Shandarov, and S. Shandarov. "Generation of spatial subharmonic gratings through mode mixing in planar waveguides." Journal of the Optical Society of America B 9, no. 9 (1992): 1661. http://dx.doi.org/10.1364/josab.9.001661.

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Jiang, Yang, Guangfu Bai, Lin Hu, et al. "Subharmonic Generation in a Bandwidth Clamped Actively Mode-Locked Fiber Laser." IEEE Photonics Technology Letters 25, no. 23 (2013): 2331–34. http://dx.doi.org/10.1109/lpt.2013.2286172.

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42

Nguyen, T. T., and W. Derek Humpage. "z-plane load modelling with particular reference to subharmonic mode responses." Electric Power Systems Research 16, no. 1 (1989): 33–45. http://dx.doi.org/10.1016/0378-7796(89)90035-7.

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43

Fang, Chung-Chieh. "Unified subharmonic oscillation conditions for peak or average current mode control." International Journal of Circuit Theory and Applications 43, no. 8 (2014): 995–1014. http://dx.doi.org/10.1002/cta.1989.

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Serra-Garcia, Marc, Miguel Molerón, and Chiara Daraio. "Tunable, synchronized frequency down-conversion in magnetic lattices with defects." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2127 (2018): 20170137. http://dx.doi.org/10.1098/rsta.2017.0137.

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We study frequency conversion in nonlinear mechanical lattices, focusing on a chain of magnets as a model system. We show that, by inserting mass defects at suitable locations, we can introduce localized vibrational modes that nonlinearly couple to extended lattice modes. The nonlinear interaction introduces an energy transfer from the high-frequency localized modes to a low-frequency extended mode. This system is capable of autonomously converting energy between highly tunable input and output frequencies, which need not be related by integer harmonic or subharmonic ratios. It is also capable

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Ji, C., N. Chubun, R. G. Broeke, et al. "Electrical subharmonic hybrid mode locking of a colliding pulse mode-locked laser at 28 GHz." IEEE Photonics Technology Letters 17, no. 7 (2005): 1381–83. http://dx.doi.org/10.1109/lpt.2005.848555.

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Jones, C. A. "The transition to wavy Taylor vortices." Journal of Fluid Mechanics 157 (August 1985): 135–62. http://dx.doi.org/10.1017/s0022112085002336.

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The transition from steady axisymmetric Taylor vortices to time-dependent wavy vortices is examined. The critical Taylor number and frequency at the transition point are determined in the infinite-cylinder approximation for a wide range of parameters. The results are compared with long-aspect-ratio experiments. The variation with axial wavelength is examined, and is found to be important when the radius ratio η < 0.75. A new spatially subharmonic mode is found to be the most unstable mode in some parameter regimes. This mode is identified with the jet mode recently discovered experimentally

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Chang, Chau-Lyan, and Mujeeb R. Malik. "Oblique-mode breakdown and secondary instability in supersonic boundary layers." Journal of Fluid Mechanics 273 (August 25, 1994): 323–60. http://dx.doi.org/10.1017/s0022112094001965.

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Laminar–turbulent transition mechanisms for a supersonic boundary layer are examined by numerically solving the governing partial differential equations. It is shown that the dominant mechanism for transition at low supersonic Mach numbers is associated with the breakdown of oblique first-mode waves. The first stage in this breakdown process involves nonlinear interaction of a pair of oblique waves with equal but opposite angles resulting in the evolution of a streamwise vortex. This stage can be described by a wave–vortex triad consisting of the oblique waves and a streamwise vortex whereby t

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Popovic, Pavol, Ali H. Nayfeh, Kyoyul Oh, and Samir A. Nayfeh. "An Experimental Investigation of Energy Transfer from a High- Frequency Mode to a Low-Frequency Mode in a Flexible Structure." Journal of Vibration and Control 1, no. 1 (1995): 115–28. http://dx.doi.org/10.1177/107754639500100108.

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The objective of the present article is to experimentally observe and characterize the transfer of energy from low-amplitude, high-frequency modes to high-amplitude, low-frequency modes. The subject of the study is a three-beam frame. The excitation amplitude is restricted to below 2 g peak. The authors have focused on observing, characterizing, and documenting the excitation of the first mode by high-frequency forcing. The energy-transfer processes are identified by power spectra and characterized further by frequency and amplitude sweeps. The energy-transfer routes observed in the experiment

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Wu, Xuesong. "On an active resonant triad of mixed modes in symmetric shear flows: a plane wake as a paradigm." Journal of Fluid Mechanics 317 (June 25, 1996): 337–68. http://dx.doi.org/10.1017/s0022112096000778.

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In this paper, we identify a new type of resonant triad which operates in a parallel or nearly parallel shear flow with a symmetric profile. The triad consists of a planar sinuous mode, an oblique sinuous mode and an oblique varicose mode, but is not of the usual subharmonic-resonance form. The development of the triad is studied in the non-equilibrium critical-layer régime. The equations governing the evolution of the modes are derived. We show that the quadratic resonance can significantly enhance the growth of both the oblique sinuous and varicose modes, and may cause them to grow super-exp

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MacKinnon, J. A., M. H. Alford, Oliver Sun, Rob Pinkel, Zhongxiang Zhao, and Jody Klymak. "Parametric Subharmonic Instability of the Internal Tide at 29°N." Journal of Physical Oceanography 43, no. 1 (2013): 17–28. http://dx.doi.org/10.1175/jpo-d-11-0108.1.

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Abstract Observational evidence is presented for transfer of energy from the internal tide to near-inertial motions near 29°N in the Pacific Ocean. The transfer is accomplished via parametric subharmonic instability (PSI), which involves interaction between a primary wave (the internal tide in this case) and two smaller-scale waves of nearly half the frequency. The internal tide at this location is a complex superposition of a low-mode waves propagating north from Hawaii and higher-mode waves generated at local seamounts, making application of PSI theory challenging. Nevertheless, a statistica

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