Journal articles on the topic 'Small-amplitude oscillations'
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1
Becker, E., W. J. Hiller, and T. A. Kowalewski. "Experimental and theoretical investigation of large-amplitude oscillations of liquid droplets." Journal of Fluid Mechanics 231 (October 1991): 189–210. http://dx.doi.org/10.1017/s0022112091003361.
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Finite-amplitude, axially symmetric oscillations of small (0.2 mm) liquid droplets in a gaseous environment are studied, both experimentally and theoretically. When the amplitude of natural oscillations of the fundamental mode exceeds approximately 10% of the droplet radius, typical nonlinear effects like the dependence of the oscillation frequency on the amplitude, the asymmetry of the oscillation amplitude, and the interaction between modes are observed. As the amplitude decreases due to viscous damping, the oscillation frequency and the amplitude decay factor reach their asymptotical values predicted by linear theory. The initial behaviour of the droplet is described quite satisfactorily by a proposed nonlinear inviscid theoretical model.
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Kozlov, Victor, Stanislav Subbotin, and Ivan Karpunin. "Supercritical Dynamics of an Oscillating Interface of Immiscible Liquids in Axisymmetric Hele-Shaw Cells." Fluids 8, no. 7 (July 12, 2023): 204. http://dx.doi.org/10.3390/fluids8070204.
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The oscillation of the liquid interface in axisymmetric Hele-Shaw cells (conical and flat) is experimentally studied. The cuvettes, which are thin conical layers of constant thickness and flat radial Hele-Shaw cells, are filled with two immiscible liquids of similar densities and a large contrast in viscosity. The axis of symmetry of the cell is oriented vertically; the interface without oscillations is axially symmetric. An oscillating pressure drop is set at the cell boundaries, due to which the interface performs radial oscillations in the form of an oscillating “tongue” of a low-viscosity liquid, periodically penetrating into a more viscous liquid. An increase in the oscillation amplitude leads to the development of a system of azimuthally periodic structures (fingers) at the interface. The fingers grow when the viscous liquid is forced out of the layer and reach their maximum in the phase of maximum displacement of the interface. In the reverse course, the structures decrease in size and, at a certain phase of oscillations, take the form of small pits directed toward the low-viscosity fluid. In a conical cell, a bifurcation of period doubling with an increase in amplitude is found; in a flat cell, it is absent. A slow azimuthal drift of finger structures is found. It is shown that the drift is associated with the inhomogeneity of the amplitude of fluid oscillations in different radial directions. The fingers move from the region of a larger to the region of a lower amplitude of the interface oscillations.
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Dolgopolov, S. I. "Mathematical simulation of hard excitation of cavitation self-oscillations in a liquid-propellant rocket engine feed system." Technical mechanics 2021, no. 1 (April 30, 2021): 29–36. http://dx.doi.org/10.15407/itm2021.01.029.
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Hard self-oscillation excitation differs from soft excitation in that self-oscillations are set up only if the initial departure of an oscillating system from equilibrium is strong enough. Experimental studies of cavitation oscillations in hydraulic systems with cavitating pumps of liquid-propellant rocket engines ((LPREs) include works that describe hard excitation of cavitation oscillations. By mow, hard excitation regimes have not been explained theoretically, to let alone their mathematical simulation. This paper presents a mathematical model of hard excitation of cavitation oscillations in a LPRE feed system, which comprises a mathematical model of cavitation self-oscillations in a LPRE feed system that accounts for pump choking and an external disturbance model. A mechanism of hard excitation of cavitation oscillations in a LPRE feed system is proposed. It is well known that hard excitation of cavitation self-oscillations may take place in cases where the pump feed system is near the boundary of the cavitation self-oscillation region. In this case, the self-oscillation amplitudes are small, and they are limited only by one nonlinearity (cavity volume vs. pump inlet pressure and flow relationship). Under excitation of sufficient intensity, the pump inlet pressure and flow find themselves in the choking characteristic; this may be responsible for choking and developed cavitation self-oscillations, which remain of interrupted type and do not go into the initial small-amplitude oscillations even after excitation removal. A mathematical simulation of hard excitation of cavitation self-oscillations was conducted to determine the parameters of cavitation self-oscillations in a bench feed system of a test pump. The simulation results show that without an external disturbance the pump system exhibits small-amplitude self-oscillations. On an external disturbance, developed (interrupted) cavitation oscillations are set up in the system, which is in agreement with experimental data. The proposed mathematical model of hard excitation of cavitation self-oscillations in a LPRE feed system allows one to simulate a case observed in an experiment in which it was possible to eliminate cavitation self-oscillations by an external disturbance.
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Mashnich, G. P., V. S. Bashkirtsev, and A. I. Khlystova. "Small-amplitude oscillations in solar filaments." Astronomy Reports 56, no. 3 (March 2012): 241–49. http://dx.doi.org/10.1134/s1063772912030055.
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Oliver, Ramón. "Prominence Seismology Using Small Amplitude Oscillations." Space Science Reviews 149, no. 1-4 (May 27, 2009): 175–97. http://dx.doi.org/10.1007/s11214-009-9527-4.
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Kazakevič, Michael I., and Victoria E. Volkova. "THE INDUCED OSCILLATIONS OF FLEXIBLE PRESTRESSED ELEMENTS OF STRUCTURES (SYMMETRICAL SYSTEM)." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 6, no. 1 (February 28, 2000): 55–59. http://dx.doi.org/10.3846/13921525.2000.10531564.
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The results of the investigations of dynamic behaviour of the flexible prestressed structure elements are presented in the paper. The given physical model can be applied to the flexible structures like sloping arches, shells, bending plates, elements of the large space antenna fields (LSAF). The dynamic behaviour of the investigated systems is described by the equations where ϵ is damping coefficient, α,β are coefficients determining the character of non-linear restoring force are parameters of outer effect. The analysis of the “skeleton” curves disclosed the double qualities of system (1). Thus, “large” oscillations possess the peculiarities of the rigid system behaviour, and “small” oscillations possess the qualities of soft systems. The character of the oscillation amplitude changing with the increase or decrease of the excitation frequencies is followed in Fig 1. The establishment of the forced oscillation regimes from one branch to another is accompanied not only by the transition from “large” oscillations to “small”, or vice versa, but also by the development of the combination tones (2ω, 3ω 5ω, …, ω/2, ω/3). The analytical solutions for “large” and “small” forced oscillations are given by harmonic balance method. The solution was found in the form φ = Acosωt for “large” oscillation, and for “small” oscillation, where . The for curves disclosed unstable branches of amplitude-frequency curves and critical value amplitude of “large” oscillations were obtained. The methods and results of the computing experiment are presented in the paper. For working out the software necessary for the given task, the method of numerical integration (Runge-Kutta method of the fourth order), spectral analysis (Hertzel algorithm), computer graphics, etc were used. The results of the numerical integration are well-coordinated with the analytical solution for the “framework” curves and for the amplitude-frequency curves of forced oscillations.
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LI, QIAN SHU, and RUI ZHU. "MESOSCOPIC DESCRIPTION OF CHEMICAL SUPERCRITICAL HOPF BIFURCATION." International Journal of Bifurcation and Chaos 14, no. 07 (July 2004): 2393–97. http://dx.doi.org/10.1142/s0218127404010643.
