Self-sustained Oscillations Research Articles

Prediction of Self-Sustained Oscillations of an Isothermal Impinging Slot Jet

The present results are focused on the self-sustained oscillations of a confined impinging slot jet and their role in the flow structure and modeling requirements. Unsteady laminar, large-eddy simulation (LES), and Reynolds-averaged Navier–Stokes (RANS) predictions of an isothermal confined impinging jet were validated for several nozzle-to-plate ratios (H/B=4–15) and for laminar (Re=340 and 480) and turbulent (Re=104–2.7×104) conditions. The impinging flow structure was found to be highly influenced by the H/B ratio. For high ratios (H/B>5), the studied steady RANS turbulence models could not satisfactorily predict the high diffusion reported experimentally in the jet-impinging influence zone. The failure of these models has been attributed to the modeling issues of turbulence closures. However, for H/B=8, unsteady laminar 3D and LES calculations were verified, and a sinuous oscillation mode was developed, revealing self-sustained oscillations and the display of periodic flapping of the impinging jet in good agreement with the experiments. The predicted flapping oscillation is one of the reasons for the higher diffusion near the impingement wall, which was verified in several time-averaged experimental studies. The presence of jet flapping matters for clarifying the already long discussion on the RANS model’s validation in predicting impinging jets with high H/B ratios, adding justification to the failure of these turbulence models. This unsteady behavior is correctly computed through LES.

A novel period mutation implicating nuclear export in temperature compensation of the Drosophila circadian clock

Circadian clocks are self-sustained molecular oscillators controlling daily changes of behavioral activity and physiology. For functional reliability and precision, the frequency of these molecular oscillations must be stable at different environmental temperatures, known as "temperature compensation." Despite being an intrinsic property of all circadian clocks, this phenomenon is not well understood at the molecular level. Here, we use behavioral and molecular approaches to characterize a novel mutation in the period (per) clock gene of Drosophila melanogaster, which alters a predicted nuclear export signal (NES) of the PER protein and affects temperature compensation. We show that this new perI530A allele leads to progressively longer behavioral periods and clock oscillations with increasing temperature in both clock neurons and peripheral clock cells. While the mutant PERI530A protein shows normal circadian fluctuations and post-translational modifications at cool temperatures, increasing temperatures lead to both severe amplitude dampening and hypophosphorylation of PERI530A. We further show that PERI530A displays reduced repressor activity at warmer temperatures, presumably because it cannot inactivate the transcription factor CLOCK (CLK), indicated by temperature-dependent altered CLK post-translational modification in perI530A flies. With increasing temperatures, nuclear accumulation of PERI530A within clock neurons is increased, suggesting that wild-type PER is exported out of the nucleus at warm temperatures. Downregulating the nuclear export factor CRM1 also leads to temperature-dependent changes of behavioral rhythms, suggesting that the PER NES and the nuclear export of clock proteins play an important role in temperature compensation of the Drosophila circadian clock.

Half-integer vs. integer effects in quantum synchronization of spin systems

We study the quantum synchronization of a single spin driven by an external semiclassical signal for spin numbers larger than S=1, the smallest system to host a quantum self-sustained oscillator. The occurrence of interference-based quantum synchronization blockade is found to be qualitatively different for integer vs. half-integer spin number S. We explain this phenomenon as the interplay between the external signal and the structure of the limit cycle in the generation of coherence in the system. Moreover, we show that the same dissipative limit-cycle stabilization mechanism leads to very different levels of quantum synchronization for integer vs. half-integer S. However, by choosing an appropriate limit cycle for each spin number, comparable levels of quantum synchronization can be achieved for both integer and half-integer spin systems.

Self-sustained oscillations of lift and drag forces, heat fluxes, and flowfield parameters over supersonic bodies under asymmetrical energy deposition

Self-sustained oscillations of lift and drag forces, heat fluxes, and flowfield parameters over supersonic bodies under asymmetrical energy deposition

Liquid crystal elastomer composite-based photo-oscillator for microrobots

In recent years, photoactive materials have attracted extensive interest in microrobots for their attractive abilities of untethered and tunable control with light. Conventional photo-oscillators based on Azo-containing liquid crystal network require complex surface alignment techniques and light sources with specific wavelengths and polarity, which limits their application in controlled autonomy. Here, we report a facile strategy to create self-oscillating microrobots powered and controlled by a wide spectrum of constant light. The oscillators are composed of a layer of candle soot (CS)-containing liquid crystal elastomer (LCE) attached to a layer of polydimethylsiloxane (PDMS). The strip-shaped oscillators with one end fixed can execute self-sustained oscillation through a self-shadowing mechanism. LCEs with CS as an excellent photo-absorber provides superior photothermal actuation, while PDMS with low viscoelasticity accelerates the actuation-recovery cycle of the oscillator. Our LCE composite photo-oscillators show tunable frequencies and amplitudes by structural and light intensity modulation, showing potential for autonomous soft robotic applications.

