Oscillation Modes Research Articles

Possible anticorrelations between pulsation amplitudes and the disc growth of Be stars in giant-outbursting Be X-ray binaries

ABSTRACT The mechanism of X-ray outbursts in Be X-ray binaries remains a mystery, and understanding their circumstellar discs is crucial for a solution of the mass-transfer problem. In particular, it is important to identify the Be star activities (e.g. pulsations) that cause mass ejection and, hence, disc formation. Therefore, we investigated the relationship between optical flux oscillations and the infrared (IR) excess in a sample of five Be X-ray binaries. Applying the Lomb–Scargle technique to high-cadence optical light curves from the Transiting Exoplanet Survey Satellite (${\it TESS}$), we detected several significant oscillation modes in the 3–24 h period range for each source. We also measured the IR excess (a proxy for disc growth) of those five sources, using J-band light curves from Palomar Gattini-IR. In four of the five sources, we found anticorrelations between the IR excess and the amplitude of the main flux oscillation modes. This result is inconsistent with the conventional idea that non-radial pulsations drive mass ejections. We propose an alternative scenario where internal temperature variations in the Be star cause transitions between pulsation-active and mass-ejection-active states.

Contactless surface tension measurement of molten oxides using oscillating drop method in an aerodynamic levitator

Aerodynamic levitation stands as a contactless method for thermophysical property measurement of molten oxides at high temperatures, offering the advantage of eliminating sample contamination and enabling surface tension measurement through the oscillating drop method. However, the presence of oscillation mode splitting results in an underestimation of surface tension. By improving levitation stability and optimizing the acoustic excitation method for the levitated drops, this study successfully eliminates oscillation mode splitting for the first time. The l = 2 resonance frequency is directly measured, which is used to calculate surface tension according to the Rayleigh equation. Taking Al2O3 as a representative of oxides, this study demonstrates the accurate surface tension measurement during the frequency scan process when oscillation mode splitting is absent. Additionally, combining damped oscillation analysis with the frequency scan reduces measurement uncertainty from 2.8 % to 1.5 %. Within the temperature range of 2336K–2923K, the surface tension of molten Al2O3 is determined to be γ = −(4.071 ± 2.688) × 10−5 (T-2327)+(0.7465 ± 0.074) N/m. Underestimation of surface tension is prevented when the l = 2 resonance frequency is used for surface tension calculations. The frequency crossover method which is used for surface tension measurement is also found to be affected by oscillation mode splitting.

Marginal stability analyses for thermochemical convection and its implications for the dynamics of continental lithosphere and core–mantle boundary regions

SUMMARY Significant compositional differences may exist in the lithospheric mantle and above the core–mantle boundary (CMB) relative to the ambient mantle. The intrinsic density differences may affect the development of thermal boundary layer (TBL) instabilities associated with lithospheric delamination and formation of thermochemical plumes. In this study, we explored the instability of two-layer thermochemical fluid using two different techniques: marginal stability analysis with a propagator-matrix method and finite element modelling. We investigated both the instabilities in lithospheric mantle (i.e. lithospheric instability) and the mantle above the CMB (i.e. plume-forming instability) using a background temperature Tbg(z) with the TBL. For lithospheric instability, we found that two-layer fluid with free-slip boundary conditions mainly undergoes the same three different convective modes (i.e. two oscillatory convection modes and one layered convection regime) as that with no-slip boundary conditions reported in Jaupart et al. However, with free-slip boundary conditions, the transitions between these convection modes occur at larger values of buoyancy number B. Free-slip boundary conditions lead to smaller critical Rayleigh number Rac, but larger convective wavelength and oscillation frequency ωc, compared with those with no-slip boundary conditions. Our numerical modelling results demonstrate that Rac and ωc predicted from the classical marginal stability analyses using Tbg(z) with TBL temperature may have significant errors when the oscillatory period is comparable with or larger than the timescale of lithospheric thermal diffusion that causes Tbg(z) to vary with time significantly. In this case, using a more gently sloped background temperature profile ignoring the TBL temperature, the stability analysis predicts more accurate stability conditions, thus presenting an effective remedy to the stability analysis. For plume-forming instability, because of the reduced viscosity in the hot and compositionally dense bottom layer, the transition to the layered convection occurs at significantly smaller B values, and in the oscillatory convection regime, Rac is larger but ωc is smaller, compared with those for lithospheric instability. Finally, our study provides a successful benchmark of numerical models of thermochemical convection by comparing Rac and ωc from numerical models with those from the marginal stability analysis.

