Search Results (117)

Doubly Fed Induction Generator (DFIG)-based Wind Energy Systems (WESs) have become increasingly prominent in the global energy sector, owing to their superior efficiency and operational flexibility. Nevertheless, DFIGs are notably vulnerable to fluctuations in the grid, which can result in power quality issues—including voltage swells, sags, harmonic distortion, and flicker—while also posing difficulties in complying with Fault Ride-Through (FRT) standards established by grid regulations. To address the previously mentioned challenges, this paper develops an integrated approach utilizing a Dynamic Voltage Restorer (DVR) in conjunction with a Lithium-ion storage system. The DVR is coupled in series with the WES terminal, while the storage system is coupled in parallel with the DC link of the DFIG through a DC/DC converter, enabling rapid voltage compensation and bidirectional energy exchange. Simulation results for a 2 MW WES employing DFIG modeled in MATLAB/Simulink demonstrate the efficacy of the proposed system. The approach maintains terminal voltage stability, reduces Total Harmonic Distortion (THD) to below 0.73% during voltage sags and below 0.42% during swells, and limits DC-link voltage oscillations within permissible limits. The system also successfully mitigates voltage flicker (THD reduced to 0.41%) and harmonics (THD reduced to 0.4%), ensuring compliance with IEEE Standard 519. These results highlight the proposed system’s ability to enhance both PQ and FRT capabilities, ensuring uninterrupted wind power generation under various grid disturbances. Full article

Grid-forming converters (GFMCs) have gained significant attention for their functionality in grid voltage formation and grid-supportive services. However, managing harmonic distortions caused by nonlinear loads remains a critical challenge in weak grids. This paper presents a novel grid-forming active power filter (GFMC APF) that integrates voltage and frequency regulation with effective harmonic control. The proposed control method generates harmonic voltage commands by detecting voltage at the point of common coupling. The GFMC APF compensates harmonic voltages by creating a near short-circuit impedance path for harmonics, thereby preventing harmonic currents from propagating into the grid. In addition to improving harmonic performances, the system enhances grid stability by enhancing inertia, damping, and short-circuit capacity while suppressing wide-frequency oscillations. The proposed method avoids complex parameter tuning, ensuring simplicity and scalability. Simulation results validate the effectiveness of the GFMC APF in delivering precise harmonic control, improved power quality, and enhanced grid-forming capabilities. Full article

Quantum batteries represent a new and promising technological application of quantum mechanics, offering the potential for enhanced energy storage and fast charging. In this work, we study a quantum battery composed of three two-level systems with XXZ coupling operating under open boundary conditions. We investigate the role played by ferromagnetic and antiferromagnetic initial configurations on the charging dynamics of the battery. Two charging mechanisms are explored: static charging, where the battery interacts with a constant classical external field, and harmonic charging, where the field oscillates periodically over time. Our results demonstrate that static charging can be more efficient in the ferromagnetic case, achieving maximum energy due to complete population inversion between the ground and excited states. In contrast, harmonic charging excels in the antiferromagnetic case. By analyzing the stored energy and the average charging power in these two regimes, we highlight the impact of anisotropy on the performance of quantum batteries. Our findings provide valuable insights for optimizing quantum battery performance based on the system’s initial state and coupling configuration, paving the way for the study of more efficient quantum devices for energy storage. Full article

In many applications of quantum optics, nonlinear physics, molecular chemistry and biophysics, one can encounter models in which the coupled quantum harmonic oscillator provides an explanation for many physical phenomena and effects. In general, these are harmonic oscillators coupled via coordinates and momenta, which can be represented as $\widehat{H}={\sum }_{i=1}^2\left({\displaystyle \frac{{\widehat{p}}_i^2}{2m_i}}+{\displaystyle \frac{m_i{\omega }_i^2}{2}}{x}_i^2\right)+{\widehat{H}}_{int}$, where the interaction of two oscillators ${\widehat{H}}_{int}=i{k}_1{x}_1{\widehat{p}}_2+i{k}_2{x}_2{\widehat{p}}_1+k_3{x}_1{x}_2-k_4{\widehat{p}}_1{\widehat{p}}_2$. Despite the importance of this system, there is currently no general solution to the Schrödinger equation that takes into account arbitrary initial states of the oscillators. Here, this problem is solved in analytical form, and it is shown that the probability of finding the system in any states and quantum entanglement depends only on one coefficient $R\in (0,1)$ for the initial factorizable Fock states of the oscillator and depends on two parameters $R\in (0,1)$ and $\varphi$ for arbitrary initial states. These two parameters $R\in (0,1)$ and $\varphi$ include the entire set of variables of the system under consideration. Full article

