Self-sustained Oscillations Research Articles

Experiments on flow past cavity and the application of modal decomposition techniques

In this work, Mach 1.8 flow over a shallow open cavity is studied through time-resolved schlieren images as well as unsteady pressure measurements respectively. Additionally, the cavity shear layer dynamics are explored using modal decomposition techniques namely; proper orthogonal decomposition (POD) and spectral proper orthogonal decomposition (SPOD). The results display that the cavity undergoes a self-sustaining oscillation with a number of modes/tones that are closely related to the modified Rossiter relation. Depending on the cavity oscillation, the time-resolved images reveal various complex flow features. Through modal analysis, the shear layer structures which are responsible for the cavity oscillation are identified. It is understood that POD requires several hundreds of modes to capture 67.3% of the total intensity for resembling the cavity flow field, while SPOD shows 65.7% of the total intensity is available in the 1st mode to reconstruct the cavity flow field. Further, modal analyses have demonstrated that cavity oscillatory frequencies are very similar to unsteady pressure measurement and the modified Rossiter relation. We confirmed that, both these techniques can be successfully applied to cavity flows and are complementary.

Light-Powered Self-Sustained Oscillators of Graphene Oxide/Liquid Crystalline Network Composites Showing Amplitude and Frequency Superposition.

Light-activated self-oscillators have drawn enormous attention for their potential applications in mobile machines, energy harvesting, signal modulation, etc. Herein, we report one graphene oxide (GO)/liquid crystalline network (LCN) actuator that presents a unique light-activated oscillation with amplitude and frequency superposition. The GO/LCN composite film is prepared by the one-step polymerization of LC monomers, which favors a splay orientation in LC cells made by gluing together two glass sheets, one coated with photothermal agent GO and the other coated with a rubbed polyimide alignment layer. Owing to the asymmetric contraction/expansion, changing the cutting direction gives rise to notably different actuation behaviors for GO/LCN composite films. Moreover, it twists a little during the deflection process as a result of experimental error during the cutting process, which may cause the strip to be cut inaccurately. When the composite film is embedded in a self-shadowing system, it produces an unconventional hybrid oscillation mode upon near-infrared light irradiation, i.e., bending and twisting oscillation coupled. Furthermore, when the aspect ratio of the film decreases, the twisting mode is suppressed and the actuator changes from a coupled mode to a single bending mode. The proposed strategy may extend the application of GO/LCN composite materials and enrich light-activated self-oscillating behaviors.

Chemical Inductor.

A multitude of chemical, biological, and material systems present an inductive behavior that is not electromagnetic in origin. Here, it is termed a chemical inductor. We show that the structure of the chemical inductor consists of a two-dimensional system that couples a fast conduction mode and a slowing down element. Therefore, it is generally defined in dynamical terms rather than by a specific physicochemical mechanism. The chemical inductor produces many familiar features in electrochemical reactions, including catalytic, electrodeposition, and corrosion reactions in batteries and fuel cells, and in solid-state semiconductor devices such as solar cells, organic light-emitting diodes, and memristors. It generates the widespread phenomenon of negative capacitance, it causes negative spikes in voltage transient measurements, and it creates inverted hysteresis effects in current–voltage curves and cyclic voltammetry. Furthermore, it determines stability, bifurcations, and chaotic properties associated to self-sustained oscillations in biological neurons and electrochemical systems. As these properties emerge in different types of measurement techniques such as impedance spectroscopy and time-transient decays, the chemical inductor becomes a useful framework for the interpretation of the electrical, optoelectronic, and electrochemical responses in a wide variety of systems. In the paper, we describe the general dynamical structure of the chemical inductor and we comment on a broad range of examples from different research areas.