Tunable multicolor optomechanically induced transparency and slow-fast light in hybrid electro-optomechanical system

Abstract We investigate the tunable multicolor optomechanically induced transparency and the effect of slow/fast light in a hybrid electro-optomechanical system, in which a degenerate optical parametric amplifier (OPA) and a Λ − type three-level atomic ensemble are placed in a optical cavity with two oscillator modes. The system is driven by a strong pump field and a weak probe field, respectively. Multicolor transparency windows appear in the output field under the atom-photon-OPA-phonon-phonon coherent interaction. And the position and width of the transparent port of the output field can be manipulated by properly modifying the different parameters of the subsystem. We also research the slow/fast light effect related to phase and group delay in the probe field. Our proposal provides a great flexibility for phonon storage and has some potential applications in quantum information processing.

Space Quasi-Periodic Steady Euler Flows Close to the Inviscid Couette Flow

We prove the existence of steady space quasi-periodic stream functions, solutions for the Euler equation in a vorticity-stream function formulation in the two dimensional channel R×[-1,1]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {R}}}\ imes [-1,1]$$\\end{document}. These solutions bifurcate from a prescribed shear equilibrium near the Couette flow, whose profile induces finitely many modes of oscillations in the horizontal direction for the linearized problem. Using a Nash–Moser implicit function iterative scheme, near such equilibrium we construct small amplitude, space reversible stream functions, slightly deforming the linear solutions and retaining the horizontal quasi-periodic structure. These solutions exist for most values of the parameters characterizing the shear equilibrium. As a by-product, the streamlines of the nonlinear flow exhibit Kelvin’s cat eye-like trajectories arising from the finitely many stagnation lines of the shear equilibrium.

Modelling and analysis of a coal-fired thermal power plant to identify physically observable dominant low-frequency oscillatory modes

Modelling and analysis of a coal-fired thermal power plant to identify physically observable dominant low-frequency oscillatory modes

Analysis of Global and Key PM2.5 Dynamic Mode Decomposition Based on the Koopman Method

Understanding the spatiotemporal dynamics of atmospheric PM2.5 concentration is highly challenging due to its evolution processes have complex and nonlinear patterns. Traditional mode decomposition methods struggle to accurately capture the mode features of PM2.5 concentrations. In this study, we utilized the global linearization capabilities of the Koopman method to analyze the hourly and daily spatiotemporal processes of PM2.5 concentration in the Beijing–Tianjin–Hebei (BTH) region from 2019 to 2021. This approach decomposes the data into the superposition of different spatial modes, revealing their hierarchical spatiotemporal structure and reconstructing the dynamic processes. The results show that PM2.5 concentrations exhibit high-frequency cycles of 12 and 24 h, as well as low-frequency cycles of 124 and 353 days, while also revealing spatiotemporal modes of growth, recession, and oscillation. The superposition of these modes enables the reconstruction of spatiotemporal dynamics with a mean absolute percentage error (MAPE) of only 0.6%. Unlike empirical mode decomposition (EMD), Koopman mode decomposition (KMD) method avoids mode aliasing and provides a clearer identification of global and key modes compared to wavelet analysis. These findings underscore the effectiveness of KMD method in analyzing and reconstructing the spatiotemporal dynamics of PM2.5 concentration, offering new insights into the understanding and reconstruction of other complex spatiotemporal phenomena.