Fluxonium qubits, designed to mitigate charge noise and enhance anharmonicity, are among the most promising superconducting platforms for quantum computing. To understand and exploit their quantum properties and design novel fluxonium-based architectures with improved functionalities, these systems require an accurate Hamiltonian formulation to capture their energy level structure and quantum dynamics. This work presents a systematic method for constructing the Hamiltonian for multi-loop circuits that partitions the system into a set of uncoupled harmonic oscillators and a coupled anharmonic part originating from the Josephson circuit elements, allowing clear identification of independent modes and isolating the nonlinearity in the Josephson terms. While demonstrated for fluxonium-type multi-loop circuits, this method can be generalized to other superconducting qubit architectures within the broader context of circuit QED, making it a versatile tool for exploring different circuit configurations. Our systematic and flexible modeling approach forms the theoretical basis for the qubit measurement and control experiments validating multi-loop fluxonium architectures. Full article

Under the condition of asymmetric system voltage, grid-connected inverters exhibit obvious sequence impedance frequency coupling characteristics, which can easily lead to resonance and the misoperation of protection and control devices. Currently, targeted quantitative analyses are insufficient. To address this limitation, this paper identifies dominant harmonic pairs and develops an analytical model of an inverter’ second-order admittance under unbalanced grid voltage conditions. Considering the influence of the phase-locked loop and current control loop, the sequence impedance characteristics of a grid-connected inverter were quantitatively analyzed. The simulation results verified the accuracy of the model. The conclusion of the paper provides a foundation for subsequent research on the instability mechanism and oscillation suppression strategy of the grid-connected inverter and grid interconnection system. Full article

We show that the theory of quantum statistical mechanics is a special model in the framework of the quantum probability theory developed by mathematicians, by extending the characteristic function in the classical probability theory to the quantum probability theory. As dynamical variables of a quantum system must respect certain commutation relations, we take the group generated by a Lie algebra constructed with these commutation relations as the bridge, so that the classical characteristic function defined in a Euclidean space is transformed to a normalized, non-negative definite function defined in this group. Indeed, on the quantum side, this group-theoretical characteristic function is equivalent to the density matrix; hence, it can be adopted to represent the state of a quantum ensemble. It is also found that this new representation may have significant advantages in applications. As two examples, we show its effectiveness and convenience in solving the quantum-optical master equation for a harmonic oscillator coupled with its thermal environment, and in simulating the quantum cat map, a paradigmatic model for quantum chaos. Other related issues are reviewed and discussed as well. Full article

This study seeks to improve the performance of a low-temperature differential free-piston Stirling air conditioner (FPSAC). To achieve this, a novel approach is proposed, which replaces the conventional simple harmonic drive with a multi-harmonic drive. This modification aims to optimize the motion of the driving piston, bringing it closer to the ideal movement pattern. The research involves both thermodynamic and dynamic coupling simulations of the FPSAC, complemented by experimental verification of its key performance parameters. A thermodynamic model for the gas medium, employing a quasi-one-dimensional dynamic approach for compressible fluids, and a nonlinear two-dimensional vibration dynamic model for the solid piston are developed, focusing on the low-temperature differential FPSAC physical model. The finite difference method is employed to numerically simulate the entire system, including the electromagnetic thrust of the multi-harmonic-driven linear oscillating motor, fluid transport equations, and the nonlinear dynamic equations of the power and gas control pistons. Variations in displacement, velocity, and pressure for each control volume at any given time are obtained, along with the indicator and temperature–entropy diagrams after the system stabilizes. The simulation results show that, in cooling mode, assuming no heat loss or mechanical friction, the Stirling cooler operates at a frequency of 80 Hz. Using the COP_sin value for the simple harmonic drive as a baseline, performance is improved by altering the driving method. Under the multi-harmonic drive, the COP_c5 increased by 10.03% and COP_c7 by 14.23%. In heating mode, the COP under the multi-harmonic drive improved by 0.51% for COP_h5 and 2.61% for COP_h7. Performance experiments were conducted on the low-temperature differential FPSAC, and the key parameter test results showed good agreement with the simulation outcomes. The maximum deviation at the trough was found to be less than 2.45%, while at the peak, the maximum error did not exceed 3.61%. When compared to the simple harmonic drive, the application of the multi-harmonic drive significantly enhances the overall efficiency of the FPSAC, demonstrating its superior performance. The simulation analysis and experimental results indicate a significant improvement in the coefficient of performance of the Stirling cooler under the multi-harmonic drive at the same power level, demonstrating that the multi-harmonic drive is an effective approach for enhancing FPSAC performance. Furthermore, it should be noted that the method proposed in this study is applicable to other types of low-temperature differential free-piston Stirling air conditioners. Full article

