Oscillatory Instability Research Articles

A synthetic population-level oscillator in non-microfluidic environments

Synthetic oscillators have become a research hotspot because of their complexity and importance. The construction and stable operation of oscillators in large-scale environments are important and challenging. Here, we introduce a synthetic population-level oscillator in Escherichia coli that operates stably during continuous culture in non-microfluidic environments without the addition of inducers or frequent dilution. Specifically, quorum-sensing components and protease regulating elements are employed, which form delayed negative feedback to trigger oscillation and accomplish the reset of signals through transcriptional and post-translational regulation. We test the circuit in devices with 1 mL, 50 mL, 400 mL of medium, and demonstrate that the circuit could maintain stable population-level oscillations. Finally, we explore potential applications of the circuit in regulating cellular morphology and metabolism. Our work contributes to the design and testing of synthetic biological clocks that function in large populations.

Multi-time scale model reduction strategy of variable-speed pumped storage unit grid-connected system for small-signal oscillation stability analysis

This paper studies the time-scale characteristics, model reduction, and oscillation stability of the grid-connected variable speed pumped storage unit (VSPSU). Firstly, a method based on the modal analysis and time-scale separation ratio indicator is established to analyze the time-scale characteristics of VSPSU. The results indicate that the state variables of VSPSU can be approximately separated on four-time scales. On this basis, the singular perturbation method (SPM) is applied to obtain the reduced-order model (ROM) of VSPSU under different conditions. The results show that the accuracy of ROMs can be affected by changes in operating conditions. To balance the complexity and accuracy of ROM, a model reduction strategy combining SPM and reduction margin is proposed. The results indicate that the proposed method enables the order minimization of ROM while the selected oscillation mode reaches a given accuracy condition. Finally, the feasibility of ROM for oscillation stability analysis is verified. The ROMs obtained with the proposed strategy are more accurate than those obtained with SPM for oscillation stability analysis of VSPSU. The influence of grid strength, turbine speed, and torque conditions on system oscillation stability is also revealed. This study provides new insights for model order reduction and stability analysis of VSPSU.

Synchronization of Optomechanical Oscillator and Breathing Soliton

AbstractSynchronization and frequency locking between different oscillators are of scientific and technological importance in a wide variety of fields. The optomechanical resonator can be a good integrated oscillator, which takes place via the radiation pressure force induced by the optical fields. In addition, the breathing soliton is a particular kind of dissipative Kerr soliton that exists between the modulation instability state and the stable state, which shows periodic oscillation in pulse width and amplitude, as well as in its spectral envelope. The breathing frequency depends on the pump power and the pump detuning, which can be affected by environmental fluctuations, and the linewidth of the RF beatnote is on the order of megahertz (MHz). Here, the synchronization of these two different oscillators, that is, the optomechanical oscillator and the breathing soliton, is demonstrated. This demonstration transfers the stability and narrow linewidth of the optomechanical oscillator to the breathing soliton. The fixed phase relation between the breathing oscillation and optomechanical oscillation can be established, forming an open Lissajous diagram. These results provide a new way for the stabilization and control of the breathing soliton and may inspire the study of the interaction between the optomechanical oscillator and the breathing soliton.

On the occurrence of buoyancy-induced oscillatory growth instability in directional solidification of alloys

Recent solidification experiments identified an oscillatory growth instability during directional solidification of Ni-based superalloy CMSX4 under a given range of cooling rates. From a modeling perspective, the quantitative simulation of dendritic growth under convective conditions remains challenging, due to the multiple length scales involved. Using the dendritic needle network (DNN) model, coupled with an efficient Navier-Stokes solver, we reproduced the buoyancy-induced growth oscillations observed in CMSX4 directional solidification. These previous results have shown that, for a given alloy and temperature gradient, oscillations occur in a narrow range of cooling rates (or pulling velocity, V p ) and that the selected primary dendrite arm spacing (Λ) plays a crucial role in the activation of the flow leading to oscillations. Here, we show that the oscillatory behavior may be generalized to other binary alloys within an appropriate range of (V p ,Λ) by reproducing it for an Al-4at.%Cu alloy. We perform a mapping of oscillatory states as a function of V p and Λ, and identify the regions of occurrence of different behaviors (e.g., sustained or damped oscillations) and their effect on the oscillation characteristics. Our results suggest a minimum of V p for the occurrence of oscillations and confirm the correlation between the oscillation type (namely: damped, sustained, or noisy) with the ratio of average fluid velocity over V p . We describe the different observed growth regimes and highlight similarities and contrasts with our previous results for a CMSX4 alloy.