Current Loads on a Horizontal Floating Flexible Membrane in a 3D Channel

A 3D analytical model is formulated based on linearised small-amplitude wave theory to analyse the behaviour of a horizontal, flexible membrane subject to wave–current interaction. The membrane is connected to spring moorings for stability. Green’s function approach is used to obtain the dispersion relation and is utilised in the solution by applying the velocity decomposition method. On the other hand, a brief description of the experiment is presented. The accuracy level of the analytical results is checked by comparing the results of reflection and the transmission coefficients against experimental data sets. Several numerical results on the displacements of the membrane and the vertical forces are studied thoroughly to examine the impact of current loads, spring stiffness, membrane tension, modes of oscillations, and water depths. It is observed that as the value of the current speed (CS) rises, the deflection also increases, whereas it declines in deeper water. On the other hand, the spring stiffness has minimal effect on the vibrations of the flexible membrane. When vertical force is considered, higher oscillation modes increase the vertical loads on the membrane, and for a mid-range wavelength, the vertical wave loads on the membrane grow as the CS increases. Further, the influence of the phase and group velocities are presented. The influences of CS and comparisons between them in terms of water depth are presented and analysed. This analysis will inform the design of membrane-based wave energy converters and breakwaters by clarifying how current loads affect the dynamics of floating membranes at various water depths.

Noncontact Measurements of Resonance of Small Round Liquid Surfaces Using Sound Wave to Determine Surface Tension.

Various methods have been developed for measuring the surface tension of liquids, and the present study proposes a new method for measuring the surface tension of liquids. A small (9 mm diameter) round liquid surface was excited by sound waves with a common speaker. Nine liquids possessing various physical properties and functional groups were employed, and three resonance frequencies (frs) were observed for each liquid in a frequency range of 20-180 Hz. The resonances were analyzed with a forced oscillation model. In addition, the amplitudes and phases of the resonance oscillations at various positions of the liquid surface were measured, and the total deformations of the liquid surface were determined. The deformation was compared with the Bessel functions, and the oscillation modes and boundary conditions were decided. Finally, proportional relationships between frs and σ0.5ρ-0.5 (σ: surface tension, ρ: density) with high correlations were obtained, which were supported by a new theoretical equation using hydrodynamics.

Non-radial oscillations mimicking a brown dwarf orbiting the cluster giant NGC 4349 No. 127

Context. Several evolved stars have been found to exhibit long-period radial velocity variations that cannot be explained by planetary or brown dwarf companions. Non-radial oscillations caused by oscillatory convective modes have been put forth as an alternative explanation, but no modeling attempt has yet been undertaken. Aims. We provide a model of a non-radial oscillation, aiming to explain the observed variations of the cluster giant NGC 4349 No. 127. The star was previously reported to host a brown dwarf companion, but whose existence was later refuted in the literature. Methods. We reanalyzed 58 archival HARPS spectra of the intermediate-mass giant NGC 4349 No. 127. We reduced the spectra using the SERVAL and RACCOON pipelines, acquiring additional activity indicators. We searched for periodicity in the indicators and correlations between the indicators and radial velocities. We further present a simulation code able to produce synthetic HARPS spectra, incorporating the effect of non-radial oscillations, and compare the simulated results to the observed variations. We discuss the possibility that non-radial oscillations cause the observed variations. Results. We find a positive correlation between chromatic index and radial velocity, along with closed-loop Lissajous-like correlations between radial velocity and each of the spectral line shape indicators (full width at half maximum, and contrast of the cross-correlation function and differential line width). Simulations of a low-amplitude, retrograde, dipole (l = 1, m = 1), non-radial oscillation can reproduce the observed behavior and explain the observables. Photometric variations below the detection threshold of the available ASAS-3 photometry are predicted. The oscillation and stellar parameters are largely in agreement with the prediction of oscillatory convective modes. Conclusions. The periodic variations of the radial velocities and activity indicators, along with the respective phase shifts, measured for the intermediate-mass cluster giant NGC 4349 No. 127, can be explained by a non-radial oscillation.