Ultrasensitive nanoscale optomechanical electrometer using photonic crystal cavities

Abstract High-precision detection of electric charge is critical for physical, chemical, and biological measurements. Nanophotonic optomechanical system confines the optical field at the nanoscale and enables a strong interaction between optical cavity and mechanical resonator. Its high optical quality factor cavity and strong optomechanical coupling are promising for precision sensing applications. Here an integrated optomechanical electrometer is proposed for the electric charge sensing using a zipper cavity with a suspended photonic crystal nanobeam (PCN) acting as a movable mechanical resonator. As the electrostatic force arising from the electric voltage to be measured interacts with the mechanical motion of the movable PCN and modulates its resonance through electrostatic stiffening effect, optomechanical coupling transduces the mechanical motion to the optical field with enhanced sensitivity. The resonance shift of the mechanical resonator can be monitored to detect the electric voltage with a sensitivity of 0.007 Hz / m V 2 $\mathrm{Hz}/\mathrm{m}{\mathrm{V}}^{2}$ . Moreover, the sensing performance can be further enhanced with the operation of the optomechanical electrometer in the self-sustained oscillation above threshold power. Owing to the narrow-linewidth of detector radio frequency (RF) spectrum with a large peak-to-noise floor ratio (up to 73.5 dB), the enhanced electrical sensitivity of 0.014 Hz / m V 2 $\mathrm{Hz}/\mathrm{m}{\mathrm{V}}^{2}$ is achieved with a high resolution of 1.37 m V 2 H z − 1 / 2 $1.37\,\mathrm{m}{\mathrm{V}}^{2}\mathrm{H}{\mathrm{z}}^{-1/2}$ . A theoretical minimal detectable electrostatic charge is calculated as 1.33 × 10 − 2 eH z − 1 / 2 $1.33{\times}{10}^{-2}\,\mathrm{eH}{\mathrm{z}}^{-1/2}$ by converting the measured electric voltage versus RF shift to an approximatively linear relationship. This on-chip optomechanical electrometry scheme provides a powerful solution to the ultrasensitive determination of charged nanoparticles in biological and chemical applications.

Hydrodynamic and acoustic pressure fluctuations in water pipes due to an orifice: Comparison of measurements with Large Eddy Simulations

The present article investigates the turbulent wall pressure fluctuations due to flow through single-hole sharp-square-edged orifices (opening area ratios of 11%, 20% and 31%) in a water-filled pipe by means of measurements and incompressible Large Eddy Simulations (LES) for opening area ratios of 20% and 31%. The orifice plate thickness was half the orifice diameter. The static pressure measurements and simulations show that the vena-contracta factors of the orifices are dependent on Reynolds numbers, which is due to the finite thickness of the orifices. These LES simulations provide a good prediction of the near-field hydrodynamic wall pressure fluctuations, which dominate up to the first three pipe diameters downstream of the orifice. Upstream and far downstream wall pressure fluctuations are dominated by acoustic pressure fluctuations. The source of the radiated sound field was estimated from the surface integral of the fluctuations across the orifice in the LES. The sound field was calculated by implementing the sound source in a one dimensional acoustic model of the test section. The power spectrum density (PSD) of the wall pressure fluctuations for pipe Reynolds numbers varying from 4000 to 10000 collapsed when presented in dimensionless form, which uses the dynamic pressure in the orifice as reference pressure and the ratio of cross-sectional averaged orifice velocity and orifice diameter as characteristic frequency. In the inertial range of the turbulence a global decay of the pressure PSD and of the sound source show a power of the Strouhal number between −113 and −2.8. For higher frequencies the pressure fluctuations were dominated by acoustic resonances. For wider orifices the magnitude of these acoustic pressure fluctuations is predicted within a factor two by the acoustic model. For the narrowest orifice (opening ratio of 11%) the measured PSD of pressure fluctuations displays sharp peaks due to self-sustained oscillations (whistling). A simple power law of the sound source is not accurate due to the unstable hydrodynamic modes related to orifice thickness. However, using the simple model for the sound source the acoustic model predicts the acoustic pressure fluctuations reasonably well for all orifices. At low frequency one observes a peak in the PSD hydrodynamic wall-pressure fluctuations at one pipe diameter downstream of the orifice. It is probably due to an acoustically silent “edge-tone-like” sinusoidal self-sustained motion of the jet.