Nonlinear modelling and multi-stability characteristics of asymmetric hydro turbine governing system

The asymmetric hydro turbine governing system (AHTGS) has been widely applied in engineering practice, yet the stability characteristics and nonlinear behaviours of AHTGS are seldom studied. Therefore, the authors are motivated to study the stability characteristics and nonlinear behaviours of AHTGS by using Hopf bifurcation theory. Firstly, the refined nonlinear mathematical model of AHTGS is constructed, which takes account of the nonlinear head loss in asymmetric penstocks. Subsequently, the multi-stability characteristics of AHTGS is revealed based on the refined nonlinear mathematical model by using stable domain. Then, the multi-timescale oscillation phenomenon is revealed, i.e. system dynamic response consists of two subwaves with different frequencies. Moreover, the relationship of the two subwaves and the system multi-stability is investigated. The result indicates that the two supercritical bifurcation lines are emerged and a two-timescale oscillation is generated. The stability of the two-timescale oscillation is determined by the two emerged stable domains. In addition, the cause of high-frequency and low-frequency subwaves has been verified as the natural hydraulic oscillation and hydraulic interference between the hydro turbine generating units, respectively. The overall stability of AHTGS is determined by the intersection area of the two stable domains, therefore the reasonable tuning of control parameters within the comprehensive stable domain is critical to maintain the stability of AHTGS.

Effect of fast noise on the fidelity of trapped-ion quantum gates

High-fidelity single- and multiqubit operations compose the backbone of quantum information processing. This fidelity is based on the ability to couple single- or two-qubit levels in an extremely coherent and precise manner. A necessary condition for coherent quantum evolution is a highly stable local oscillator driving these transitions. Here we study the effect of fast noise, that is, noise at frequencies much higher than the local oscillator linewidth, on the fidelity of one- and two-qubit gates in a trapped-ion system. We analyze and measure the effect of fast noise on single-qubit operations, including resonant $\ensuremath{\pi}$ rotations and off-resonant sideband transitions. We further numerically analyze the effect of fast phase noise on the M\o{}lmer-S\o{}rensen two-qubit gate. We find a unified and simple way to estimate the performance of all of these operations through a single parameter given by the noise power spectral density at the qubit response frequency. While our analysis focuses on phase noise and on trapped-ion systems, it is relevant for other sources of fast noise as well as for other qubit systems in which spinlike qubits are coupled by a common bosonic field. Our analysis can help in guiding the design of quantum hardware platforms and gates, improving their fidelity towards fault-tolerant quantum computing.

Damping of low-frequency oscillation using renewable generation units

Nowadays there is a significant increase the number of generation units based on renewable energy sources in electric power systems, the main goal of which is to ensure global access to affordable, reliable, sustainable and modern sources of energy. However, as the penetration level of renewable generation units increases, there are power oscillations easily occur, which create biggest challenges for the power system stability. In particular, the dominant modes of modern generation units, connected to the main grid via a voltage source converter, are in the range of higher frequencies than electromechanical oscillations. Consequently, the chance of occurrence of low-frequency oscillations increases, the parameters and the trajectory of which will differ from power oscillations in power system without renewables. The results of the analysis of low-frequency oscillation parameters in part of Eastern Siberia power system and evaluation of impact of renewable generation unit on power oscillations are presented in this article. The results were obtained by the Hybrid real time simulator based on the combination of analog, physical and digital modeling levels. The developed scheme of part of Eastern Siberia power system and simulation results were verified by SCADA system. The difference between the results of simulation and SCADA system did not exceed 1%. It indicates the adequacy of the Hybrid real time simulator and the developed scheme of power system. Based on the evaluation of the parameters of power oscillations and the calculation of the degree of damping of the transient process, it can be noted that the oscillatory stability of the power system is improved: damping time decreases, the damping ratio increases with increasing of renewables penetration level.