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The mesoscopic dynamic behavior of the Oregonator model of the Belousov–Zhabotinsky chemical reaction is investigated as the model system experiences a supercritical Hopf bifurcation from focus to limit cycle oscillation. The study is performed by stochastically simulating the corresponding chemical master equation. Comparing the mesoscopic dynamic results with those obtained by the macroscopic dynamics, we find in the mesoscopic description a new type of oscillating state, in which large-amplitude oscillations and small-amplitude oscillations appear randomly alternately. This new state comes out spontaneously within a certain region called Hopf bifurcation range by us. In the mesoscopic description, the Hopf bifurcation point cannot be shown, being replaced by a Hopf bifurcation range. Furthermore, the applications of this new oscillating state to internal signal stochastic resonance are pointed out.
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LYUBIMOV, D. V., V. V. KONOVALOV, T. P. LYUBIMOVA, and I. EGRY. "Small amplitude shape oscillations of a spherical liquid drop with surface viscosity." Journal of Fluid Mechanics 677 (April 27, 2011): 204–17. http://dx.doi.org/10.1017/jfm.2011.76.
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The analysis of surface oscillations of liquid drops allows measurements of the surface tension and viscosity of the liquid. For small oscillations of spherical drops with a free surface, classical formulae by Rayleigh and Lamb relate these quantities to the frequency and damping of the oscillations. In many cases, however, the drop's surface is covered by a surface film, typically an oxide layer or a surfactant, exhibiting a rheological behaviour different from the bulk fluid. It is the purpose of this paper to investigate how such surface properties influence the oscillation spectrum of a spherical drop. For small bulk shear viscosity, the cases of small, finite and large surface viscosities are discussed, and the onset of aperiodic motion as a function of the surface parameters is also derived.
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Baier, Gerold, and Klaus Wegmann. "Notizen: Dynamical Behavior During the Oxidation of Aniline with Bromate." Zeitschrift für Naturforschung A 42, no. 12 (December 1, 1987): 1458–60. http://dx.doi.org/10.1515/zna-1987-1218.
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Spontaneous oscillations occur during the oxidation of aniline with bromate in sulfuric acid (a Körös-Orban System). In a continuous flow, stirred tank reactor besides a simple relaxation oscillation of large amplitude, a small amplitude oscillation of higher frequency was observed, so were various dynamical phenomena which can be understood as a combination of the two simple oscillations. For some regions of parameter space, the appearance of deterministic chaos seems probable. The role of metal impurities is discussed.
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Wang, Wei, Kaiming Yang, and Yu Zhu. "Optimal Frequency and Amplitude of Vertical Viewpoint Oscillation for Improving Vection Strength and Reducing Neural Constrains on Gait." Entropy 23, no. 5 (April 28, 2021): 541. http://dx.doi.org/10.3390/e23050541.
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Inducing self-motion illusions referred as vection are critical for improving the sensation of walking in virtual environments (VE). Adding viewpoint oscillations to a constant forward velocity in VE is effective for improving vection strength under static conditions. However, the effects of oscillation frequency and amplitude on vection strength under treadmill walking conditions are still unclear. Besides, due to the visuomotor entrainment mechanism, these visual oscillations would affect gait patterns and be detrimental for achieving natural walking if not properly designed. This study was aimed at determining the optimal frequency and amplitude of vertical viewpoint oscillations for improving vection strength and reducing gait constraints. Seven subjects walked on a treadmill while watching a visual scene. The visual scene presented a constant forward velocity equal to the treadmill velocity with different vertical viewpoint oscillations added. Five oscillation patterns with different combinations of frequency and amplitude were tested. Subjects gave verbal ratings of vection strength. The mediolateral (M-L) center of pressure (CoP) complexity was calculated to indicate gait constraints. After the experiment, subjects were asked to give the best and the worst oscillation pattern based on their walking experience. The oscillation frequency and amplitude had strong positive correlations with vection strength. The M-L CoP complexity was reduced under oscillations with low frequency. The medium oscillation amplitude had greater M-L CoP complexity than the small and large amplitude. Besides, subjects preferred those oscillation patterns with large gait complexity. We suggested that the oscillation amplitude with largest M-L CoP complexity should first be chosen to reduce gait constraints. Then, increasing the oscillation frequency to improve vection strength until individual preference or the boundary of motion sickness. These findings provide important guidelines to promote the sensation of natural walking in VE.
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Musat, Sorin D., and Bogdan I. Epureanu. "SMALL AMPLITUDE OSCILLATIONS OF A CENTERED GYROSCOPE." Transactions of the Canadian Society for Mechanical Engineering 25, no. 2 (June 2001): 267–72. http://dx.doi.org/10.1139/tcsme-2001-0015.
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Hutt, G. R., R. A. East, and R. D. Wilson. "Large amplitude oscillation effects on cone pitch stability in viscous hypersonic flow." Aeronautical Journal 93, no. 922 (February 1989): 50–57. http://dx.doi.org/10.1017/s0001924000016742.
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SummaryExperimental and theoretical, small and large amplitude stability data are presented for a pointed and a 0.2 bluntness ratio, 10° semi-angle cone performing pitching oscillations in hypersonic flow at a Mach number of 6.85. Analysis identifies that large amplitude model motion time histories cannot be predicted from a knowledge of small amplitude oscillation stability derivatives data. At the Reynolds numbers of the experiments the pointed and blunted cone are subject to significant hypersonic flow viscous phenomena, which are proposed as the cause of the small to large amplitude stability prediction being invalid.
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Kim, MinKyung, and UnCheol Lee. "Alpha oscillation, criticality, and responsiveness in complex brain networks." Network Neuroscience 4, no. 1 (January 2020): 155–73. http://dx.doi.org/10.1162/netn_a_00113.
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Brains in unconsciousness are characterized by significantly limited responsiveness to stimuli. Even during conscious wakefulness, responsiveness is highly dependent on ongoing brain activity, specifically, of alpha oscillations (∼10 Hz). We hypothesized that the variety of brain responses to external stimuli result from the interaction between state-specific and transient alpha oscillations and stimuli. To justify this hypothesis, we simulated various alpha oscillations in the human brain network, modulating criticality (a balanced state between order and disorder), and investigated specific alpha oscillation properties (instantaneous amplitude, phase, and global synchronization) that induce a large or small response. As a result, we found that the alpha oscillations near a critical state show a more complex and long-lasting response, which is more prominent when stimuli are given to globally desynchronized and low-amplitude oscillations. We also found specific phases of alpha oscillation that barely respond to stimuli, which implies the presence of temporal windows in the alpha cycle for a large or small response. The results explain why brain responses are so variable across conscious and unconscious states and across time windows even during conscious wakefulness, and emphasize the importance of considering ongoing alpha oscillations for effective brain stimulation.
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REPETTO, RODOLFO, JENNIFER H. SIGGERS, and ALESSANDRO STOCCHINO. "Steady streaming within a periodically rotating sphere." Journal of Fluid Mechanics 608 (July 11, 2008): 71–80. http://dx.doi.org/10.1017/s002211200800222x.
