Oscillatory Systems Research Articles

Oscillatory systems with two degrees of freedom and van der Pol coupling: Analytical approach

In this paper steady‐state vibrations of the two‐degrees‐of‐freedom oscillatory systems with van der Pol coupling are investigated. The model is a system of two differential equations with weak nonlinearity. A new solving procedure based on D′Alembert's method and the method of time‐variable amplitude and phase is developed. The main advantage of the method in comparison to others is that it gives the solution of the system of two coupled weak nonlinear equations in the form that is simple to analyze, as it has the same form as the solution of the corresponding system of linear equations. In the paper two types of systems are considered: one, a two‐mass system with two degrees of freedom, and second, the one‐mass system with two degrees of freedom. The torsional vibrations of a two‐mass system and vibrations of a Jeffcott rotor with two‐degrees‐of‐freedom are analyzed. Analytically obtained results are numerically tested. It is obtained that the difference between analytic and numeric results is small and almost negligible. As the accuracy of the analytic solution is high, it is suitable for application in technics and engineering. Conclusions about steady‐state self‐sustainable oscillators, orbital, and limit cycle motions are given.

Modification of the electronic oscillation spectrum in metallic clusters, caused by the presence of a large spatial scale of inhomogeneity

This work presents a theoretical analysis of the oscillations of a system of degenerate electrons in metallic submicron clusters, taking into account the presence of a large-scale spatial inhomogeneity caused by quantum shell effects. The analysis was carried out in a model formulation in which the large-scale effect was taken into account by the presence of an effective external field acting on the electrons. Two approaches to the description of electron dynamics were considered: kinetic and hydrodynamic. The results obtained within these approaches are in good qualitative and quantitative agreement with each other and demonstrate that for certain cluster sizes, a spectrum of oscillations of the electronic system appears with frequencies differing by the value Δω ∼ ω0/R20 and localized in the vicinity of plasmon frequency ω0 (R0, radius of cluster). The impact of the large-scale effect on the processes of light and electron scattering by metal clusters is estimated. It is shown that maxima appear in the absorption spectrum of the electromagnetic waves, and they turn out to be shifted from the plasmon frequency by value Δω ∼ ω0/R20. Within the framework of the Born approximation, it is shown that a maximum at kR0 ∼ 4π appears in the cross section of elastic scattering of electrons on a metal cluster. The results obtained are important from the point of view of interpreting experiments on plasmonic structures, in particular, on metal films.

Adaptive horizon size moving horizon estimation with unknown noise statistical properties

Abstract Moving horizon estimation (MHE) is an effective technique for state estimation. It formulates state estimation as an optimization problem over a finite time interval and is characterized by inherent robustness, flexibility, and explicit constraint handling capabilities. The horizon size is a crucial parameter influencing the estimation performance of MHE. However, the selection of the horizon size remains an open research question in the field of MHE. In this paper, we propose a novel adaptive horizon size MHE strategy that dynamically adjusts the horizon size based on the value of the objective function. This approach aims to improve the state estimation performance of MHE in real-time applications. Unlike conventional MHE methods that rely on a fixed horizon size, our adaptive strategy enhances robustness against unknown noise statistics by adjusting the horizon size. We analyze the convergence property of the estimation error and provide guidelines for parameter design to ensure optimal performance. The effectiveness and superiority of the proposed method are demonstrated through simulations involving an oscillatory system and a target tracking application under non-stationary noise conditions.

Computationally feasible bounds for the free energy of nonequilibrium steady states, applied to simple models of heat conduction

In this paper, we study computationally feasible bounds for relative free energies between two many-particle systems. Specifically, we consider systems out of equilibrium that admit a nonequilibrium steady state that is reached asymptotically in the long-time limit. The bounds that we suggest are based on the well-known Bogoliubov inequality and variants of Gibbs' and Donsker–Varadhan variational principles. As a general paradigm, we consider systems of oscillators coupled to heat baths at different temperatures. For such systems, we define the free energy of the system relative to any given reference system in terms of the Kullback–Leibler divergence between steady states. By employing a two-sided Bogoliubov inequality and a mean-variance approximation of the free energy (or cumulant generating function), we can efficiently estimate the free energy cost needed in passing from the reference system to the system out of equilibrium (characterised by a temperature gradient). A specific test case to validate our bounds are harmonic oscillator chains with ends that are coupled to Langevin thermostats at different temperatures; such a system is simple enough to allow for analytic calculations and general enough to be used as a prototype to estimate, e.g. heat fluxes or interface effects in a larger class of nonequilibrium particle systems.