Analytical DC-side stabilizing conditions for hybrid HVDC links based on dominant frequency model reduction

Incorporating the advantages of line commutated converters (LCCs) and voltage-source converters (VSCs), hybrid high voltage DC (HVDC) links have bright prospects in bulk power transmission. For this new technique, however, there is a risk of oscillatory instability in the DC link, and the mechanism behind the instability is still unclear. This paper derives analytical DC-side stabilizing conditions for hybrid HVDC links by using dominant frequency model reduction. The small-signal model of the LCC-VSC link is first truncated by reserving only the state variables highly relevant to the dominant mode so that the expression of the dominant oscillation frequency can be obtained. Dynamics of other state variables are reintroduced and then simplified while leaving their properties nearby the dominant frequency intact. Based on the reduced model, an analytical stability criterion is obtained, which reveals that the DC-side stability of hybrid HVDC links will deteriorate with reduced DC voltage operation, a heavy load, a small DC-link capacitor, slow inner loop dynamics, a small proportional and a large integral gain of the DC voltage regulator. In addition, simplified sufficient stabilizing conditions of hybrid HVDC links are further derived for control parameter design. Case studies validate the accuracy of dominant frequency model reduction and the derived stabilizing conditions.

Micromagnetic model analysis of dual field generation layer (FGL) spin torque oscillators (STO) for microwave-assisted magnetic recording (MAMR)

Dual field generation layer (FGL) spin torque oscillators (STO) were investigated for use in microwave-assisted magnetic recording. The STOs were integrated into the gaps of write heads for stable oscillation. According to preliminary calculations, a FGL thickness of 5 nm was suitable, while the volume of 7.5 nm and 10 nm thick FGLs was too large and they did not oscillate stably. The most dominant factor influencing the FGL rotation was found to be the strength of the antiferromagnetic coupling between the FGLs. Other parameters were also varied, e.g., the exchange coupling between the negative spin injection layer (nSIL) and the trailing shield (TS), however, no significant effect was found. Unlike single FGL STOs, the oscillation frequency changed drastically, from 38 GHz to 73 GHz, on varying the injected current density to the STO. Recording simulations showed that the signal-to-noise ratio was maximized for an STO oscillation frequencies between 34 GHz and 50 GHz, depending on the recording media used in the calculations. Therefore, the dual FGL STO may be suitable for a wide range of recording media. Alternatively, the dual FGL STO may be used for dual-layer recording, where different resonance frequencies are needed for each of the layers, obviating the need for a second STO.

Dynamics of cubic–quintic nonlinear [formula omitted]-symmetry mechanical oscillators

In this paper, we investigate the dynamics of two mechanical coupled oscillators (MCO) with Parity-Time (PT)-symmetry i.e., one has gain and the other has an equal and opposite amount of loss. In the linear case, the eigenmodes and breaking points were determined. In the nonlinear case, the breaking point for soft cubic or quintic potential obtained numerically was also found analytically with perfect agreement. However, instead of the breaking point, for the hard cubic or quintic potential, it is noted a transition toward a regime of periodic or quasi-periodic stable oscillation with energy transfer from the loss oscillator to the gain oscillator. This latter result suggests very important applications within the framework of the optical cavities and waveguides.

Quantum nonstationary phenomena of spin systems in collision models

We investigate the non-stationary phenomenon in a tripartite spin-1/2 system in the collision model (CM) framework. After introducing the dissipation through the system-environment collision for both Markovian and non-Markovian cases, we find the emergence of long-time oscillation in the dynamics of the system and the synchronization among subsystems. We connect the CM description and the quantum master equation in the continuous time limit and explain the existence of the stable oscillation by means of Liouvillian spectrum analysis. The time-dependence of the thermal property and the correlations are investigated, in particular we discuss the possibility of violation of the Landauer's principle in non-Markovian dynamics. In addition, we find that the imperfection of collective dissipation can be compensated by the randomness of the interaction sequence in our CM.

The interplay of symmetry with the Rabi oscillation in the non-Hermitian double Jaynes–Cummings model

We study the dynamical evolution and symmetry breaking of the non-Hermitian double Jaynes–Cummings model with symmetry. The results indicate that there exist symmetry maintained and breaking phase in this model, and the non-Hermitian terms lead to different behaviors in two phases. In the symmetry phase, there exists stable Rabi oscillation caused by the interaction between photons and atoms. At the exceptional point, the system shows critical property that the probabilities in each state over time tend to be equal. The system will undergo a transition from the symmetry phase to the symmetry breaking phase, as increasing the coupling constant. In the symmetry breaking phase, complex eigenvalues appear, and the probability in each state increases monotonically in an exponential form. This study can help us to understand the effect of symmetry on the interaction between photons and atoms in non-Hermitian systems.

Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument

A new model of inertial neural networks with a generalized piecewise constant argument as well as unpredictable inputs is proposed. The model is inspired by unpredictable perturbations, which allow to study the distribution of chaotic signals in neural networks. The existence and exponential stability of unique unpredictable and Poisson stable motions of the neural networks are proved. Due to the generalized piecewise constant argument, solutions are continuous functions with discontinuous derivatives, and, accordingly, Poisson stability and unpredictability are studied by considering the characteristics of continuity intervals. That is, the piecewise constant argument requires a specific component, the Poisson triple. The B-topology is used for the analysis of Poisson stability for the discontinuous functions. The results are demonstrated by examples and simulations.

Stability analysis and estimation of domain of attraction for hydropower station with surge tank

The surge tank is extensively used pressure reduction facility in the hydropower station, and its stability of the water level oscillation (WLO) has always been a significant issue in academia and engineering. The stability of the WLO in the nonlinear hydropower station with surge tank (HSST) system is closely related to the external disturbance. This paper aims to study the stability and domain of attraction in the HSST system. Firstly, the nonlinear mathematical model of the HSST system is established. The critical stable cross-sectional area (CSCA) of surge tanks is investigated based on Lyapunov's first method. Subsequently, the estimation of domain of attraction is conducted based on Lyapunov's second method. Finally, the global asymptotic stability of the HSST system under Thoma stable area is analyzed. of surge tanks. The results show that when the surge tank area is smaller than Thoma stable area, the HSST system is unstable, so the CSCA is large than Thoma stable area. When the surge tank area is larger than Thoma stable area, the HSST system is locally asymptotically stable. The general method for constructing Lyapunov function is presented. The domain of attraction of the WLO is drawn, which defines the disturbance range of asymptotic stability of the HSST system. The domain of attraction rises with the increase of the surge tank area. When the surge tank area is taken as Thoma stable area, the system is not asymptotically stable under any disturbance. The proposed conclusions can provide theoretical reference for the design of surge tanks in practical engineering.

Stability of Periodic Orbits and Bifurcation Analysis of Ship Roll Oscillations in Regular Sea Waves

Response, stability, and bifurcation of roll oscillations of a biased ship under regular sea waves are investigated. The primary and subharmonic response branches are traced in the frequency domain employing the Incremental Harmonic Balance (IHB) method with a pseudo-arc-length continuation approach. The stability of periodic responses and bifurcation points are determined by monitoring the eigenvalues of the Floquet transition matrix. The primary and higher-order subharmonic responses experience a cascade of period-doubling bifurcations, eventually culminating in chaotic responses detected by numerical integration (NI) of the equation of motion. Bifurcation diagrams are obtained through the period-doubling route to chaos. Solutions are aided with phase portrait, Poincaré map, time history and Fourier spectrum for better clarity as and when required. Finally, the same ship model is investigated under variable excitation moments that may result from different wave heights in regular seas. The biased ship roll model exhibits primary and subharmonic responses, jump phenomena, coexistence of multiple responses, and chaotically modulated motion. The stable, periodic, and steady-state roll responses obtained by the IHB method are validated by the NI method. Results obtained by both methods are found to agree very well.

Information-theoretical analysis of statistical measures for multiscale dynamics.

Multiscale entropy (MSE) has been widely used to examine nonlinear systems involving multiple time scales, such as biological and economic systems. Conversely, Allan variance has been used to evaluate the stability of oscillators, such as clocks and lasers, ranging from short to long time scales. Although these two statistical measures were developed independently for different purposes in different fields, their interest lies in examining the multiscale temporal structures of physical phenomena under study. We demonstrate that from an information-theoretical perspective, they share some foundations and exhibit similar tendencies. We experimentally confirmed that similar properties of the MSE and Allan variance can be observed in low-frequency fluctuations (LFF) in chaotic lasers and physiological heartbeat data. Furthermore, we calculated the condition under which this consistency between the MSE and Allan variance exists, which is related to certain conditional probabilities. Heuristically, natural physical systems including the aforementioned LFF and heartbeat data mostly satisfy this condition, and hence, the MSE and Allan variance demonstrate similar properties. As a counterexample, we demonstrate an artificially constructed random sequence, for which the MSE and Allan variance exhibit different trends.