Dissipative coupling-induced phonon lasing

Phonon lasers, as the counterpart of photonic lasers, have been intensively studied in a large variety of systems; however, (all) most of them are based on the directly coherent pumping. Intuitively, dissipation is unfavorable for lasing. Here, we experimentally demonstrate a mechanism of generating phonon lasing from the dissipative coupling in a multimode optomechanical system. By precisely engineering the dissipations of two membranes and tuning the intensity modulation of the cavity light, the two-membrane-in-the-middle system exhibits non-Hermitian characteristics and the cavity-mediated interaction between two nanomechanical resonators becomes purely dissipative. The level attraction and damping repulsion are clearly exhibited as the signature of dissipative coupling. After the exceptional point, a non-Hermitian phase transition, where eigenvalues and the corresponding eigenmodes coalesce, two phonon modes are simultaneously excited into the self-sustained oscillation regime by increasing the interaction strength over a critical value (threshold). In distinct contrast to conventional phonon lasers, the measurement of the second-order phonon correlation reveals the oscillatory and biexponential phases in the nonlasing regime as well as the coherence phase in the lasing regime. Our study provides a method to study phonon lasers in a non-Hermitian open system and could be applied to a wide range of disciplines, including optics, acoustics, and quantum many-body physics.

Giant injection-locking bandwidth of a self-pulsing limit-cycle in an optomechanical cavity

Locking of oscillators to ultra-stable external sources is of paramount importance for improving close-to-carrier phase noise in free running oscillators. In most of them, such as Micro-Electro-Mechanical-Systems or LC circuit-based oscillators, the locking frequency range is limited by the robustness of their natural frequency, which comes explicitly related with intrinsic parameters of the system. In this work we report the synchronization of an optically-driven self-pulsing limit-cycle taking place in a silicon optomechanical crystal cavity to an external harmonic signal that modulates the driving laser. Because of the extreme ductility of the natural self-pulsing frequency (several tens of MHz), the injection-locking mechanism is highly efficient and displays giant relative bandwidths exceeding 60%. The external modulation reveals itself as a knob to explore dynamical attractors that are otherwise elusive and, in particular, as a means to initialize a mechanical resonator into a state of self-sustained oscillations driven by radiation pressure forces. Moreover, we exploit the large anharmonicity of the studied limit-cycle to induce injection-locking to integer multiples and fractions of the frequency of the external reference, which can be used for frequency conversion purposes in nano-electro-opto-mechanical systems.

Computation of Intrinsic Instability and Sound Generation From Auto-Ignition Fronts

Abstract Burning carbon-free fuels such as hydrogen in gas turbines promise power generation with minimal emissions of greenhouse gases. A two-stage sequential combustor architecture with a propagation-stabilized flame in the first stage and an auto-ignition-stabilized flame in the second stage allows for efficient combustion of hydrogen fuels. However, interactions between the auto-ignition-stabilized flame and the acoustic modes of the combustor may result in self-sustained thermoacoustic oscillations, which severely affect the stable operation of the combustor. In this paper, we study an “intrinsic” thermoacoustic feedback mechanism in which acoustic waves generated by unsteady heat release rate oscillations of the auto-ignition front propagate upstream and induce flow perturbations in the incoming reactant mixture, which, in turn, act as a disturbance source for the ignition front. We first perform detailed reactive Navier–Stokes (direct numerical simulation (DNS)) and Euler computations of an auto-ignition front in a one-dimensional setting to demonstrate the occurrence of intrinsic instability. Self-excited ignition front oscillations are observed at a characteristic frequency and tend to become more unstable as the acoustic reflection from the boundaries is increased. The Euler computations yield identical unsteady ignition front behavior as the DNS computations, suggesting that diffusive mechanisms have a minor effect on the instability. In the second part of this work, we present a simplified framework based on the linearized Euler equations (LEE) to compute the sound field generated by an unsteady auto-ignition front. Unsteady auto-ignition fronts create sources of sound due to local fluctuations in gas properties, in addition to heat release oscillations, which must be accounted for. The LEE predictions of the fluctuating pressure field in the combustor agree well with the DNS data. The findings of this work are essential for understanding and modeling thermoacoustic instabilities in reheat combustors with auto-ignition-stabilized flames.