The Effect of the Movement of a Passive Reflector on the Atomization of a Levitating Drop

Abstract This study investigates the instability of distilled water drops under acoustic levitation induced by the movement of a reflector toward the transducer. The experimental setup consisted of a passive concave reflector and a Langevin transducer in a uniaxial-resonance configuration. The experiment consists of achieving a stable levitation of the droplet and then moving the reflector constantly toward the transducer, shortening the distance h between them (reflector-transducer). All experiments were recorded using a high-speed camera to analyze the drop’s behavior. The results revealed three distinct instabilities: radial atomization occurred when the drop volume (VD ) was ≤ 3.74 μl, beyond which central atomization was observed. A third instability is observed when a low reflector velocity (Vr < 0.67 mm/s) is used, where the droplet exhibited modes of oscillation with pulsed central atomization.

Multi-scale analysis of harmonic resonance in cylindrical bubbles under acoustic excitation

In this paper, the dimensionless oscillation equation of a cylindrical bubble is analyzed using the multi-scale method, Lyapunov stability theory, and the Routh–Hurwitz stability criterion. The corresponding second-order analytical solution and stability criterion are obtained. By examining the cases of second-order super-harmonic resonance and 1/2-order sub-harmonic resonance, the harmonic resonance characteristics of cylindrical bubbles and the influencing factors are revealed. The conclusions are summarized as follows: (1) Super-harmonic resonance can exhibit up to three solutions, along with unstable phenomena such as jump and hysteresis. Sub-harmonic resonance, however, shows at most two solutions simultaneously, without jump or hysteresis phenomena. (2) As the acoustic excitation amplitude increases, both the response amplitude and the unstable zone significantly enlarge. An increase in nonlinear coefficients can reduce the response amplitude and increase instability. (3) When the acoustic excitation amplitude reaches a certain threshold, the oscillation mode of the bubble shifts from periodic to chaotic. Under the same initial conditions, the chaos threshold for sub-harmonic resonance is higher than that for super-harmonic resonance.

Evaluation of highly sensitive vibration states of nanomechanical resonators in liquid using a convolutional neural network

Nanomechanical resonators can detect various small physical quantities with high sensitivity using changes in resonant properties. However, viscous damping in liquids significantly reduces the measurement sensitivity. This study proposes convolutional neural network (CNN) vibration spectrum analysis to evaluate the highly sensitive vibration states of nanomechanical resonators, which are useful for in-liquid measurements. This research was carried out through the measurement of acetone concentration. First, we compared the concentration classification ability between the proposed and conventional methods and determined that the proposed method of analyzing vibration spectral changes using the CNN model can provide higher measurement sensitivity than the conventional measurement method of observing resonance properties changes and comparing the values for each measurement condition. This result shows that CNN-based spectral analysis is effective for the vibration spectra of in-liquid measurements. Next, gradient-weighted class activation mapping (Grad-CAM) was applied to verify which frequency bands are important for concentration classification in CNN model decision-making. The vibration states in these frequency bands were analyzed in terms of oscillation modes. This analysis revealed significant oscillation modes of the nanomechanical resonator in the liquid environment. Notably, in addition to the resonance states utilized in the conventional method, several other oscillation modes were found to be significant for measurements. This finding suggests that these oscillation modes may be highly sensitive for measurements in liquid environments. Among these oscillation modes, the mode with very small amplitude is highly promising for achieving unprecedented levels of sensitivity in sensing technologies.