Complexity and operator growth for quantum systems in dynamic equilibrium

Krylov complexity is a measure of operator growth in quantum systems, based on the number of orthogonal basis vectors needed to approximate the time evolution of an operator. In this paper, we study the Krylov complexity of a PT-symmetric system of oscillators, which exhibits two phase transitions that separate a dissipative state, a Rabi-oscillation state, and an ultra-strongly coupled regime. We use a generalization of the su(1) algebra associated to the Bateman oscillator to describe the Hamiltonian of the coupled system, and construct a set of coherent states associated with this algebra. We compute the Krylov (spread) complexity using these coherent states, and find that it can distinguish between the PT-symmetric and PT symmetry-broken phases. We also show that the Krylov complexity reveals the ill-defined nature of the vacuum of the Bateman oscillator, which is a special case of our system. Our results demonstrate the utility of Krylov complexity as a tool to probe the properties and transitions of PT-symmetric systems.

Research on out-of-plane vibration band gap calculation of two-dimensional periodic grillage structures based on spectral element method

The vibration of ship and marine structures directly impacts their structural performance and noise levels. Therefore, the vibration band gap characteristics of two-dimensional periodic grillage structures are investigated based on spectral element method in this article. Firstly, the governing motion equation of out-of-plane vibration of periodic grid structures is established in light of the Bloch theorem, and the shear spring oscillator system is introduced to simulate the first-order vertical shear vibration of bottom plate. As a result, the periodic oscillator coupling grid structure model can be proposed. Based on the periodic grid structures, the influence of material distribution on vibration band gap is obtained. Meanwhile, the dispersion relations and vibration transmission of periodic coupling model are calculated and the coupling effect of local resonance system on the band gap characteristics is analyzed. At last, a general approach for equating periodic grillage unit to numerical model is outlined and summarized on basis of the similarity of dynamic properties. The effectiveness and accuracy of the numerical method in out-of-plane vibration band gap analysis of periodic grillage structures are validated through the computation and model test.

Large basins of attraction for control-based continuation of unstable periodic states

Numerical continuation tools are nowadays standard to analyse nonlinear dynamical systems by numerical means. These powerful methods are unfortunately not available in real experiments without having access to an accurate mathematical model. Implementing such a concept in real world experiments using control and data processing to track unstable states and their bifurcations, requires robust control techniques with large basins and good global properties. Here we propose design principles for control techniques for periodic states which lead to large basins and which are robust, without the need to have access to a detailed mathematical model. Our analytic considerations for the control design will be based on weakly nonlinear analysis of periodically driven oscillator systems. We then demonstrate by numerical means that in strong nonlinear regimes successful control with large basins of attraction can be achieved when only plain time series data are available.

A Low-Frequency Oscillation Suppression Method for Regional Interconnected Power Systems with High-Permeability Wind Power.

With the integration of large-scale wind power into the power grid, the impact on system stability, especially the issue of low-frequency oscillations caused by small disturbances, is becoming increasingly prominent. Therefore, this paper proposes a damping quantitative analysis method for regional interconnected power systems incorporating large-scale wind power. Using the cross-entropy particle swarm optimization (CE-PSO) algorithm, the control parameters of wind turbines are optimized to suppress low-frequency oscillations in interconnected systems. The method begins with the state equation of the interconnected power system in two regions; it deduces the characteristic polynomial of the interconnected system, including wind farms, and takes into account the influence of wind power integration on the electrical connectivity of the system. Subsequently, the influence of wind turbine control parameters on the system is quantified, and a quantitative analysis model of the impact of wind power integration on system damping characteristics is constructed. Based on this, an optimization model for wind turbine control parameters is established, and the CE-PSO algorithm is utilized to achieve suppression of low-frequency oscillations in interconnected power grids with wind power integration. Finally, the accuracy and effectiveness of the proposed method are verified through a typical electromagnetic transient simulation model of the two-region interconnected power system.