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We consider the flow in a spherical chamber undergoing periodic torsional oscillations about an axis through its centre, and analyse it both theoretically and experimentally. We calculate the flow in the limit of small-amplitude oscillations in the form of a series expansion in powers of the amplitude, finding that at second order, a steady streaming flow develops consisting of two toroidal cells. This streaming behaviour is also observed in our experiments. We find good quantitative agreement between theory and experiments, and we discuss the dependence of the steady streaming behaviour as both the oscillation frequency and amplitude are varied.
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REN, XIU-BIN, and XIANG-YUN GUO. "INFLUENCE OF THE REACTION TEMPERATURE ON THE OSCILLATORY BEHAVIOR DURING PARTIAL OXIDATION OF METHANE." Surface Review and Letters 15, no. 06 (December 2008): 769–74. http://dx.doi.org/10.1142/s0218625x0801213x.
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The oscillatory behavior during partial oxidation of methane was studied by the Monte Carlo simulation with Langmuir–Hinshelwood mechanism and oxide formation and removal. The well-developed reaction rate oscillations can be observed when the CH 4 adsorption probability varies in a small window. The oscillation window is very sensitive to the variation of reaction temperature. When the temperature increases, the window for sustained oscillation becomes narrow and has an obvious shift. In the meantime, the oscillation period tends to become small and the amplitude decreases. When the temperature increases to a certain value, the oscillations will disappear.
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Wang, Gang, and Jin-Hai Zheng. "SUBHARMONIC GENERATION OF TRANSVERSE OSCILLATIONS INDUCED BY INCIDENT REGULAR WAVES." Coastal Engineering Proceedings 1, no. 33 (September 27, 2012): 11. http://dx.doi.org/10.9753/icce.v33.waves.11.
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It is generally accepted that there are transverse oscillation, which are concentrated and confined to the backwall and decay asymptotically offshore, existed in the harbor of constant slope, however, whether these oscillations can be induced by the normally incident waves is not clear. This numerical investigation aims at providing the subharmonic generations of transverse oscillations within the harbor of a plane slope by waves normally impacting on. For the harbor of perfectly plane slopes, the subharmonic transverse oscillations are small on the mild and moderate slopes but evident on the steep slope. This instability can take place only if the incident wave amplitude exceeds a threshold value, and transverse oscillations can even grow up to a larger value than that of longitudinal oscillations. The magnitudes of transverse oscillations are approximately the same, only their growth rates are affected by the incident wave amplitude.
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KAWANO, Satoyuki, Hiroyuki HASHIMOTO, Akio IHARA, and Takahiro AZIMA. "Small-Amplitude Oscillations of Encapsulated Liquid Drop Interfaces." JSME International Journal Series B 40, no. 1 (1997): 33–41. http://dx.doi.org/10.1299/jsmeb.40.33.
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Kawano, Satoyuki, Hiroyuki Hashimoto, Akio Ihara, and Takahiro Azima. "Small-Amplitude Oscillations of Encapsulated Liquid Drop Interfaces." Transactions of the Japan Society of Mechanical Engineers Series B 61, no. 581 (1995): 116–23. http://dx.doi.org/10.1299/kikaib.61.116.
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Chu, Zhaobi, Yan Wang, Min Zhu, Xueping Dong, and Hua Li. "A Robust Online Identification of Sustained Low Frequency Oscillation in Steady-State Power Systems." Mathematical Problems in Engineering 2019 (June 10, 2019): 1–9. http://dx.doi.org/10.1155/2019/8435838.
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For sustained low frequency oscillations in steady-state power systems, an algorithm is proposed for precise online identification of oscillation frequency, oscillation amplitude, and fundamental amplitude. The algorithm consists of a robust low frequency estimator and a notch filter in parallel. The asymptotical convergence property is analyzed by slow integral manifold, averaging method, and Lyapunov stability theorem sequentially. The steady-state antinoise property is investigated by perturbed system theorem. The robust advantages of the proposed algorithm are embodied in the following aspects: the fundamental amplitude identification is little influenced by oscillation frequency and oscillation amplitude, both oscillation frequency identification and oscillation amplitude identification have small steady-state errors under high order harmonics or bounded noises, the ramp variations of both fundamental amplitude and oscillation amplitude are also significantly tracked, and three design parameters have different effects on identification performance of oscillation frequency, oscillation amplitude, and fundamental amplitude, respectively. Simulation results verify the validity.
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ERMANYUK, EUGENY V., and NIKOLAI V. GAVRILOV. "On internal waves generated by large-amplitude circular and rectilinear oscillations of a circular cylinder in a uniformly stratified fluid." Journal of Fluid Mechanics 613 (October 1, 2008): 329–56. http://dx.doi.org/10.1017/s0022112008003261.
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This paper presents an experimental study of internal waves generated by circular and rectilinear oscillations of a circular cylinder in a uniformly stratified fluid. The synthetic schlieren technique is used for quantitative analysis of the internal-wave parameters. It is shown that at small oscillation amplitudes, the wave pattern observed for circular oscillations is in good agreement with linear theory: internal waves are radiated in the wave beams passing through the first and third quadrants of a Cartesian coordinate system for the clockwise direction of the cylinder motion, and the intensity of these waves is twice the intensity measured for ‘St Andrew's cross’ waves generated by purely horizontal or vertical oscillations of the same frequency and amplitude. As the amplitude of circular oscillations increases, significant nonlinear effects are observed: (i) a strong density-gradient ‘zero-frequency’ disturbance is generated, and (ii) a region of intense fluid stirring is formed around the cylinder serving as an additional dissipative mechanism that changes the shape of wave envelopes and decreases the intensity of wave motions. In the same range of oscillation amplitudes, the wave generation by rectilinear (horizontal and vertical) oscillations is shown to be by and large a linear process, with moderate manifestations of nonlinearity such as weak ‘zero-frequency’ disturbance and weak variation of the shape of wave envelopes with the oscillation amplitude. Analysis of spatiotemporal images reveals different scenarios of transient effects in the cases of circular and rectilinear oscillations. In general, circular oscillations tend to generate disturbances evolving at longer time scales.
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Wang, Kun, Wei Chen, Jiangtao Li, Jinhui Shi, and Zhanhong Wei. "A method for analyzing bursting oscillations in grid-connected renewable energy generation systems based on a complex network." Journal of Renewable and Sustainable Energy 14, no. 2 (March 2022): 026302. http://dx.doi.org/10.1063/5.0086934.
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For analyzing the problem of frequent wideband oscillations in grid-connected renewable energy generation systems, an analysis method based on small-world networks and fast-slow dynamics is proposed. A direct-driven permanent magnet synchronous generator (DPMSG) was chosen as an example to discuss the process of bursting oscillations in a single system with both alternating large-amplitude and micro-amplitude oscillations due to the multi-timescale coupling effect introduced by the disturbance. Meanwhile, a complex network consisting of multiple DPMSGs connected to the grid was selected to investigate the process of bursting oscillations in generation nodes spreading among the system nodes. The results showed that the bursting oscillations created by the power generation nodes in grid-connected renewable energy generation systems can lead to oscillation instability of the entire system. Our simulation verified the feasibility and effectiveness of the method proposed in this paper.