Collaborative fault detection and diagnosis method for dual single-axis RINSs configuration in GNSS-denied environment

To ensure the reliability and safety of the long-endurance navigation, two or more rotational inertial navigation systems (RINSs) are usually equipped on ships. Through the redundant configuration, fault detection and diagnosis (FDD) can be realized. In this paper, a collaborative FDD method applied to dual homogeneous single-axis RINSs is proposed. The method utilizes geometric constraint observation to construct a detection filter, processes the filtering outputs through the modified Bayesian algorithm, and incorporates a fault confirmation stage to achieve fault diagnosis with stronger robustness. Besides, an azimuth gyro drift variation estimation method using least-squares is further proposed by exploiting the difference in Schuler oscillation mode resulting from an azimuth gyro fault as opposed to the fault-free state when the system is damped by the log. The efficiency and reliability are demonstrated through comparative and repeated experiments. According to the results based on repeated experiments, the proposed method achieves a comprehensive correct diagnosis rate of over 99% across various fault scenarios. When relatively significant faults occur, the average diagnosis time for horizontal gyros, horizontal accelerometers, and azimuth gyros is 0.4569h, 0.2686h, and 1.2204h respectively. In the case of more subtle faults, although the average diagnosis time is extended to 0.5920h, 0.2991h, and 1.9641h, the effectiveness of the method is still well demonstrated.

Weyl fermions in a (2+1)-dimensional gravitational wave spacetime

In this study, we work on understanding the behavior of relativistic fermions within the framework of a (2+1)-dimensional gravitational wave environment. Our main objective is to uncover an analytical solution for the massless Dirac equation in this particular scenario. Initially, we derive a set of coupled equations that describe the quantum dynamics of the system under consideration. Subsequently, we embark on finding an analytical solution for the resulting wave equation governing Weyl fermions by utilizing the generators associated with the [Formula: see text] algebra. This approach enables us to determine the relativistic frequency modes of the system. We then delve into examining how the parameters of the gravitational wave spacetime influence the real oscillation modes of Weyl fermions. Our findings highlight the sensitivity of Weyl fermions to the specific gravitational wave spacetime background being considered.

Multi-method piecewise low-frequency identification

Inter-area frequency modes of electromechanical oscillations are decisive factors that influence the performance of electrical power systems. However, the accurate estimation of these frequencies remains a challenge due to the non-linear behavior of the response system following a disturbance and the strong coupling among the frequencies. This work describes a curve fitting and electromechanical frequency estimation algorithm, called Multi-method Piecewise Identification (MPI), based on a combination of the Matrix Pencil Method (MPM), the Prony method, and Subspace Identification (SSI), choosing the best approximation of an interval basis according to the model accuracy index (MAI) and the mean square error (MSE). The advantages and limitations of MPI were analyzed by computational analyses that were carried out with Python-based code that estimates the low frequencies for several ringdown signals, including oscillating signals from Australian and Brazilian systems that arise after large disturbances. To ensure robustness to random and noisy conditions, the method was tested with a synthetic signal with Gaussian white noise and time-variant frequencies, and compared to the methods mentioned above, the Hilbert–Huang Transform (HHT), and Eigensystem Realization Algorithm (ERA). The MPI has shown robust results and is capable of obtaining a better fitting for the signal than the other methods.

Magnetic field induced spin wave reflection by a domain wall in synthetic antiferromagnets

Micromagnetic simulations are used to investigate the effect of an external magnetic field on the interaction between domain walls and linearly polarized propagating spin waves in synthetic antiferromagnets. Two regimes with a sharp transition between them are found. At large fields, spin waves are strongly reflected by the domain wall and, consequently, the latter is propelled forward. At low fields, however, there is no reflection and yet the domain wall undergoes a small forward displacement, which is attributed to the change in linear momentum of the magnons as they pass through the domain wall and to the imbalance in the population of the two oscillation modes present in the linearly polarized excitation. The transition between the two regimes occurs at the field value for which the excitation frequency falls below the threshold of the high-frequency mode.