Optoelectronic oscillator based on a silicon microring modulator

An optoelectronic oscillator (OEO) system is built up with a high-speed silicon microring modulator. The modulator is based on a p-n doped ring resonator with a radius of 10 μm. Its electro-optic (EO) 3 dB bandwidth is ∼31.7 GHz, which makes it suitable for generating multi-GHz radio frequency signals. By using this modulator, one of the essential components of an OEO, the EO converter, has been dramatically miniaturized. At the same time, assisted by the ring resonator, the phase noise of the generated 10 GHz signal (nearly −90 dBc/Hz at 10 kHz offset) is not compromised compared to other integrated OEOs with mm footprint modulators. This is an important step toward a compact, scalable, and fully integrated silicon photonics-based OEO system together with our existing integrated light sources and photodetectors.

Development and Validation of a Mathematical Model for Pyroelectric Temperature Measurement Sensors for Application in Mobile Robotic Systems

A pyroelectric temperature sensor for measuring human body temperature with increased accuracy and speed for application in mobile robotic systems has been developed. This pyroelectric temperature sensor for measuring human body temperature is intended for use in various educational institutions. Its usage will allow for identifying sick or potentially ill people and providing them with preliminary advice and avoid infecting other people. This is particularly important considering the seasonality of dangerous infectious diseases and the emergence of new ones (e.g., COVID-19). It is also advisable to use this pyroelectric sensor in hospitals, where temperature measurement is very crucial for monitoring the course of various diseases. The proposed pyroelectric temperature sensor is based on a nonlinear oscillatory system, which provides high sensitivity and allows for solving the problem of increasing the accuracy of measuring the human body temperature in a non-contact way. Measurement error is ±0.1% in the operating range (32–43) °C, measurement time—1 s, and the frequency instability is 3·10−4.

The Light-Fueled Self-Rotation of a Liquid Crystal Elastomer Fiber-Propelled Slider on a Circular Track.

The self-excited oscillation system, owing to its capability of harvesting environmental energy, exhibits immense potential in diverse fields, such as micromachines, biomedicine, communications, and construction, with its adaptability, efficiency, and sustainability being highly regarded. Despite the current interest in track sliders in self-vibrating systems, LCE fiber-propelled track sliders face significant limitations in two-dime nsional movement, especially self-rotation, necessitating the development of more flexible and mobile designs. In this paper, we design a spatial slider system which ensures the self-rotation of the slider propelled by a light-fueled LCE fiber on a rigid circular track. A nonlinear dynamic model is introduced to analyze the system's dynamic behaviors. The numerical simulations reveal a smooth transition from the static to self-rotating states, supported by ambient illumination. Quantitative analysis shows that increased light intensity, the contraction coefficient, and the elastic coefficient enhance the self-rotating frequency, while more damping decreases it. The track radius exhibits a non-monotonic effect. The initial tangential velocity has no impact. The reliable self-rotating performance under steady light suggests potential applications in periodic motion-demanding fields, especially in the construction industry where energy dissipation and utilization are of utmost urgency. Furthermore, this spatial slider system possesses the ability to rotate and self-vibrate, and it is capable of being adapted to other non-circular curved tracks, thereby highlighting its flexibility and multi-use capabilities.