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Peslin, R., C. Saunier, C. Gallina, and C. Duvivier. "Small-amplitude pressure oscillations do not modify respiratory mechanics in rabbits." Journal of Applied Physiology 76, no. 3 (March 1, 1994): 1011–13. http://dx.doi.org/10.1152/jappl.1994.76.3.1011.
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Changes in respiratory mechanics have occasionally been observed during high-frequency ventilation. In this study we investigated whether small pressure oscillations such as those used for respiratory impedance measurements modified total respiratory resistance (Rrs) and total respiratory elastance (Ers). The latter were measured in six paralyzed artificially ventilated rabbits with and without superimposed pressure oscillations at the airway opening. Rrs and Ers were obtained by least square fitting of low-pass filtered tracheal pressure and flow to the usual first-order model. Pressure oscillations of 2–4 hPa peak-to-peak at 10, 20, and 30 Hz applied for periods of 10 min had virtually no effect on Ers (changes ranging from -2.5 to 2.6%) and Rrs (0-8.2%). Analysis of variance did not show a significant difference on the pooled data. Pressure oscillations were also applied every other minute after a histamine aerosol. Ers and Rrs were similarly unchanged. We conclude that the small pressure oscillations used in respiratory impedance measurements do not modify lung mechanical properties and lung response to bronchomotor agents.
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Sawkmie, Ivan Skhem, and Mangal C. Mahato. "Free Oscillations of a Damped Simple Pendulum: An Analog Simulation Experiment." Physics Educator 01, no. 04 (December 2019): 1950015. http://dx.doi.org/10.1142/s266133951950015x.
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The frequency of free oscillation of a damped simple pendulum with large amplitude depends on its amplitude unlike the amplitude-independent frequency of oscillation of a damped simple harmonic oscillator. This aspect is not adequately emphasized in the undergraduate courses due to experimental and theoretical difficulties. We propose an analog simulation experiment to study the free oscillations of a simple pendulum that could be performed in an undergraduate laboratory. The needed sinusoidal potential is obtained approximately by using the available AD534 IC by suitably augmenting the electronic circuitry. To keep the circuit simple enough we restrict the initial angular amplitude of the simple pendulum to a maximum of [Formula: see text]. The results compare well qualitatively with the theoretical results. The small quantitative discrepancy is attributed to the inexact nature of the used “sinusoidal potential”.
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Fumagalli, Jacopo, Mauro Pieroni, Sébastien Renaux-Petel, and Lukas T. Witkowski. "Detecting primordial features with LISA." Journal of Cosmology and Astroparticle Physics 2022, no. 07 (July 1, 2022): 020. http://dx.doi.org/10.1088/1475-7516/2022/07/020.
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Abstract Oscillations in the frequency profile of the stochastic gravitational wave background are a characteristic prediction of small-scale features during inflation. In this paper we present a first investigation of the detection prospects of such oscillations with the upcoming space-based gravitational wave observatory LISA. As a proof of principle, we show for a selection of feature signals that the oscillations can be reconstructed with LISA, employing a method based on principal component analysis. We then perform a Fisher forecast for the parameters describing the oscillatory signal. For a sharp feature we distinguish between the contributions to the stochastic gravitational wave background induced during inflation and in the post-inflationary period, which peak at different frequencies. We find that for the latter case the amplitude of the oscillation is expected to be measurable with < 10% accuracy if the corresponding peak satisfies h 2ΩGW ≳ 10-12-10-11, while for inflationary-era gravitational waves a detection of the oscillations requires a higher peak amplitude of h 2ΩGW, as the oscillations only appear on the UV tail of the spectrum. For a resonant feature the detection prospects with LISA are maximised if the frequency of the oscillation falls into the range ω log = 4 to 10. Our results confirm that oscillations in the frequency profile of the stochastic gravitational wave background are a worthwhile target for future detection efforts and offer a key for experimentally testing inflation at small scales.
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Voytik, V. V., and N. G. Migranov. "Small nutation of a symmetic gyroscope: two viewpoints." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 31, no. 1 (March 2021): 89–101. http://dx.doi.org/10.35634/vm210107.
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The paper is devoted to the small nutation of an axisymmetric gyroscope in the field of gravity. The expansion of the known solution of the nutation equation as a function of time in powers of the amplitude is obtained. In this case, the frequencies of third order Raman oscillations are both the tripled frequency and the frequency coinciding with the initial one. A formula is found for the nutation amplitude as a function of the integrals of the gyroscope motion. The frequency of zero nutation is also calculated. Another way to obtain the decomposition is to use the results of the general theory of free one-dimensional oscillations. This method is based on the ability to represent the gyro nutation as the movement of a material point of unit mass in a field that cubically-quadratically depends on the coordinate. In this case the only frequency of the third-order Raman oscillation is a triple of the original frequency. Thus, both methods give the same result only for oscillations no higher than second order. In the third approximation, the existing theory of oscillations is insufficient.
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Wu, Ying, Fue-Sang Lien, Eugene Yee, and Guang Chen. "Numerical Investigation of Flow-Induced Vibration for Cylinder-Plate Assembly at low Reynolds Number." Fluids 8, no. 4 (March 31, 2023): 118. http://dx.doi.org/10.3390/fluids8040118.
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The transverse flow-induced vibration (FIV) of an elastically-supported cylinder-plate assembly (viz., a rigid splitter-plate attached to the downstream side of a circular cylinder) with a low mass ratio of 10 and zero structural damping is investigated using numerical simulations at a Reynolds number of 100. The structural oscillations and characteristics of the flow around the structure are analyzed in terms of the vibration characteristics and the fluid forces as a function of the plate length LSP and the reduced velocity Ur. These investigations involve a wide range of plate lengths LSP/D = 0–4 (where D is the cylinder diameter) over an extensive span of reduced velocities Ur = 2–30. For LSP/D ≤ 0.5, self-limiting oscillations are induced in the assembly—these oscillations correspond to either a vortex-induced vibration (VIV) or an integrated VIV-galloping response. For LSP/D ≥ 0.75, the amplitude response is no longer self-limiting in the sense that the oscillation amplitude increases linearly with increasing Ur—these oscillations correspond to either a strongly correlated VIV-galloping regime (for LSP/D = 0.75), or two clearly separated regimes: namely, a VIV regime with small-amplitude oscillation and a non-limiting galloping regime (for LSP/D > 0.75).
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Ueda, Yoshisuke, Yoshinori Ueda, H. Bruce Stewart, and Ralph H. Abraham. "Nonlinear Resonance in Basin Portraits of Two Coupled Swings Under Periodic Forcing." International Journal of Bifurcation and Chaos 08, no. 06 (June 1998): 1183–97. http://dx.doi.org/10.1142/s0218127498000930.
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A model of a simple electric power supply network involving two generators connected by a transmission network to a bus is studied by numerical simulation. In this model, the bus is supposed to maintain a voltage of fixed amplitude, but with a small periodic fluctuation in the phase angle. In such a case, traditional analysis using direct methods is not applicable. The frequency of the periodic fluctuation is varied over a range of values near a nonlinear resonance of the two-generator network. When the bus fluctuation frequency is away from resonance, the system has several attractors; one is a small-amplitude periodic oscillation corresponding to synchronized, quasi-normal operation (slightly swinging), while others are large amplitude periodic oscillations which, if realized, would correspond to one or both generators operating in a desynchronized steady state. When the bus fluctuation frequency approaches resonance, a new periodic attractor with large amplitude oscillations appears. Although it does correspond to a synchronized steady state, this attractor has a disastrously large amplitude of oscillation, and represents an unacceptable condition for the network. Basin portraits show that this resonant attractor erodes large, complicated regions of the basin of the safe operating condition. Under conditions of small periodic fluctuation in bus voltage, this basin erosion would not be detected by traditional analysis using direct methods. Further understanding of such complicated basin structures will be essential to correctly predict the stability of electric power supply systems.