A quantitative variational phase field framework

The finite solid–liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models, results in solute trapping that is well captured when realistic parameters, such as interface width, are employed. However, increasing the interface width, which is desirable for computational reasons, leads to artificially enhanced trapping thus making it difficult to model departure from equilibrium quantitatively. In the present work, we develop a variational phase field model that guarantees a temporal decrease in the free energy with independent kinetic equations for the solid and liquid phases. Separate kinetic equations for the phase concentrations obviate the assumption of point wise equality of diffusion potentials, as is done in previous works. Non-equilibrium effects such as solute trapping, drag and interface kinetics can be introduced in a controlled manner in the present model. In addition, the model parameters can be tuned to obtain “experimentally-relevant” trapping while using significantly larger interface widths than prior efforts. A comparison with these other phase field models suggests that interface width of about three to twenty-five times larger than current best-in-class models can be employed depending upon the material system at hand leading to a speed-up by a factor of W(d+2), where W and d denote the interface width and spatial dimension, respectively. Finally the capacity to model non-equilibrium phenomena is demonstrated by simulating oscillatory instability leading to the formation of solute bands.

Chaos in a Pendulum Adaptive Frequency Oscillator Circuit Experiment

Adaptive oscillators can learn and encode information in dynamic, plastic states. The pendulum has recently been proposed as the base oscillator of an adaptive system. In a mechanical setup, the horizontally forced pendulum adaptive frequency oscillator seeks a resonance condition by modifying the length of the pendulum's rod. This system stores the external forcing frequency when the external amplitude is small, while it can store the resonance frequency, which is affected by the nonlinearity of the pendulum, when the external amplitude is large. Furthermore, for some frequency ranges, the pendulum adaptive frequency oscillator can exhibit chaotic motion when the amplitudes are large. This adaptive oscillator could be used as a smart vibratory energy harvester device, but this chaotic region could degrade its performance by using supplementary energy to modify the rod length. The pendulum adaptive frequency oscillator’s equations of motions are discussed, and a field-programmable analog array is used as an experimental realization of this system as an electronic circuit. Bifurcation diagrams are shown for both the numerical simulations and experiments, while period-3 motion is shown for the numerical simulations. As little work has been done on the stability of adaptive oscillators, the authors believe that this work is the first demonstration of chaos in an adaptive oscillator.

Oscillatory translational instabilities of spot patterns in the Schnakenberg system on general 2D domains

For a bounded 2D planar domain Ω, we investigate the impact of domain geometry on oscillatory translational instabilities of N-spot equilibrium solutions for a singularly perturbed Schnakenberg reaction-diffusion system with activator-inhibitor diffusivity ratio. An N-spot equilibrium is characterized by an activator concentration that is exponentially small everywhere in Ω except in N well-separated localized regions of extent. We use the method of matched asymptotic analysis to analyze Hopf bifurcation thresholds above which the equilibrium becomes unstable to translational perturbations, which result in -frequency oscillations in the locations of the spots. We find that stability to these perturbations is governed by a nonlinear matrix-eigenvalue problem, the eigenvector of which is a 2N-vector that characterizes the possible modes (directions) of oscillation. The matrix contains terms associated with a certain Green’s function on Ω, which encodes geometric effects. For the special case of a perturbed disk with radius in polar coordinates with , , and 2π-periodic, we show that only the mode-2 coefficients of the Fourier series of f impact the bifurcation threshold at leading order in σ. We further show that when , the dominant mode of oscillation is in the direction parallel to the longer axis of the perturbed disk. Numerical investigations on the full Schnakenberg PDE are performed for various domains Ω and N-spot equilibria to confirm asymptotic results and also to demonstrate how domain geometry impacts thresholds and dominant oscillation modes.

Dynamic Characteristics of a Small-Size Beam Mounted on an Accelerating Structure

This study focuses on the nonlinear vibration of a small-size beam hosted in a high-speed moving structure. The equation of the beam’s motion is derived using the coordinate transformation. The small-size effect is introduced by applying the modified coupled stress theory. The equation of motion involves quadratic and cubic terms due to mid-plane stretching. Discretization of the equation of motion is achieved via the Galerkin method. The impact of several parameters on the non-linear response of the beam is investigated. Bifurcation diagrams are used to investigate the stability of the response, whereas softening/hardening characteristics of the frequency curves are used as an indication of nonlinearity. Results indicate that increasing the magnitude of the applied force tends to signify the nonlinear hardening behavior. In terms of the periodicity of the response, at a lower amplitude of the applied force, the response appears to be a one-period stable oscillation. Increasing the length scale parameter, the response moves from chaotic to period-doubling to the stable one-period response. The impact of the axial acceleration of the moving structure on the stability as well as on the nonlinearity of the response of the beam is also investigated.