Multi-modal thermoacoustic instability suppression via locally resonant and Bragg bandgaps.

Thermoacoustic instability is a common occurrence in combustors, yielding self-sustained oscillations and causing potential risk, such as severe structural damage. In this paper, modal instability suppression inside a duct is studied using periodically arranged membranes within the framework of a linear heat release n-τ model embedded into a fully coupled energy-based model. The periodic arrangement of the membranes along the duct sidewall enables locally resonant and Bragg scattering bandgaps, shown to be conducive for the stabilization of unstable thermoacoustic modes. Eigen-modes are classified into different groups, which call for specific control actions in relation with the bandgap frequencies. While multi-modal instability control of low-order modes can be achieved through the tuning of the resonant bandgaps, the densely packed modal cluster, regrouping modes featuring similar mode shapes, requires proper adjustment of the flame position for avoiding modal instability. Compared with the Bragg bandgaps, locally resonant bandgaps, which should be formed near the unstable modes even without stringent periodicity, are shown to play a decisive role in the control process. Meanwhile, strict periodicity is not necessary for the proposed control strategy, showing the practicability of the proposed control strategy. The study shows a promising route to achieve simultaneous suppression of multi-modal instability.

Comparison between an exact and a heuristic neural mass model with second-order synapses

Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear transfer function (NMM1). However, a recent exact mean-field theory for quadratic integrate-and-fire (QIF) neurons challenges this view by showing that the mean firing rate is not a static function of the neuronal state but follows two coupled nonlinear differential equations (NMM2). Here we analyze and compare these two descriptions in the presence of second-order synaptic dynamics. First, we derive the mathematical equivalence between the two models in the infinitely slow synapse limit, i.e., we show that NMM1 is an approximation of NMM2 in this regime. Next, we evaluate the applicability of this limit in the context of realistic physiological parameter values by analyzing the dynamics of models with inhibitory or excitatory synapses. We show that NMM1 fails to reproduce important dynamical features of the exact model, such as the self-sustained oscillations of an inhibitory interneuron QIF network. Furthermore, in the exact model but not in the limit one, stimulation of a pyramidal cell population induces resonant oscillatory activity whose peak frequency and amplitude increase with the self-coupling gain and the external excitatory input. This may play a role in the enhanced response of densely connected networks to weak uniform inputs, such as the electric fields produced by noninvasive brain stimulation.

Evolution of self-sustained circadian rhythms is facilitated by seasonal change of daylight.

Self-sustained oscillation is a fundamental property of circadian rhythms and has been repeatedly tested since the early days of circadian research, resulting in the discovery of almost all organisms possessing self-sustained circadian oscillations. However, the evolutionary advantage of self-sustainability has been only speculatively discussed. In this theoretical study, we sought the environmental constraints and selection pressure that drive the acquisition or degeneration of self-sustainability through the process of evolution. We considered the dynamics of a gene regulatory network having a light input pathway under 12 h light and 12 h dark cycles or multiple day length conditions and then optimized the network structure using an evolutionary algorithm. By designing the fitness function in the evolutionary algorithm, we investigated the environmental conditions that led to the evolution of the self-sustained oscillators. Then, we found that self-sustained oscillation is rarer than damped oscillation and hourglass-type behaviour. Moreover, networks with self-sustainability have a markedly high fitness score when we assume that a network has to generate a constantly periodic expression profile regardless of day length. This study is, to our knowledge, the first to show that seasonality facilitated the evolution of the self-sustained circadian clock, which was consistent with empirical records.

Negative inductor effects in nonlinear two-dimensional systems: Oscillatory neurons and memristors

Many chemical and physical systems show self-sustained oscillations that can be described by a set of nonlinear differential equations. The system enters oscillatory behavior by an intrinsic instability that leads to bifurcation. We analyze conducting systems that present oscillating response under application of external voltage or current. Phenomena like electrochemical corrosion and the spiking response of a biological neuron are well-known examples. These systems have applications in artificial neurons and synapses for neuromorphic computation. Their dynamical properties can be characterized by normal mode analysis of small expansion of the constituent nonlinear equations. The linearized model leads to the technique of ac frequency response impedance spectroscopy that can be obtained experimentally. We show a general description of two-variable systems formed by a combination of a fast variable (the voltage) and a slowing down internal variable, which produce a chemical inductor. A classification of bifurcations and stability is obtained in terms of the parameters of the intrinsic equivalent circuit including the case of a negative inductor. Thereafter, we describe a number of physical examples and establish the characterization of their properties: The electrocatalytic reaction with adsorbed intermediate species, an oscillating metal oxide memristor, and finally we discuss the signs of the equivalent circuit elements in the central model of neuroscience, the Hodgkin–Huxley model for an oscillating neuron.