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Ballester, J. L. "The damping of small-amplitude oscillations in quiescent prominences." Advances in Space Research 46, no. 4 (August 2010): 364–76. http://dx.doi.org/10.1016/j.asr.2009.09.015.
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Lin, Yong. "Filament Thread-like Structures and Their Small-amplitude Oscillations." Space Science Reviews 158, no. 2-4 (November 3, 2010): 237–66. http://dx.doi.org/10.1007/s11214-010-9672-9.
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Georgiou, Miltiades, and Thomas Erneux. "Pulsating laser oscillations depend on extremely-small-amplitude noise." Physical Review A 45, no. 9 (May 1, 1992): 6636–42. http://dx.doi.org/10.1103/physreva.45.6636.
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SCHUSTER, STEFAN, and MARKO MARHL. "BIFURCATION ANALYSIS OF CALCIUM OSCILLATIONS: TIME-SCALE SEPARATION, CANARDS, AND FREQUENCY LOWERING." Journal of Biological Systems 09, no. 04 (December 2001): 291–314. http://dx.doi.org/10.1142/s021833900100044x.
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The behavior of calcium oscillations near bifurcations is analyzed for three different models. For the model developed by Somogyi and Stucki [42], it is shown that the range of oscillations is bounded by supercritical and subcritical Hopf bifurcations. Near the latter, canard orbits arise, that is, quasi-harmonic oscillations with a very small amplitude grow very fast to become pulsed oscillations. The potential biological significance of this behavior is discussed. A time-scale analysis of this model is performed and an approximation formula for the oscillation period is derived. For two models that we presented earlier [30, 31], it is shown that a homoclinic bifurcation and an infinite period bifurcation, respectively, occur. These imply that the oscillation period can reach arbitrarily high values. This behavior is discussed in the light of frequency encoding, and the scaling laws of the oscillation period are given.
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Karachevtseva, Iuliia, Arcady V. Dyskin, and Elena Pasternak. "The Cyclic Loading as a Result of the Stick-Slip Motion." Advanced Materials Research 891-892 (March 2014): 878–83. http://dx.doi.org/10.4028/www.scientific.net/amr.891-892.878.
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We investigate the influence of oscillating normal force on the frictional sliding. Frictional sliding in the case of a simple mass-spring model of Burridge and Knopoff type demonstrates stick-slip even when the friction coefficient is constant. Oscillations of the normal force in this case do not produce noticeable changes in the stick-slip sliding mode. A completely different picture is observed when the oscillations of normal force are applied to the system, which is in the state of steady sliding. In this case the normal oscillations turn the steady sliding into stick slip. A special case is observed when the normal force oscillates with the eigen frequency of the stick-slip motion. Then, no matter how small the amplitude of oscillations is the system reaches the same final stick-slip regime. The time required to reach this limiting regime is inversely proportional to the amplitude of oscillations of the normal force.
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Basaran, Osman A. "Nonlinear oscillations of viscous liquid drops." Journal of Fluid Mechanics 241 (August 1992): 169–98. http://dx.doi.org/10.1017/s002211209200199x.
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A fundamental understanding of nonlinear oscillations of a viscous liquid drop is needed in diverse areas of science and technology. In this paper, the moderate- to large-amplitude axisymmetric oscillations of a viscous liquid drop, which is immersed in dynamically inactive surroundings, are analysed by solving the free boundary problem comprised of the Navier–Stokes system and appropriate interfacial conditions at the drop–ambient fluid interface. The means are the Galerkin/finite-element technique, an implicit predictor-corrector method, and Newton's method for solving the resulting system of nonlinear algebraic equations. Attention is focused here on oscillations of drops that are released from an initial static deformation. Two dimensionless groups govern such nonlinear oscillations: a Reynolds number, Re, and some measure of the initial drop deformation. Accuracy is attested by demonstrating that (i) the drop volume remains virtually constant, (ii) dynamic response to small-and moderate-amplitude disturbances agrees with linear and perturbation theories, and (iii) large-amplitude oscillations compare well with the few published predictions made with the marker-and-cell method and experiments. The new results show that viscous drops that are released from an initially two-lobed configuration spend less time in prolate form than inviscid drops, in agreement with experiments. Moreover, the frequency of oscillation of viscous drops released from such initially two-lobed configurations decreases with the square of the initial amplitude of deformation as Re gets large for moderate-amplitude oscillations, but the change becomes less dramatic as Re falls and/or the initial amplitude of deformation rises. The rate at which these oscillations are damped during the first period rises as initial drop deformation increases; thereafter the damping rate is lower but remains virtually time-independent regardless of Re or the initial amplitude of deformation. The new results also show that finite viscosity has a much bigger effect on mode coupling phenomena and, in particular, on resonant mode interactions than might be anticipated based on results of computations incorporating only an infinitesimal amount of viscosity.
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Zhao, Hong Sheng, Wei Biao Chen, Jin Wang, Dong Jun Yang, Jing You Xu, Yuan Liu, and Zi Quan Liu. "Fluctuation Magnitude Calculation and Oscillation Probability Analysis of Tie-Line Active Power in Interconnected Power System." Advanced Materials Research 1070-1072 (December 2014): 861–68. http://dx.doi.org/10.4028/www.scientific.net/amr.1070-1072.861.
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The historical data of wide area measurement system (WAMS) contains the daily record of the number of oscillations. The phenomenon, which the number of these oscillations suddenly increases at a certain frequency, indicates that the risk of weak damping oscillation with this frequency will increase. In other words, the statistical characteristics of these oscillations can reflect the system stability level. In this paper, the formulation of the small signal analysis including power disturbance on the power grid is given firstly. Then the relationship between the oscillation probability and damping ratio is obtained theoretically. Finally, a case study is carried out based on a 10-machine 39-bus power system. Simulation results verify the validity of the expression of oscillation amplitude of tie-line active power and the relationship between the oscillation probability and damping ratio. These theoretical results can be used to guide the power operator to assess the damping level of the power grid based on the daily number of oscillations recored by WAMS.
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Manor, Yair, John Rinzel, Idan Segev, and Yosef Yarom. "Low-Amplitude Oscillations in the Inferior Olive: A Model Based on Electrical Coupling of Neurons With Heterogeneous Channel Densities." Journal of Neurophysiology 77, no. 5 (May 1, 1997): 2736–52. http://dx.doi.org/10.1152/jn.1997.77.5.2736.