An investigation into the Box Assembly with Removable Component (BARC) structure is conducted by utilizing computational simulations and experimental structural testing in order to determine the complex dynamical responses instigated by the central cut of the system. Because the dynamics of the BARC system is complex, this study focuses primarily on analyzing the behavior of the box assembly (BA) system. The investigation explores the dynamics of the BA system by varying the central cut widths, ranging from a cut as wide as 0.5” cut to a 0.25” cut system, as well as a 0.1” cut and a system with no cut at all. Experimental testing is performed on each system including a free vibration test using an impact hammer to excite and identify the dominant frequencies of each structure. This testing is followed by pseudo-random vibration tests and swept sinusoidal excitation tests to determine the nonlinear aspects of these systems, such as the possible existence of nonlinear softening, hardening, and/or damping. The results show that nonlinear softening and nonlinear damping are present in each system. The no-cut system demonstrated the highest peak frequencies throughout all the tests, being the most rigid structure. The 0.25” cut system was shown to have the highest peak frequencies among all the cut systems in both the finite elemenet analysis (FEA) and impact testing. This trend did not continue, though, in the random and harmonic testing, possibly due to the added stiffness of the test setup with the slip table and stinger. The results show the importance of accurately measuring the central cut width and how possible geometric uncertainties change the overall dynamical behaviors of complex systems, such as natural characteristics, nonlinear responses, coupling of modes, and oscillating amplitudes. Full article

In this paper, we present a “non-linear” factorization of a family of non-normal operators arising from Gribov’s theory of the following form: ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }={\lambda }^{\prime }{A}^{{*}^2}{A}^2+\mu A^{*}A+i\lambda A^{*}}$$(A+A^{*})A,$ where the quartic Pomeron coupling ${\lambda }^{\prime }$, the Pomeron intercept $\mu$ and the triple Pomeron coupling $\lambda$ are real parameters, and $i^2=-1$. $A^{*}$ and A are, respectively, the usual creation and annihilation operators of the one-dimensional harmonic oscillator obeying the canonical commutation relation $[A,A^{*}]=I$. In Bargmann representation, we have ${\displaystyle A⟷\frac{d}{dz}}$ and ${\displaystyle A^{*}⟷z}$, $z=x+iy$. It follows that ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }}$ can be written in the following form: ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }=p\left(z\right)\frac{d^2}{d{z}^2}+q\left(z\right)\frac{d}{dz},}$ where $p\left(z\right)={\lambda }^{\prime }{z}^2+i\lambda z$ and $q\left(z\right)=i\lambda z^2+\mu z.$ This operator is an operator of the Heun type where the Heun operator is defined by $H=p\left(z\right){\displaystyle \frac{d^2}{d{z}^2}}+q\left(z\right){\displaystyle \frac{d}{dz}}+v\left(z\right),$ where $p\left(z\right)$ is a cubic complex polynomial, $q\left(z\right)$ and $v\left(z\right)$ are polynomials of degree at most 2 and 1, respectively, which are given. For $z=-iy$, $H_{{\lambda }^{\prime },\mu ,\lambda }$ takes the following form: $H_{{\lambda }^{\prime },\mu ,\lambda }=-a\left(y\right){\displaystyle \frac{d^2}{d{y}^2}}+b\left(y\right){\displaystyle \frac{d}{dz}},$ with $a\left(y\right)=y(\lambda -{\lambda }^{\prime }y)$ and ${\displaystyle b\left(y\right)=y(\lambda y+\mu ).}$ We introduce the change of variable $y={\displaystyle \frac{\lambda }{2{\lambda }^{\prime }}}(1-cos\left(\theta \right))$, $\theta \in [0,\pi ]$ to obtain the main result of transforming ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }}$ into a product of two first-order operators: ${\displaystyle {\tilde{H}}_{{\lambda }^{\prime },\mu ,\lambda }={\lambda }^{\prime }(\frac{d}{d\theta }+\alpha \left(\theta \right))(-\frac{d}{d\theta }+\alpha \left(\theta \right)),}$ with $\alpha \left(\theta \right)$ being explicitly determined. Full article