Minimal energy thresholds for triggering in the Rijke tube: the effect of the time delay

Triggering is the process by which a linearly stable thermoacoustic system can reach self-sustained oscillations. This nonlinear phenomenon is activated only for sufficiently large amplitudes of perturbations to the equilibrium state. In this work, using a nonlinear variational optimisation method coupled with energy bisection, we compute the minimal thresholds for triggering in the Rijke tube. In particular, extending previous works, we take into account the effect of the time delay by optimising not only the perturbations at initial time, but also the velocity at the hot-wire position in the time-delay interval. We found that, for sufficiently large time delays, the nonlinearity linked to the delayed flow velocity bears a strong potential for energy growth, leading to transient amplifications of the energy reaching ${O}(10^{2})$, two orders of magnitude larger than those reported in previous studies. Notably, the gain increases with the time delay, but decreases with the initial energy of the perturbation, thus reaching very high values close to the triggering threshold of the system. The minimal energy for triggering self-sustained oscillations achieves energy values as low as ${O}(10^{-4})$, two orders of magnitude smaller than previous estimates. This indicates that, for thermoacoustic systems characterised by a non-negligible time delay, taking into account the effect of the time-delayed variables, as well as the system nonlinearity, is crucial for correctly evaluating the triggering energy thresholds.

Physical Interaction between Cyclin-Dependent Kinase 5 (CDK5) and Clock Factors Affects the Circadian Rhythmicity in Peripheral Oscillators.

Circadian rhythms are self-sustained oscillators with a period of 24 h that is based on the output of transcriptional and post-translational feedback loops. Phosphorylation is considered one of the most important post-translational modifications affecting rhythmicity from cyanobacteria to mammals. For example, the lack of cyclin-dependent kinase 5 (CDK5) shortened the period length of the circadian oscillator in the Suprachiasmatic Nuclei (SCN) of mice via the destabilization of the PERIOD 2 (PER2) protein. Here, we show that CDK5 kinase activity and its interaction with clock components, including PER2 and CLOCK, varied over time in mouse embryonic fibroblast cells. Furthermore, the deletion of Cdk5 from cells resulted in a prolonged period and shifted the transcription of clock-controlled genes by about 2 to 4 h with a simple delay of chromatin binding of ARNTL (BMAL1) CLOCK. Taken together, our data indicate that CDK5 is critically involved in regulating the circadian clock in vitro at the molecular level.

Central pattern generator based on self-sustained oscillator coupled to a chain of oscillatory circuits.

We have proposed and studied both numerically and experimentally a multistable system based on a self-sustained Van der Pol oscillator coupled to passive oscillatory circuits. The number of passive oscillators determines the number of multistable oscillatory regimes coexisting in the proposed system. It is shown that our system can be used in robotics applications as a simple model for a central pattern generator (CPG). In this case, the amplitude and phase relations between the active and passive oscillators control a gait, which can be adjusted by changing the system control parameters. Variation of the active oscillator's natural frequency leads to hard switching between the regimes characterized by different phase shifts between the oscillators. In contrast, the external forcing can change the frequency and amplitudes of oscillations, preserving the phase shifts. Therefore, the frequency of the external signal can serve as a control parameter of the model regime and realize a feedback in the proposed CPG depending on the environmental conditions. In particular, it allows one to switch the regime and change the velocity of the robot's gate and tune the gait to the environment. We have also shown that the studied oscillatory regimes in the proposed system are robust and not affected by external noise or fluctuations of the system parameters. Moreover, using the proposed scheme, we simulated the type of bipedal locomotion, including walking and running.