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Manor, Yair, John Rinzel, Idan Segev, and Yosef Yarom. Low-amplitude oscillations in the inferior olive: a model based on electrical coupling of neurons with heterogeneous channel densities. J. Neurophysiol. 77: 2736–2752, 1997. The mechanism underlying subthreshold oscillations in inferior olivary cells is not known. To study this question, we developed a single-compartment, two-variable, Hodgkin-Huxley-like model for inferior olive neurons. The model consists of a leakage current and a low-threshold calcium current, whose kinetics were experimentally measured in slices. Depending on the maximal calcium and leak conductances, we found that a neuron model's response to current injection could be of four qualitatively different types: always stable, spontaneously oscillating, oscillating with injection of current, and bistable with injection of current. By the use of phase plane techniques, numerical integration, and bifurcation analysis, we subdivided the two-parameter space of channel densities into four regions corresponding to these behavioral types. We further developed, with the use of such techniques, an empirical rule of thumb that characterizes whether two cells when coupled electrically can generate sustained, synchronized oscillations like those observed in inferior olivary cells in slices, of low amplitude (0.1–10 mV) in the frequency range 4–10 Hz. We found that it is not necessary for either cell to be a spontaneous oscillator to obtain a sustained oscillation. On the other hand, two spontaneous oscillators always form an oscillating network when electrically coupled with any arbitrary coupling conductance. In the case of an oscillating pair of electrically coupled nonidentical cells, the coupling current varies periodically and is nonzero even for very large coupling values. The coupling current acts as an equalizing current to reconcile the differences between the two cells' ionic currents. It transiently depolarizes one cell and/or hyperpolarizes the other cell to obtain the regenerative response(s) required for the synchronized oscillation. We suggest that the subthreshold oscillations observed in the inferior olive can emerge from the electrical coupling between neurons with different channel densities, even if the inferior olive nucleus contains no or just a small proportion of spontaneously oscillating neurons.
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Ballester, José Luis. "Recent progress in prominence seismology." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1839 (December 19, 2005): 405–15. http://dx.doi.org/10.1098/rsta.2005.1706.
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Prominence seismology is a rapidly developing topic which seeks to infer the internal structure and properties of solar prominences from the study of their oscillations. An extense observational background about oscillations in quiescent solar prominences has been gathered during the last 70 years. These observations point out the existence of two different types of oscillations: flare-induced oscillations (winking filaments) which affect the whole prominence and are of large amplitude and small amplitude oscillations which seem to be of local nature. From the theoretical point of view, few models have been set up to explain the phenomenon of winking filaments while, on the contrary, for small amplitude oscillations a large number of models trying to explain the observed features have been proposed. Here, recent theoretical and observational developments on both types of oscillations are reviewed, and suggestions about future research topics which should provide us with a more in-depth knowledge of solar prominences are made.
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Liu, Chen, Ezequiel E. Ferrero, Eduardo A. Jagla, Kirsten Martens, Alberto Rosso, and Laurent Talon. "The fate of shear-oscillated amorphous solids." Journal of Chemical Physics 156, no. 10 (March 14, 2022): 104902. http://dx.doi.org/10.1063/5.0079460.
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The behavior of shear-oscillated amorphous materials is studied using a coarse-grained model. Samples are prepared at different degrees of annealing and then subjected to athermal and quasi-static oscillatory deformations at various fixed amplitudes. The steady-state reached after several oscillations is fully determined by the initial preparation and the oscillation amplitude, as seen from stroboscopic stress and energy measurements. Under small oscillations, poorly annealed materials display shear-annealing, while ultra-stabilized materials are insensitive to them. Yet, beyond a critical oscillation amplitude, both kinds of materials display a discontinuous transition to the same mixed state composed of a fluid shear-band embedded in a marginal solid. Quantitative relations between uniform shear and the steady-state reached with this protocol are established. The transient regime characterizing the growth and the motion of the shear band is also studied.
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Gao, Yuhang, Hui Tian, Tom Van Doorsselaere, and Yajie Chen. "Decayless Oscillations in Solar Coronal Bright Points." Astrophysical Journal 930, no. 1 (May 1, 2022): 55. http://dx.doi.org/10.3847/1538-4357/ac62cf.
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Abstract Decayless kink oscillations of solar coronal loops (or decayless oscillations for short) have attracted great attention since their discovery. Coronal bright points (CBPs) are mini-active regions and consist of loops with a small size. However, decayless oscillations in CBPs have not been widely reported. In this study, we identified this kind of oscillations in some CBPs using 171 Å images taken by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. After using the motion magnification algorithm to increase oscillation amplitudes, we made time–distance maps to identify the oscillatory signals. We also estimated the loop lengths and velocity amplitudes. We analyzed 23 CBPs and found 31 oscillation events in 16 of them. The oscillation periods range from 1 to 8 minutes (on average about 5 minutes), and the displacement amplitudes have an average value of 0.07 Mm. The average loop length and velocity amplitude are 23 Mm and 1.57 km s−1, respectively. Relationships between different oscillation parameters are also examined. Additionally, we performed a simple model to illustrate how these subpixel oscillation amplitudes (less than 0.4 Mm) could be detected. Results of the model confirm the reliability of our data processing methods. Our study shows for the first time that decayless oscillations are common in small-scale loops of CBPs. These oscillations allow for seismological diagnostics of the Alfvén speed and magnetic field strength in the corona.
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Bubanja, I. N., S. Maćešić, A. Ivanović-Šašić, Ž. Čupić, S. Anić, and Lj Kolar-Anić. "Intermittent chaos in the Bray–Liebhafsky oscillator. Temperature dependence." Physical Chemistry Chemical Physics 18, no. 14 (2016): 9770–78. http://dx.doi.org/10.1039/c6cp00759g.
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Intermittent oscillations as a chaotic mixture of large amplitude relaxation oscillations, grouped in bursts and small-amplitude sinusoidal ones or even quiescent parts between them known as gaps, were found and examined in the Bray–Liebhafsky (BL) reaction performed in CSTR under controlled temperature variations.
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Ballard, Trevor, David Peak, and Keith Mott. "Blue and red light effects on stomatal oscillations." Functional Plant Biology 46, no. 2 (2019): 146. http://dx.doi.org/10.1071/fp18104.
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The response of stomata to red and blue light was investigated using small fibre optics (66µm diameter) to control light levels on a single pair of guard cells without affecting the surrounding tissue. Low intensity red light (50µmolm–2s–1) applied to the entire leaf caused stomata to oscillate continuously for several hours with no apparent decrease in amplitude with time. Adding low intensity blue light (50µmolm–2s–1) caused stomata to stop oscillating, but oscillations resumed when the blue light was removed. Adding the same intensity of red light to an oscillating leaf changed the amplitude of the oscillations but did not stop them. When blue light was added to a single guard cell pair (using a fibre optic) in a red-light-illuminated leaf, the stoma formed by that pair stopped oscillating, but adjacent stomata did not. Red light added to a single guard cell pair did not stop oscillations. Finally, blue light applied through a fibre optic to areas of leaf without stomata caused proximal stomata to stop oscillating, but distal stomata continued to oscillate. The data suggest that blue light affects stomata via direct effects on guard cells as well as by indirect effects on other cells in the leaf.
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Wang, Zhixiang, Zhengdi Zhang, and Qinsheng Bi. "Relaxation Oscillations in a Nonsmooth Oscillator with Slow-Varying External Excitation." International Journal of Bifurcation and Chaos 29, no. 07 (June 30, 2019): 1930019. http://dx.doi.org/10.1142/s0218127419300192.