In the initial part of this paper, we survey (in arbitrary spacetime dimension) the general FLRW cosmologies with non-interacting perfect fluids and with a canonical or phantom scalar field, minimally coupled to gravity and possibly self-interacting; after integrating the evolution equations for the fluids, any model of this kind can be described as a Lagrangian system with two degrees of freedom, where the Lagrange equations determine the evolution of the scale factor and the scalar field as functions of the cosmic time. We analyze specific solvable models, paying special attention to cases with a phantom scalar; the latter favors the emergence of nonsingular cosmologies in which the Big Bang is replaced, e.g., with a Big Bounce or a periodic behavior. As a first example, we consider the case with dust (i.e., pressureless matter), radiation, and a scalar field with a constant self-interaction potential (this is equivalent to a model with dust, radiation, a free scalar field and a cosmological constant in the Einstein equations). In the phantom subcase (say, with nonpositive spatial curvature), this yields a Big Bounce cosmology, which is a non-absurd alternative to the standard ($\Lambda$CDM) Big Bang cosmology; this Big Bounce model is analyzed in detail, even from a quantitative viewpoint. We subsequently consider a class of cosmological models with dust and a phantom scalar, whose self-potential has a special trigonometric form. The Lagrange equations for these models are decoupled passing to suitable coordinates $(x,y)$, which can be interpreted geometrically as Cartesian coordinates in a Euclidean plane: in this description, the scale factor is a power of the radius $r=\sqrt{x^2+y^2}$. Each one of the coordinates $x,y$ evolves like a harmonic repulsor, a harmonic oscillator, or a free particle (depending on the signs of certain constants in the self-interaction potential of the phantom scalar). In particular, in the case of two harmonic oscillators, the curves in the plane described by the point $(x,y)$ as a function of time are the Lissajous curves, well known in other settings but not so popular in cosmology. A general comparison is performed between the contents of the present work and the previous literature on FLRW cosmological models with scalar fields, to the best of our knowledge. Full article

We study two harmonic oscillators with high quality factors, driven by equilibrium and off equilibrium thermal noise, the latter mimicked by establishing a temperature gradient. The two oscillators are coupled via a third reciprocal harmonic interaction. We deepen the case of a weak coupling between the two oscillators, and show the emergence of a “spike” in the displacement variance of the colder oscillator, when the respective elastic constants approach each other. Away from the peak, the displacement variance of each oscillator only reflects the value of the local temperature. We name this phenomenon the variance resonance, or alternatively covariance resonance, in the sense that it comes about as one element of the covariance matrix describing both oscillators. In fact, all of the elements of the covariance matrix show some distinctive behavior. The oscillator at the lower temperature, therefore, oscillates as if driven by a higher temperature, resonating with the other one. By converse, the variance of the hotter oscillator develops a deep dent, or depression, around the same region. We could not reproduce this behavior if either the coupling constant is not small compared to those of the two oscillators, or if the quality factors are not large enough. In fact, in such instances the system tends to resemble one which is in equilibrium at the average temperature, regardless of the relative strengths of the elastic constants of the two oscillators. Our results could have various applications including for example precision measurement systems, when not all parts of the apparatuses are at the same temperature. Full article