Numerical investigation of transonic buffet on a prescribed-pitching OAT15A airfoil

The transonic buffet over a prescribed-pitching OAT15A airfoil was numerically investigated using a well-validated delayed detached eddy simulation approach. The present approach successfully reproduced self-sustained shock wave oscillations. The computational results show that the amplitude of the lift fluctuations in the pitching case is approximately six times that of the fixed case. Compared to the fixed case, the presence of a larger shock motion region, two shock wave interactions, and severe boundary separation give rise to higher pressure and velocity fluctuation levels on the whole upper surface in the pitching case. In particular, the highly disordered flow replaces the periodic vortex shedding in the wake, resulting in the disappearance of the secondary fluctuation in unsteady lift coefficients, which is observed at 2274 Hz in the fixed case. A proper orthogonal decomposition analysis shows that the buffet flow in the fixed case exhibits the feature of regular motion, which is closely related to the coherent flow structure of shock oscillations and Karman vortices. Strong interactions between the Karman vortex structure and the shock oscillations are also observed. Compared to those in the fixed case, the fluctuation amplitudes of the coefficients of the first mode pair and the second to fourth mode pairs in the pitching case are 2.5 times and 5 times larger, respectively, and the energy ratio of the nonlinear component in the total mode energy is significantly increased. Furthermore, the main frequencies of modes 1–10 in the pitching case are all located at the shock buffet frequency or its higher-order harmonics.

Hopf bifurcations in electrochemical, neuronal, and semiconductor systems analysis by impedance spectroscopy

Spontaneous oscillations in a variety of systems, including neurons, electrochemical, and semiconductor devices, occur as a consequence of Hopf bifurcation in which the system makes a sudden transition to an unstable dynamical state by the smooth change of a parameter. We review the linear stability analysis of oscillatory systems that operate by current–voltage control using the method of impedance spectroscopy. Based on a general minimal model that contains a fast-destabilizing variable and a slow stabilizing variable, a set of characteristic frequencies that determine the shape of the spectra and the associated dynamical regimes are derived. We apply this method to several self-sustained rhythmic oscillations in the FitzHugh–Nagumo neuron, the Koper–Sluyters electrocatalytic system, and potentiostatic oscillations of a semiconductor device. There is a deep and physically grounded analogy between different oscillating systems: neurons, electrochemical, and semiconductor devices, as they are controlled by similar fundamental processes unified in the equivalent circuit representation. The unique impedance spectroscopic criteria for widely different variables and materials across several fields provide insight into the dynamical properties and enable the investigation of new systems such as artificial neurons for neuromorphic computation.

Frequency-Response of Non-Singular Terminal Sliding Mode Control With Actuators

Non-singular terminal sliding mode control (NTSMC) is widely popular due to its various industrial applications. In many practical circuit systems, the control input is actually given to an actuator rather than directly to the plant. Therefore, it is important to study the effect of actuators on NTSMC performance. In this brief, frequency-domain characteristics of NTSMC are analyzed using the describing function method. It is shown that in the presence of actuator dynamics, the system exhibits a self-sustained periodic oscillation known as chattering. The relationship between the fundamental frequency, the amplitude of this periodic motion and the NTSMC parameters is explored. The effectiveness of the theoretical analysis is verified via a practical example based on an industrial emulator system.

Self-Sustained Divertor Oscillation Driven by Magnetic Island Dynamics in Torus Plasma

A new type of self-sustained divertor oscillation is discovered in the Large Helical Device stellarator, where the peripheral plasma is detached from material diverters by means of externally applied perturbation fields. The divertor oscillation is found to be a self-regulation of an isolated magnetic field structure (the magnetic island) width induced by a drastic change in a poloidal inhomogeneity of the plasma radiation across the detachment-attachment transitions. A predator-prey model between the magnetic island width and a self-generated local plasma current (the bootstrap current) is introduced to describe the divertor oscillation, which successfully reproduces the experimental observations.

Vibrational Kerr Solitons in an Optomechanical Microresonator.