Stability Analysis Method of a Hierarchical Control Structure Microgrid Based on a Small-Signal Model and Hopf Bifurcation Theory

To the oscillation and stability problem caused by multi-scale and broadband electromagnetic dynamics among many isomerized power electronic devices in a microgrid, a small-signal model of hierarchical control structure microgrid and stability analysis method based on oscillation trajectories are proposed. Moreover, a hierarchical control structure is used as the research object in microgrid, and the analysis is performed based on the small-signal model and Hopf bifurcation theory. First, the small-signal model of the hierarchical control structure microgrid is established, combining the dominant eigenvalue and participation factor analysis methods, to analyze the influence of the controller and related sensitive parameters on the dynamic performance of the system. Then, based on the small-signal model and Hopf bifurcation theory, a stability analysis method based on oscillation trajectories is proposed. The relationship between different oscillation modes and limit cycles in the microgrid system and the influence of the sag control parameter values on the oscillation trajectory and stability domain of the system are researched on. Combining Hopf bifurcation theory and oscillation trajectory to delineate the stable domain of parameter trajectories, the influence of secondary control on the system stability is analyzed under different oscillation trajectories and load disturbances, revealing the corresponding relationship between the state trajectories of different oscillation modes and system stability of a hierarchical control structure microgrid. Based on the proposed oscillating trajectories, the stability analysis method has sufficient universality for studying the impact of system stability, establishing the parameter selection standards for the design of microgrids. Finally, according to the verification results, the correctness and applicability of above methods are verified.

Using Shunt Capacitors to Mitigate the Effects of Increasing Renewable Energy Penetration

Over the past two decades, Renewable Energy Sources (RESs) have gained global popularity. Control issues are becoming more difficult as the system inertia decreases due to the absence of typical synchronous generators. Innovative methods like fault current limiters, energy storage devices, and alternative control systems are utilized to deal with these difficulties. This study provides a summary of the challenges associated with incorporating high-level RESs into the existing grid. The increased penetration of the RESs has a negative impact on the system oscillations and harmonics, generating the need for power quality improvement techniques, such as adaptive control, adding energy systems, power stream assessment, or weight stream examination. This paper presents a framework of the power stream issue, its arrangement as well as different game plan methods. The power stream model of a power structure can be built using the significant association, weight, and age data.

A novel microgroove-based absorber for sorption heat transformation systems: Analytical modeling and experimental investigation

This study proposes a novel sorber bed design, a stationary thin film microgroove-based absorber, that can address the low specific power and oversized sorber bed issues in existing oscillatory solid sorption heat transformation systems. An analytical heat and mass transfer model is developed for the proposed stationary thin film microgroove-based absorber. A highly-wettable microgrooved aluminum substrate is fabricated by the deposition of a hybrid Al2O3/TiO2 layer, and experimental water uptake measurements are obtained using a custom-built gravimetric large pressure jump setup to validate the analytical model. The model examines how key design parameters affect specific cooling power, cooling power density, and energy storage density. Findings indicate that cycle time and groove depth significantly impact system performance. Also, it is found that there is an optimum groove depth, or film thickness, to achieve maximum power. Trapezoidal grooves achieve higher specific cooling power and cooling power density, while rectangular grooves yield a higher maximum energy storage density. It is experimentally shown that a specific cooling power enhancement of up to 600 % can be obtained compared to the experimental data available for oscillatory sorber beds. Also, the absorption rate of the present sorber bed is up to three times higher than that of falling film absorbers.

Torsional behaviors of motor rotor of permanent magnet semi-direct drive system for aerial passenger device

Considering the influence of motor shaft torsional damping, the torsional dynamics equations of a permanent magnet semi-direct drive rotor system in an aerial passenger device are derived. The derivation relies on the coupling between the mathematical model and the gear dynamics model of the permanent magnet motor, and the Lagrange–Maxwell equations are used for streamlined analysis. To protect the motor under extreme working conditions, the influence of supercritical Hopf bifurcation caused by different torsional dampings of the motor shaft on the torsional vibration of the motor rotor is investigated. Based on the Hurwitz criterion, the influence of the linear control gain and nonlinear gain of the washout filter on the system bifurcation point and the limit cycle amplitude of the system is analyzed. Then, from the perspective of the system instability and oscillation caused by friction damping change of the drive motor and the complex electromechanical coupling behavior in the permanent magnet semi-direct drive cutting drive system of the aerial passenger device, the system stability domain is defined. The results can be applied to effectively suppress the torsional vibration of the shaft system in the permanent magnet semi-direct drive system of the aerial passenger device, providing a theoretical guidance for stable operation of the system.