Anxiety is a widespread mental health issue, and binaural beats have been explored as a potential non-invasive treatment. EEG data reveal changes in neural oscillation and connectivity linked to anxiety reduction; however, harmonics introduced during signal acquisition and processing often distort these findings. Existing methods struggle to effectively reduce harmonics and capture the fine-grained temporal dynamics of EEG signals, leading to inaccurate feature extraction. Hence, a novel Denoised Harmonic Subtraction and Transient Temporal Feature Extraction is proposed to improve the analysis of the impact of binaural beats on anxiety levels. Initially, a novel Wiener Fused Convo Filter is introduced to capture spatial features and eliminate linear noise in EEG signals. Next, an Intrinsic Harmonic Subtraction Network is employed, utilizing the Attentive Weighted Least Mean Square (AW-LMS) algorithm to capture nonlinear summation and resonant coupling effects, effectively eliminating the misinterpretation of brain rhythms. To address the challenge of fine-grained temporal dynamics, an Embedded Transfo XL Recurrent Network is introduced to detect and extract relevant parameters associated with transient events in EEG data. Finally, EEG data undergo harmonic reduction and temporal feature extraction before classification with a cross-correlated Markov Deep Q-Network (DQN). This facilitates anxiety level classification into normal, mild, moderate, and severe categories. The model demonstrated a high accuracy of 95.6%, precision of 90%, sensitivity of 93.2%, and specificity of 96% in classifying anxiety levels, outperforming previous models. This integrated approach enhances EEG signal processing, enabling reliable anxiety classification and offering valuable insights for therapeutic interventions. Full article

We investigate the interaction of fermion fields with oscillating domain walls, inspired by breather-type solutions of the sine-Gordon equation, a nonlinear system of fundamental importance. Our study focuses on the fermionic bound states and particle production induced by a time-dependent scalar background field. The fermions couple to two domain walls undergoing harmonic motion, and we explore the resulting dynamics of the fermionic wave functions. We demonstrate that while fermions initially form bound states around the domain walls, the energy provided by the oscillatory motion of the scalar field induces an outward flux of fermions and antifermions, leading to particle production and eventual flux propagation toward spatial infinity. Through numerical simulations, we observe that the fermion density exhibits quasiperiodic behavior, with partial recurrences of the bound state configurations after each oscillation period. However, the fermion wave functions do not remain localized, and over time, the density decreases as more particles escape the vicinity of the domain walls. Our results highlight that the sine-Gordon-like breather background, when coupled non-supersymmetrically to fermions, does not preserve integrability or stability, with the oscillations driving a continuous energy transfer into the fermionic modes. This study sheds light on the challenges of maintaining steady-state fermion solutions in time-dependent topological backgrounds and offers insights into particle production mechanisms in nonlinear dynamical systems with oscillating solitons. Full article

The article highlights the importance of analytical computational models of torsionally oscillating systems and their simulation for estimating the lowest resonance frequencies. It also identifies the pitfalls of the application of these models in terms of the accuracy of their outputs. The aim of the paper is to control the dangerous vibration of a mechanical system actuator using a pneumatic elastic coupling using different approaches such as analytical calculations, experimental measurement results, and simulation models. Based on the known mechanical properties of the laboratory system, its dynamic model in the form of a twelve-mass chain torsionally oscillating mechanical system is developed. Subsequently, the model is reduced to a two-mass system using the method of partial frequencies according to Rivin. The total load torque of the piston compressor under fault-free and fault conditions is simulated to obtain the amplitudes and phases of the harmonic components of the dynamic torque. After calculating the natural frequency and the natural shape of the oscillation, the Campbell diagram is processed to determine the critical revolutions. There is a pneumatic flexible coupling between the rotating masses, which changes the dynamic torsional stiffness. The dynamic torque curves transmitted by the coupling are compared with different dynamic torsional stiffnesses during steady-state operation and one cylinder failure. The monitored values are the position of the critical revolutions, the natural frequency, the natural shape of the oscillation, and the RMS of the dynamic load torque. The experimental model is verified by the simulation model. The accuracy of the developed simulation model with the experimental data are apparently very good (even more than 99% of the critical revolutions value obtained by calculation); however, it depends on the dynamic stiffness of the coupling. In this study, a detailed, comprehensive approach combining analytical procedures with simulation models is presented. Experimental data are verified with simulation results, which show a good agreement in the case of 700 kPa coupling pressure. The inaccuracy of some of the experiments (at 300 and 500 kPa pressures) is due to the interaction of the coupling’s apparent stiffness and the level of the damped vibration energy in the coupling, which is manifested by its different heating. Based on further experiments, a solution to these problems will be proposed by introducing this phenomenon effectively into the simulation model. Full article