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The main purpose of the paper is to explore the influence of the coupling of two scales on the dynamics of a nonsmooth dynamical system. Based on a typical Chua’s circuit, by introducing a nonlinear resistor with piecewise characteristics as well as a harmonically changed electric source, a modified nonsmooth model is established, in which the coupling of two scales in frequency domain exists. Different types of bursting oscillations, appearing in the combination of large-amplitude oscillations, called spiking oscillations ([Formula: see text]), and small-amplitude oscillations or at rest, denoted by quiescent states ([Formula: see text]), can be observed with the variation of the exciting amplitude. When the exciting frequency is relatively small, by regarding the whole exciting term as a slow-varying parameter, the original system can be transformed into a generalized autonomous system. The phase space can be divided into three regions by the nonsmooth boundaries, in which the trajectory is governed by three different subsystems, respectively. Based on the analysis of the three subsystems as well as the behaviors on the nonsmooth boundaries, all the equilibrium branches and their bifurcations can be obtained, which can be employed to investigate the mechanism of the bursting oscillations. It is found that, for relatively small exciting amplitude, since no bifurcation on the equilibrium branches can be realized with the variation of the slow-varying parameter, the system behaves in periodic movement, which may evolve to bursting oscillations when a pair of fold bifurcations occurs with the increase of the exciting amplitude. Further increase of the exciting amplitude may lead to more complicated bursting oscillations, which may bifurcate into two coexisted asymmetric bursting attractors via symmetric breaking. Interaction between the two attractors may result in an enlarged symmetric bursting attractor, in which more forms of bifurcations at the transitions between the quiescent states and repetitive spiking states can be observed.
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Zhang, Q. M. "Simultaneous transverse oscillations of a coronal loop and a filament excited by a circular-ribbon flare." Astronomy & Astrophysics 642 (October 2020): A159. http://dx.doi.org/10.1051/0004-6361/202038557.
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Aims. The aim of this study is to investigate the excitation of kink oscillations in coronal loops and filaments, by analyzing a C3.4 circular-ribbon flare associated with a blowout jet in active region 12434 on 2015 October 16. Methods. The flare was observed in ultraviolet and extreme-ultraviolet wavelengths by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO) spacecraft. The line-of-sight (LOS) magnetograms of the photosphere were observed by the Helioseismic and Magnetic Imager on board SDO. Soft X-ray fluxes of the flares in 0.5−4 and 1−8 Å were recorded by the GOES spacecraft. Results. The flare excited small-amplitude kink oscillation of a remote coronal loop. The oscillation lasted for ≥4 cycles without significant damping. The amplitude and period are 0.3 ± 0.1 Mm and 207 ± 12 s. Interestingly, the flare also excited transverse oscillation of a remote filament. The oscillation lasted for ∼3.5 cycles with decaying amplitudes. The initial amplitude is 1.7−2.2 Mm. The period and damping time are 437−475 s and 1142−1600 s. The starting times of simultaneous oscillations of coronal loop and filament were concurrent with the hard X-ray peak time. Though small in size and short in lifetime, the flare set off a chain reaction. It generated a bright secondary flare ribbon (SFR) in the chromosphere, remote brightening (RB) that was cospatial with the filament, and intermittent, jet-like flow propagating in the northeast direction. Conclusions. The loop oscillation is most probably excited by the flare-induced blast wave at a speed of ≥1300 km s−1. The excitation of the filament oscillation is more complicated. The blast wave triggers secondary magnetic reconnection far from the main flare, which not only heats the local plasma to higher temperatures (SFR and RB), but produces jet-like flow (i.e., reconnection outflow) as well. The filament is disturbed by the secondary magnetic reconnection and experiences transverse oscillation. These findings provide new insight into the excitation of transverse oscillations of coronal loops and filaments.
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Awal, Naziru M., Irving R. Epstein, Tasso J. Kaper, and Theodore Vo. "Symmetry-breaking rhythms in coupled, identical fast–slow oscillators." Chaos: An Interdisciplinary Journal of Nonlinear Science 33, no. 1 (January 2023): 011102. http://dx.doi.org/10.1063/5.0131305.
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Symmetry-breaking in coupled, identical, fast–slow systems produces a rich, dramatic variety of dynamical behavior—such as amplitudes and frequencies differing by an order of magnitude or more and qualitatively different rhythms between oscillators, corresponding to different functional states. We present a novel method for analyzing these systems. It identifies the key geometric structures responsible for this new symmetry-breaking, and it shows that many different types of symmetry-breaking rhythms arise robustly. We find symmetry-breaking rhythms in which one oscillator exhibits small-amplitude oscillations, while the other exhibits phase-shifted small-amplitude oscillations, large-amplitude oscillations, mixed-mode oscillations, or even undergoes an explosion of limit cycle canards. Two prototypical fast–slow systems illustrate the method: the van der Pol equation that describes electrical circuits and the Lengyel–Epstein model of chemical oscillators.
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Fedorovich, Vladimir, and Andrii Mitsyk. "REGULARITIES OF VIBRATION FINISHING AND GRINDING PROCESSING AND DIRECTIONS OF IMPROVEMENT OF ITS INTENSITY AND QUALITY." Cutting & Tools in Technological System, no. 98 (May 25, 2023): 41–48. http://dx.doi.org/10.20998/2078-7405.2023.98.04.
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The data on the labor intensity of manufacturing engineering products and the share of finishing and grinding operations in the total labor costs of their manufacture are presented. The list and the degree of mastering the technological operations of finishing and grinding processing, performed in the conditions of machine-building industries during the last years are given. The grounds are given for highlighting the method of vibration processing as the most promising for ensuring complete mechanization of the process of finishing and cleaning, as well as achieving high technological characteristics of the surface roughness of parts. An assessment was made of the influence of modes, the trajectory of the movement of the reservoir and the grain size of the granules of the abrasive medium on metal removal. It is indicated that the intensity and quality of vibration treatment is estimated quantitatively by the weight removal of metal and qualitatively by the roughness of the processed surface. It is indicated that the determining factor in this case is the speed of the oscillating movement of granules and parts, the difference of which represents the speed of vibration processing, depending on the speed of the oscillating movement of the medium. It is noted that in order to increase the productivity of the process, it is necessary to increase the speed of the medium by increasing the frequency and amplitude of the reservoir oscillations. The layer-by-layer transmission of a force impulse from the bottom of the reservoir to the bulk medium is considered. The physical meaning of increasing productivity by increasing the amplitude of the reservoir oscillations is indicated. The conditions for obtaining metal removal are indicated, which provide increased efforts for the interaction of granules with parts at high micro-cutting speeds. Experimental studies are described to determine the influence of the amplitude and frequency of oscillations on the results of vibration finishing and grinding. Graphic dependences of metal removal were obtained for various ratios of the sample weight to the weight of the medium granule. The dependence of metal removal on the ellipticity coefficient and the amplitude of the reservoir oscillations was obtained in a similar way. It is noted that the vertical component of the amplitude during in-plane oscillations of the reservoir is the determining factor of the complex influence of the parameters of the ellipse coefficient of the trajectory of the reservoir and its amplitude of oscillations. It has been established that when using a coarse-grained abrasive, the penetration of grains into the metal of the part occurs to a greater depth and larger metal chips are removed with a large metal removal. With a small grain size of the abrasive, small chips are removed with a small metal removal and a decrease in the height of micro-roughness.