Voice Simulation: The Next Generation

Simulation of the acoustics and biomechanics of sound production in humans and animals began half a century ago. The three major components are the mechanics of tissue under self-sustained oscillation, the transport of air from the lungs to the lips, and the propagation of sound in the airways. Both low-dimensional and high-dimensional computer models have successfully predicted control of pitch, loudness, spectral content, vowel production, and many other features of speaking and singing. However, the problems of computational efficiency, validity, and accuracy have not been adequately addressed. Low-dimensional models are often more revealing of nonlinear phenomena in coupled oscillators, but the simplifying assumptions are not always validated. High-dimensional models can provide more accuracy, but interpretations of results are sometimes clouded by computational redundancy and uncertainty of parameters. The next generation will likely combine pre-calculations and machine learning with abbreviated critical calculations.

Adjoint-based limit cycle oscillation instability sensitivity and suppression

Dynamical systems often exhibit limit cycle oscillations (LCOs), self-sustaining oscillations of limited amplitude. LCOs can be supercritical or subcritical. The supercritical response is benign, while the subcritical response can be bi-stable and exhibit a hysteretic response. Subcritical responses can be avoided in design optimization by enforcing LCO stability. However, many high-fidelity system models are computationally expensive to evaluate. Thus, there is a need for an efficient computational approach that can model instability and handle hundreds or thousands of design variables. To address this need, we propose a simple metric to determine the LCO stability using a fitted bifurcation diagram slope. We develop an adjoint-based formula to efficiently compute the stability derivative with respect to many design variables. To evaluate the stability derivative, we only need to compute the time-spectral adjoint equation three times, regardless of the number of design variables. The proposed adjoint method is verified with finite differences, achieving a five-digit agreement between the two approaches. We consider a stability-constrained LCO parameter optimization problem using an analytic model to demonstrate that the optimizer can suppress the instability. We also consider a more realistic LCO speed and stability-constrained airfoil problem that minimizes the normalized mass and stiffness. The proposed method could be extended to optimization problems with a partial differential equation (PDE)-based model, opening the door to other applications where high-fidelity models are needed.

Pumping and Cooling of Nanomechanical Vibrations Generated by Cooper-Pair Exchange

We consider a nanoelectromechanical system composed of a carbon nanotube suspended between two normal leads and coupled to a superconducting scanning tunneling microscope (STM) tip via vacuum tunnel barrier. Treating the nanotube as a single-level quantum dot, it is shown that an applied voltage between the superconducting STM tip and normal leads gives rise to a pumping or a cooling of the mechanical subsystem depending on the direction of the electronic flow. It is also demonstrated that the transition between these two regimes is controlled by the strength of the tunnel coupling between the nanotube and superconducting STM tip and the relative position of the electronic level. Such phenomena are realized due to a specific electromechanical coupling that is fully governed by the quantum dynamics of the Cooper pairs. The amplitude of the self-sustained oscillations in the pumping regime is analyzed numerically, and the effective temperature of the mechanical subsystem in the cooling regime is obtained.

Numerical investigation of self-sustained oscillations of stall cells around a leading edge-separating airfoil

The flow around a stalled airfoil is investigated using zonal detached-eddy simulation (mode 2), including transition effects through a coupling with the γ−Reθ,t framework. The airfoil exhibits mixed trailing edge-leading edge stall type properties. The chord length-based Reynolds number and Mach number, respectively, amount to 1·106 and 0.16. Two computations with different initial conditions are performed for 40 and 120 chord-passing durations, respectively (or equivalently 0.23 and 0.67 s), allowing the capture of several periods of the low frequency dynamics of the flow—compared to typical von Kármán vortex shedding. A stall hysteresis is observed: the computation initiated from an attached flow remains thus, but the computation which starts from a separated flow yields a quasi-permanent low-frequency oscillatory behavior, which bifurcates to the previously attached topology after 90 chord-passing durations (0.45 s). The oscillatory phase displays events of emergence and disappearance of stall cells. The partly- and fully attached flows are validated against experimental data. The oscillatory bistable flow is then analyzed with regard to the characteristics and frequency contents of both massive separation and partial transient reattachments. It is shown that the low-frequency separated shear layer flapping at the leading edge is forced by high-frequency fluctuations, which travel from the trailing edge upstream, close to the wall in the separated flow. The flapping phenomenon displays a Strouhal number based on the front-section height of the airfoil around St=fc sin (α)/u∞≃0.02. Conversely, the high-frequency fluctuations have Strouhal numbers closer to 3, which is in close agreement with leading-edge shear-layer instability frequencies. The spectral content of the flow is then explored in search of the source of these high-frequency fluctuations. It is proposed that they stem from the instability of the trailing edge shear layer between the pressure side boundary layer and the separated flow from the suction side. Finally, a scenario describing a cycle of the low-frequency oscillation of a stall cell is proposed.