Linear–quadratic GUP and thermodynamic dimensional reduction

In this paper we investigate the statistical mechanics within the Linear–Quadratic GUP (LQGUP, i.e, GUP with linear and quadratic terms in momentum) models in the semiclassical regime. Then, some thermodynamic properties of a system of 3-dimensional harmonic oscillators are investigated by calculating the deformed partition functions. According to the equipartition theorem, we show that the number of accessible microstates decreases sharply in the very high temperatures regime. When the thermal de Broglie wavelength is of the order of the Planck length, three degrees of freedom are frozen in this setup. In other words, it is observed that there is an effective reduction of the degrees of freedom from 6 to 3 for a system of 3D harmonic oscillators in this framework. The calculations are carried out using both approximate analytical and exact numerical methods. The results of the analytical method are also presented in the form of thermal wavelengths for better understanding. Finally, the case of a 2-dimensional harmonic is treated as another example to comprehend the results, leading to a reduction of the degrees of freedom from 4 to 2.

Finding maximum independent set based on multi-stage simulated quantum adiabatic evolution

The ubiquitous nature of the maximum independent set (MIS) problem across diverse fields, including biology and chip design, presents a significant challenge. Recently, quantum algorithms have been recognized for their increased potential in addressing combinatorial optimization problems, including the MIS problem. Several quantum systems, including optical quantum circuits and Rydberg atomic systems, have been designed specifically for the MIS problem. However, elucidating the precise nature of instances that pose challenges for quantum algorithms constitutes a formidable task. In an effort to comprehend this issue, we endeavor to delineate the conditions under which instances become hard to solve by analyzing the Hamiltonian of the k-independent set (k-IS). Furthermore, we present two multi-stage strategies grounded in the simulated quantum adiabatic evolution (SQAE) of Kerr-nonlinear parametric oscillator (KPO) system for identifying the MIS in instances deemed hard to solve. More specifically, we present the algorithm leveraging SQAE of the KPO system for approximating the MIS. Our investigation of the SQAE algorithm reveals that optimal solutions are unattainable under two distinct conditions: (1) when the number of solutions is exponentially smaller to the problem’s scale, and (2) when the counts of non-optimal independent sets (IS) with m overlaps between the optimal k-IS (k>m) is exponentially smaller relative to the problem’s scale. With these two distinctive features, we propose two multi-stage SQAE strategies tailored for hard-to-solve instances. In the first approach, the SQAE algorithm is executed multiple times to identify a set of candidate vertices for the MIS. For each vertex or combinations of vertices in this set, we extract the subgraphs induced by the vertices not adjacent to them. Subsequently, the SQAE algorithm is applied to the subgraph to obtain the (k−1)-IS. In the second multi-stage strategy, we consider each vertex vi in the given graph, generating the subgraph induced by the vertices not adjacent to vi. The SQAE algorithm is then employed to find the (k−1)-IS of the subgraph. Experimental results demonstrate that both multi-stage strategies significantly enhance the performance of the SQAE algorithm for hard-to-solve instances.

Adaptive delayed feedback control for stabilizing unstable steady states.

Delayed feedback control is a commonly used control method for stabilizing unstable periodic orbits and unstable steady states. The present paper proposes an adaptive tuning delay time rule for delayed feedback control focused on stabilizing unstable steady states. The rule is designed to slowly vary the delay time, increasing the difference between the past and current states of dynamical systems, which induces the delay time to automatically fall into the stability region. We numerically confirm that the tuning rule works well for the Stuart-Landau oscillator, FitzHugh-Nagumo model, and Lorenz system.

Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems

Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems

High-order double-coupled Duffing oscillator system with additional damping term and its application in ship-radiated noise signal detection

High-order double-coupled Duffing oscillator system with additional damping term and its application in ship-radiated noise signal detection