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Shao, L. M., G. S. Xu, R. Chen, L. Chen, G. Birkenmeier, Y. M. Duan, W. Gao, et al. "Small amplitude oscillations before the L-H transition in EAST." Plasma Physics and Controlled Fusion 60, no. 3 (February 5, 2018): 035012. http://dx.doi.org/10.1088/1361-6587/aaa57a.
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Choi, Jeong Ryeol. "Quadrature Squeezing and Geometric-Phase Oscillations in Nano-Optics." Nanomaterials 10, no. 7 (July 17, 2020): 1391. http://dx.doi.org/10.3390/nano10071391.
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The geometric phase, as well as the familiar dynamical phase, occurs in the evolution of a squeezed state in nano-optics as an extra phase. The outcome of the geometric phase in that state is somewhat intricate: its time behavior exhibits a combination of a linear increase and periodic oscillations. We focus in this work on the periodic oscillations of the geometric phase, which are novel and interesting. We confirm that such oscillations are due purely to the effects of squeezing in the quantum states, whereas the oscillation disappears when we remove the squeezing. As the degree of squeezing increases in q-quadrature, the amplitude of the geometric-phase oscillation becomes large. This implies that we can adjust the strength of such an oscillation by tuning the squeezing parameters. We also investigate geometric-phase oscillations for the case of a more general optical phenomenon where the squeezed state undergoes one-photon processes. It is shown that the geometric phase in this case exhibits additional intricate oscillations with small amplitudes, besides the principal oscillation. Such a sub-oscillation exhibits a beating-like behavior in time. The effects of geometric-phase oscillations are crucial in a wide range of wave interferences which are accompanied by rich physical phenomena such as Aharonov–Bohm oscillations, conductance fluctuations, antilocalizations, and nondissipative current flows.
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Grigorenko, A., and T. Duyun. "SIMULATION OF NATURAL FREQUENCIES AND FORCED OSCILLATION MAGNITUDES OF A VERTICAL MILLING MACHINE." Bulletin of Belgorod State Technological University named after. V. G. Shukhov 8, no. 6 (April 12, 2023): 76–84. http://dx.doi.org/10.34031/2071-7318-2023-8-6-76-84.
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The article demonstrate the technique for modeling the form of natural oscillations, as well as the amplitude and mode of forced oscillations of the HAAS VF-1 vertical milling machine. As initial data, a publicly available 3D model of load-bearing elements, information on the mass and dimensions of the spindle motor are used. In preparation for the simulation, the original solid model is idealized by removing small chamfers, fillets, and small diameter holes. Movable joints with linear rolling guides and ball bearings are replaced by rigid joints, since vibration damping in these units is not considered. During the first simulation, ten natural frequencies with the largest values of the oscillation amplitude are obtained. The second simulation shows, the influence of the spindle drive layout (coaxial installation of the electric motor with the spindle through a cam clutch or connection using a toothed belt transmission) and additional devices for dissipating vibration energy (mass and structural dampers in the form of structural elements articulated through plastic bushings) is revealed by the magnitude of forced steady-state oscillations that may occur during the processing of the part.
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Filler, J. R., P. L. Marston, and W. C. Mih. "Response of the shear layers separating from a circular cylinder to small-amplitude rotational oscillations." Journal of Fluid Mechanics 231 (October 1991): 481–99. http://dx.doi.org/10.1017/s0022112091003476.
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The frequency response of the shear layers separating from a circular cylinder subject to small-amplitude rotational oscillations has been investigated experimentally in water for the Reynolds number (Re) range 250 to 1200. A hot-film anemometer was placed in the separated shear layers from 1 to 1.5 diameters downstream of the cylinder, and connected to a lock-in analyser. by referencing the lock-in analyser to the cylinder oscillations, the amplitude and phase of the response to different frequency oscillations were measured directly. It is shown that rotational oscillations corresponding to cylinder peripheral speeds between 0.5 and 3% of the free stream can be used to influence the primary (Kármán) mode of vortex generation. For Re greater than ≈ 500, such oscillations can also force the shear-layer vortices associated with the instability of the separating shear layers. Corresponding to the primary and shear-layer modes are two distinct peaks in response amplitude versus frequency curves, and two very different phase versus frequency curves. The response of the shear layers (and near wake) in the range of Kármán frequency suggests qualitative similarities with the response of an oscillator near resonance. Forced oscillations in the higher-frequency shear-layer mode range are simply convected by the shear layers. Close to the cylinder, the shear-layer response is shown to be comparable to that of generic free shear layers studied by others.
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LUO, X. Y., and T. J. PEDLEY. "The effects of wall inertia on flow in a two-dimensional collapsible channel." Journal of Fluid Mechanics 363 (May 25, 1998): 253–80. http://dx.doi.org/10.1017/s0022112098001062.
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The effect of wall inertia on the self-excited oscillations in a collapsible channel flow is investigated by solving the full coupled two-dimensional membrane–flow equations. This is the continuation of a previous study in which self-excited oscillations were predicted in an asymmetric channel with a tensioned massless elastic membrane (Luo & Pedley 1996). It is found that a different type of self-excited oscillation, a form of flutter, is superposed on the original large-amplitude, low-frequency oscillations. Unlike the tension-induced oscillations, the flutter has high frequency, and grows with time from a small amplitude until it dominates the original slower mode. The critical value of tension below which oscillations arise (at fixed Reynolds number) is found to increase as the wall inertia is increased. The rate at which energy is (a) dissipated in the flow field and (b) transferred to the wall during the flutter is discussed, and results at different parameter values are compared with those of a massless membrane. There is also a discussion of whether the onset of flutter, or that of the slower oscillations, is correlated with the appearance of flow limitation, as is thought to be the case in the context of wheezing during forced expiration of air from the lungs.
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SMITH, WARREN R. "Modulation equations for strongly nonlinear oscillations of an incompressible viscous drop." Journal of Fluid Mechanics 654 (May 11, 2010): 141–59. http://dx.doi.org/10.1017/s0022112010000480.
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Large-amplitude oscillations of incompressible viscous drops are studied at small capillary number. On the long viscous time scale, a formal perturbation scheme is developed to determine original modulation equations. These two ordinary differential equations comprise the averaged condition for conservation of energy and the averaged projection of the Navier–Stokes equations onto the vorticity vector. The modulation equations are applied to the free decay of axisymmetric oblate–prolate spheroid oscillations. On the long time scale, only the modulation equation for energy is required. In this example, the results compare well with linear viscous theory, weakly nonlinear inviscid theory and experimental observations. The new results show that previous experimental observations and numerical simulations are all manifestations of a single-valued relationship between dimensionless decay rate and amplitude. Moreover, if the amplitude of the oscillations does not exceed 30% of the drop radius, this decay rate may be approximated by a quadratic. The new results also show that, when the amplitude of the oscillations exceeds 20% of the drop radius, fluid in the inviscid bulk of the drop is undergoing abrupt changes in its acceleration in comparison to the acceleration during small-amplitude deformations.