Self-Sustained Oscillations of the Torque under High-Pressure Torsion in an NdFeB Alloy

Self-Sustained Oscillations of the Torque under High-Pressure Torsion in an NdFeB Alloy

On the use of negative thermal expansion engineered structures in flexural-mode solid-state thermoacoustics

Recent numerical studies have shown evidence of self-sustained oscillations in solids due to externally-applied spatial thermal gradients. In analogy with its acoustic counterpart in gases, this phenomenon was dubbed solid-state thermoacoustics (SSTA). Such heat-driven oscillation can give rise to either longitudinal or flexural motion, depending on the specific design of the system. Although an experimental proof of self-sustained motion in flexural-mode SSTA (F-SSTA) devices has yet to be produced, previous experimental studies pointed to the reduction of the effective damping as a clear indicator of the thermo-mechanical energy conversion process at the core of the F-SSTA mechanism. The F-SSTA theory suggested that negative thermal expansion (NTE), which is not a common property in natural materials, offers a remarkable opportunity to enhance the F-SSTA instability. The present study explores a design approach that leverages the unique features afforded by the solid state design in order to improve the overall performance of F-SSTA’s devices and reduce the technological gap to achieve, in a near future, a successful experimental validation. The proposed design approach leverages a hybrid bilayer beam concept where one of the two layers is designed to exhibit NTE properties. More specifically, the NTE layer is composed of a bi-material octet truss that contracts in the axial direction upon heating. This axial contraction is particularly beneficial to induce a strong thermal bending moment that ultimately enhances the F-SSTA instability. In addition, this work also furthers the conceptual understanding of the F-SSTA process by presenting an analytical perturbation energy budget developed on the basis of a simplified discrete model. These theoretical considerations provide new important insights in the energy conversion mechanism at the basis of the F-SSTA process, hence helping reducing the gap of knowledge towards a successful experimental realization of the F-SSTA effect. • Improved performance of F-SSTA systems via architectured NTE materials. • Identification of parameters controlling the flexural thermoacoustic instability. • A simplified analytical energy budget to understand the energy conversion mechanism.

Theoretical study of the emergence of periodic solutions for the inhibitory NNLIF neuron model with synaptic delay

Among other models aimed at understanding self-sustained oscillations in neural networks, the NNLIF model with synaptic delay was developed almost twenty years ago to model fast global oscillations in networks of weakly firing inhibitory neurons. Periodic solutions were numerically observed in this model, but despite its intensive study by researchers in PDEs and probability, there is up-to-date no analytical result on this topic. In this article, we propose to approximate formally these solutions by a Gaussian wave whose periodic movement is described by an associate delay differential equation (DDE). We prove the existence of a periodic solution for this DDE and we give a rigorous asymptotic result on these solutions when the connectivity parameter $b$ goes to $-\infty$. Lastly, we provide heuristic and numerical evidence of the validity of our approximation.

Evolution and distribution of the anode overpotential and its oscillations in a polymer electrolyte membrane fuel cell exposed to carbon monoxide

Carbon monoxide (CO) poisoning of polymer electrolyte membrane fuel cells (PEMFCs) remains a challenge for their deployment, and a deeper understanding of the spatiotemporal dynamics involved is needed to develop effective mitigation strategies. In this work, localised reference electrodes were used to measure the anode overpotential at three locations across the active area of a galvanostatically operated cell (0.3 A cm−2) exposed to 100 ppm CO/H2. The anode region closest to the inlet was poisoned more rapidly than the rest of the cell, following a sigmoidal variation, and presented a higher CO coverage. The varying CO concentration, combined with local operating conditions, had a direct impact on the distribution of CO coverage. Additionally, complex self-sustained oscillations of the cell voltage and the anode overpotential were observed and correlated with the rate of CO oxidation in the overall cell. The coexistence of a dominant mean-field coupling area closer to the anode inlet, and a dominant migration coupling region closer to the outlet was identified, consistent with reported modelling predictions for a single straight channel cell. Finally, the cell recovery with pure H2 was shown to be a faster process than the CO adsorption, which follows first-order kinetics and is affected by local conditions.