Effect of oscillation parameters on weld surface morphology during laser beam oscillation welding of stainless steel

During laser beam oscillation welding (LBOW), the weld surface morphology is important because it influences the appearance of the workpiece and reflects the welding quality, and the oscillation parameters have an important effect on the weld surface morphology. Therefore, a combination of experimental research and numerical simulation is conducted to investigate the influence of oscillation parameters, including oscillation mode, oscillation frequency, and oscillation amplitude, on the weld surface morphology during LBOW. The calculation encompasses the oscillation trajectory, combined velocity, and energy distribution on the weld surface, varying with different oscillation parameters. A three-dimensional heat transfer and fluid flow model with the oscillation heat source is established to simulate the temperature and fluid flow behavior inside the weld pool. When the heat input is constant, an increase in oscillation frequency results in a decrease in weld width and a smoother surface. As the oscillation frequency increases, the weld width decreases, the surface becomes smooth, and the energy distribution on the weld surface becomes more uniform. The fact that the period of the surface pattern is almost equal to the oscillation period indicates a direct correlation between the formation of weld surface pattern and the oscillation trajectory in LBOW. Among all the oscillation modes, the minimum combined velocity which is equal to the welding velocity occurs at the inflection point in the linear oscillation mode, and the variation in combined velocity of the laser beam is the smallest for circular oscillation mode. The surface pattern is primarily influenced by the oscillation trajectory and fluid flow within the weld pool. Under conditions of lower oscillation frequencies or larger oscillation amplitudes, the fluid flow is weaker, and the surface pattern is primarily influenced by the oscillation trajectory. Conversely, when the fluid flow is stronger, the surface pattern is mainly determined by the fluid flow within the weld pool under conditions of higher oscillation frequencies or smaller oscillation amplitudes. This study explains the formation mechanisms of weld surface patterns and provides insights and guidance for selecting optimal oscillation parameters in LBOW.

On the Optimum Distribution of Multiple Helmholtz Resonators for Annular Combustors

Abstract The combustors of many modern land-based gas turbines and aero-engines are annular. This kind of combustors often suffer from thermoacoustic oscillations, with the occurrence of mostly the circumferential first-order, second-order and third-order oscillation modes in the annular combustion chamber. To solve this problem, passive control methods are widely used adding passive acoustic dampers such as Helmholtz resonators (HRs). Depending on the type and number of HRs, and the possible positions over the circumference to install them, there could easily have millions, or even billions, of possible arrangment patterns. Finding a good design is the key to solve this problem. In this paper, we perform a theoretical and numerical study of an annular combustor installed with multiple types of HRs over the circumference. Firstly, a simple annular duct with arbitrary distributions of these HRs is studied analytically by solving the nonlinear eigenvalue problem of a 1D network model. Based on the results of the analytical method, the impact of the HRs on the acoustic modes of the combustion chamber is studied and the optimum arrangement of multiple resonators is obtained. This arrangement usually gives a null (or small) mode splitting strength and a good damping effect. Finally, we apply the optimum arrangement to damp the thermoacoustic modes that have been captured by numerical simulation for a real annular combustor. We use numerical simulations based on solving the 3D Helmholtz equation in COMSOL to verify the feasibility of the optimum arrangement.

Modeling compact objects with quark matter and dark energy: A comparative study of the radial oscillation modes of HESS J1731-347 and PSR J0740+6620

We model the massive pulsar J0740+6620 and the light HESS J1731-347 compact object assuming (i) quark matter and (ii) dark energy stars. Within Einstein’s General Relativity, and assuming objects made of isotropic matter, we adopt analytic equations-of-state for both matter contents. Although the inner composition of the objects is very different in each case, both equations-of-state imply qualitatively very similar mass-to-radius relationships. We compute the spectra of radial equations for all four cases and the corresponding wave functions as well as the large frequency separations. A comparison between the different matter contents is made as well.