Kerr soliton microcombs in microresonators have been a prominent miniaturized coherent light source. Here, for the first time, we demonstrate the existence of Kerr solitons in an optomechanical microresonator, for which a nonlinear model is built by incorporating a single mechanical mode and multiple optical modes. Interestingly, an exotic vibrational Kerr soliton state is found, which is modulated by a self-sustained mechanical oscillation. Besides, the soliton provides extra mechanical gain through the optical spring effect, and results in phonon lasing with a red-detuned pump. Various nonlinear dynamics is also observed, including limit cycle, higher periodicity, and transient chaos. This work provides a guidance for not only exploring many-body nonlinear interactions, but also promoting precision measurements by featuring superiority of both frequency combs and optomechanics.

Global modes of viscous heated jets with real gas effects

This study investigates the stability features of spatially spreading heated jets in the viscous regime with real gas effects, using both unsteady two-dimensional axisymmetric simulations and linear analyses of the steady state and time-averaged states. At a Reynolds number of $400$ , the heated jets are found to undergo a subcritical Hopf bifurcation, marking the start of self-sustained oscillations when decreasing the temperature ratio $S=T_{\infty }/T_{{c}}$ , which highly depends on the thermodynamic and transport property assumptions imposed in the simulations. Once the flow enters a limit cycle past the Hopf bifurcation, the linear analyses over the steady base state are unable to capture the oscillation's frequency. Nevertheless, this study confirms that including real gas effects in the stability equations has a strong effect on the growth rate of the global mode once the centreline temperature of the jet reaches that of the dissociation reaction onset, which is $T=2800$ K for air at $p_s=100$ mbar. The linear global analyses over the time-averaged states lead to a satisfying prediction of the oscillation's frequency for the cases studied, and the baroclinic torque obtained from the resulting global mode matches well with that of the simulations.

Stochastic P-bifurcation in a self-sustained tristable oscillator under random excitations

Stochastic P-bifurcation in a self-sustained tristable oscillator under random excitations

Analysis of the linear oscillation dynamics of Fluidyne engines

A Fluidyne engine is a liquid piston Stirling engine that uses thermally induced self-sustained oscillations of water and air that are filled in a looped tube and tuning column. It presents high potential for use as a low-temperature-difference Stirling engine with a simple structure. This study analyzes the linear oscillation dynamics of the Fluidyne from a thermoacoustic point of view, with particular emphasis on the local specific acoustic impedance of the working gas, which is given by the ratio of the complex amplitudes of the pressure and velocity oscillations in the regenerator of the Fluidyne. The frequency dependence of the specific acoustic impedance indicates that the gas in the regenerator region undergoes a thermodynamic cycle equivalent to the Stirling cycle when the oscillation frequency is equal to the natural oscillation frequency of the U-shaped liquid column in the Fluidyne. The analysis of the natural oscillation modes determined two key parameters for the desired specific acoustic impedance: the tuning column length and the connecting position to the loop. Experimental verification was achieved via measurements of the onset temperature ratio and acoustic field of a prototype Fluidyne engine.

Selection of spatial modes in an ensemble of non-locally coupled chaotic maps

Purpose of this work is to determine regularities of formation of spatial structures in an ensemble of chaotic systems with non-local diffusion couplings and to study how these structures depend on the wave response of the digital filter formed by the ensemble couplings structure. Methods. The study was carried out by numerical simulation of an ensemble of logistic maps, calculation of its typical oscillatory regimes and their spectral analysis. The network was considered as a digital filter with a frequency response depending on the coupling parameters. Correlation between the spatial spectra and the amplitude-frequency response of the coupling filter and the mutual coherence of oscillations when the coupling parameters change were considered. Results. The system of couplings between chaotic maps behaves like a wave filter with selective properties, allowing spatial modes with certain wavelengths to exist and suppressing others. The selection of spatial modes is based on the wave characteristic of the coupling filter, the type of which is determined by the radius and the magnitude of couplings. At strong coupling the wave characteristics for ensembles with local and non-local couplings are qualitatively different, therefore they demonstrate essencially different behavior. Discussion. Using spectral methods for dynamics analysis systems with complex network topologies seems to be a promising approach, especially for research of synchronization and multistability in ensembles of chaotic oscillators and maps. The found regularities generalize the results known for ensembles of maps with local couplings. They also can be applied to ensembles of self-sustained oscillators.

Abscisic Acid Machinery Is under Circadian Clock Regulation at Multiple Levels

Abscisic acid (ABA) is recognized as the key hormonal regulator of plant stress physiology. This phytohormone is also involved in plant growth and development under normal conditions. Over the last 50 years the components of ABA machinery have been well characterized, from synthesis to molecular perception and signaling; knowledge about the fine regulation of these ABA machinery components is starting to increase. In this article, we review a particular regulation of the ABA machinery that comes from the plant circadian system and extends to multiple levels. The circadian clock is a self-sustained molecular oscillator that perceives external changes and prepares plants to respond to them in advance. The circadian system constitutes the most important predictive homeostasis mechanism in living beings. Moreover, the circadian clock has several output pathways that control molecular, cellular and physiological downstream processes, such as hormonal response and transcriptional activity. One of these outputs involves the ABA machinery. The circadian oscillator components regulate expression and post-translational modification of ABA machinery elements, from synthesis to perception and signaling response. The circadian clock establishes a gating in the ABA response during the day, which fine tunes stomatal closure and plant growth response.

The Physical-Biogeochemical Responses to a Subsurface Anticyclonic Eddy in the Northwest Pacific

Due to the unique physical processes of mesoscale eddies, the physical and biogeochemical properties within the subsurface anticyclonic eddy (SSAE) and in the surrounding water are distinct. Analyses using satellite and model data have revealed distinct seasonal variations in the central potential density structure of a long-standing SSAE south of Japan; this SSAE exhibits a normal concave isopycnals structure from January to April and a convex lens isopycnals structure from May to December, and these variations may be related to the subduction of low-potential vorticity (PV) mode water. In contrast to the idea of the self-sustained oscillation mechanism, the strength of the SSAE was enhanced due to the eddy kinetic energy provided by dramatic increasing of the positive baroclinic conversion rate during the Kuroshio path transition period from the non-large meander (NLM) path to the large meander (LM) path. Twofold to threefold enhancement of chlorophyll (CHL) was detected in the subsurface CHL maximum layers at the core of the SSAE, and this enhancement was related to the injection of nutrients into the euphotic layer due to winter mixing and the convex of isopycnals. During the period from May to December, elevated CHL and dissolved oxygen (DO) levels and reduced nitrate levels were observed along the periphery of the eddy below the maximum subsurface CHL anomaly depth. The combined result of these two processes: (1) the central downward displaced isopycnals caused by intensified SSAE, and (2) winter mixing deepened to the nutricline due to the thickened mixed layer depth (MLD) and weakened stratification in winter 2017 (during the NLM period) may have led to numerous nutrients and CHL enrichments throughout the mixed layer, thus generating a CHL bloom in the following April. The SSAE intensified in winter 2018 (during the LM period), whereas the shallower MLD and stronger stratification limited the depth of CHL downward displacement.

Laboratory experiments reveal intrinsic self-sustained oscillations in ocean relevant rotating fluid flows

Several ocean Western Boundary Currents (WBCs) encounter a lateral gap along their path. Examples are the Kuroshio Current penetrating into the South China Sea through the Luzon Strait and the Gulf of Mexico Loop Current leaping from the Yucatan peninsula to Florida as part of the Gulf Stream system. Here, we present results on WBC relevant flows, generated in the world’s largest rotating platform, where the Earth’s sphericity necessary to support WBCs is realized by an equivalent topographic effect. The fluid is put in motion by a pump system, which produces a current that is stationary far from the gap. When the jet reaches the gap entrance, time-dependent patterns with complex spatial structures appear, with the jet leaking, leaping or looping through the gap. The occurrence of these intrinsic self-sustained periodic or aperiodic oscillations depending on current intensity is well known in nonlinear dynamical systems theory and occurs in many real systems. It has been observed here for the first time in real rotating fluid flows and is thought to be highly relevant to explain low-frequency variability in ocean WBCs.