Complex Frequency Research Articles

An Explanation for the Flutter Paradox in the Supercritical Region of a Simply-Supported Fluid-Conveying Pipe

Abstract Employing traditional Galerkin method, a coupled-mode flutter is predicted in the supercritical region of simply-supported pipes which constitutes a paradox since the internal flow effect is conservative and there is no energy to sustain the oscillation. Although there is a consensus that the flutter does not exist, the intrinsic mechanism remains to be clarified. This study has found that the internal flow induced Coriolis force term cannot be decoupled in traditional Galerkin method which leads to the dissatisfaction of the convergence conditions required in weighted residual approach (WRA). Moreover, the disparities in the predicted complex frequencies have been witnessed at different base function numbers when the internal flow velocity is sufficiently large. A modified Galerkin method adopting a new set of weighting functions is proposed based on WRA, and the Coriolis force term disappears by use of the orthogonality relations (it is stated that the Coriolis force is not directly omitted). Thus, a convergent solution for the set of residual functions which are identically equal to zeros can be guaranteed. Employing the modified method, the convergence in simulations is confirmed and the flutter phenomenon does not occur. This study can be a workbench for the study on the unsolved or partly solved issues in simulations of fluid-conveying pipes. Moreover, it has demonstrated that the predictions in traditional Galerkin method overestimate the natural frequencies, and it becomes more profound in higher-order natural modes at larger internal flow velocities which are of practice significance for dynamic analysis of flexible pipeline systems.

A ResNet-Based Audio-Visual Fusion Model for Piano Skill Evaluation

With the rise in piano teaching in recent years, many people have joined the ranks of piano learners. However, the high cost of traditional manual instruction and the exclusive one-on-one teaching model have made learning the piano an extravagant endeavor. Most existing approaches, based on the audio modality, aim to evaluate piano players’ skills. Unfortunately, these methods overlook the information contained in videos, resulting in a one-sided and simplistic evaluation of the piano player’s skills. More recently, multimodal-based methods have been proposed to assess the skill level of piano players by using both video and audio information. However, existing multimodal approaches use shallow networks to extract video and audio features, which limits their ability to extract complex spatio-temporal and time-frequency characteristics from piano performances. Furthermore, the fingering and pitch-rhythm information of the piano performance is embedded within the spatio-temporal and time-frequency features, respectively. Therefore, we propose a ResNet-based audio-visual fusion model that is able to extract both the visual features of the player’s finger movement track and the auditory features, including pitch and rhythm. The joint features are then obtained through the feature fusion technique by capturing the correlation and complementary information between video and audio, enabling a comprehensive and accurate evaluation of the player’s skill level. Moreover, the proposed model can extract complex temporal and frequency features from piano performances. Firstly, ResNet18-3D is used as the backbone network for our visual branch, allowing us to extract feature information from the video data. Then, we utilize ResNet18-2D as the backbone network for the aural branch to extract feature information from the audio data. The extracted video features are then fused with the audio features, generating multimodal features for the final piano skill evaluation. The experimental results on the PISA dataset show that our proposed audio-visual fusion model, with a validation accuracy of 70.80% and an average training time of 74.02 s, outperforms the baseline model in terms of performance and operational efficiency. Furthermore, we explore the impact of different layers of ResNet on the model’s performance. In general, the model achieves optimal performance when the ratio of video features to audio features is balanced. However, the best performance achieved is 68.70% when the ratio differs significantly.

Structural vibration-based identification of delamination in CFRP cylinders using complex frequency domain correlation and CNN

A novel method based on complex frequency domain correlation (CFDC) and convolutional neural network (CNN) is proposed to identify the delamination in CFRP cylinders. Firstly, the CFDC based on the fusion of FRFs at multiple measuring positions of cylinders is constructed to characterize the delamination. Subsequently, the normalized CFDC is used as the input of a CNN model, so as to predict the circumferential angle and axial distance of delamination in cylinders. Moreover, the linear model between the complex frequency domain correlation indicator (CFDCI) and the delamination area is established due to the high linearity between them. Finally, the area of delamination is predicted based on the linear model, whose coefficients are predicted by another CNN model. The proposed method performs well in localization and area evaluation of delamination with high accuracy in the numerical cases. The delamination in each experimental case is identified within certain error even with serious noise in measurement. In addition, the comparison with other common methods indicates higher accuracy of the proposed method in delamination identification for CFRP cylinders.

Efficient 1.5D full waveform inversion in the Laplace-Fourier domain

Accurate near-surface characterization and velocity model building are important for a number of geotechnical and geophysical applications. 3D full waveform inversion (FWI) can be used to generate a detailed velocity model, but must be provided with a good initial velocity model. A method for producing such an initial velocity model is explored in this paper. Assuming that the near-subsurface can be locally approximated by an effective flat-layered medium, a specialized form of acoustic FWI is proposed. The inversion is based on regularized least-squares in the Laplace-Fourier domain as a measure to mitigate the cycle-skipping problem. Forward modeling is carried out by solving a number of independent finite-difference problems in parallel, for a set of horizontal wavenumbers. The set is determined adaptively, using a pair of algorithms discussed in detail. A numerical implementation of the inverse Hankel transform, used to synthesize data in the frequency-offset domain, is also described. The forward modeling scheme is validated against analytic solutions of the Helmholtz equation, showing good agreement between the two. FWI is tested by inverting a synthetic dataset consisting of flat layers with embedded velocity anomalies. Important features are recovered after inversion at a small number of complex frequencies, providing a detailed initial model for successive 3D FWI.

Non-Hermitian control between absorption and transparency in perfect zero-reflection magnonics

Recent works in metamaterials and transformation optics have demonstrated exotic properties in a number of open systems, including perfect absorption/transmission, electromagnetically induced transparency, cloaking or invisibility, etc. Meanwhile, non-Hermitian physics framework has been developed to describe the properties of open systems, however, most works related to this focus on the eigenstate properties with less attention paid to the reflection characteristics in complex frequency plane, despite the usefulness of zero-reflection (ZR) for applications. Here we demonstrate that the indirectly coupled two-magnon system not only exhibits non-Hermitian eigenmode hybridization, but also ZR states in complex frequency plane. The observed perfect-ZR (PZR) state, i.e., ZR with pure real frequency, is manifested as infinitely narrow reflection dips (~67 dB) with infinite group delay discontinuity. This reflection singularity of PZR distinguishes from the resonant eigenstates but can be adjusted on or off resonance with the eigenstates. Accordingly, the absorption and transmission can be flexibly tuned from nearly full absorption (NFA) to nearly full transmission (NFT) regions.

On the stability of viscoelastic tapered rotors with internal flow

In this paper, the stability of viscoelastic tapered rotors with internal flow is investigated. The constitutive equation of the viscoelastic material is described on the basis of the Kelvin–Voigt model. Using Hamilton's principle, the governing equation of motion for the rotor system is formulated. The Galerkin discretization technique is then employed to discrete the partial differential equations. Thus, the complex frequencies in the first two modes of the simply supported rotor system are calculated, which are utilized to discriminate the stability of the system. Then, the stability evolution process of the system is analyzed. Also, the divergence flow velocity and spinning speed are computed numerically. Finally, a comprehensive parametric discussion is carried out to evaluate the effect of parameters such as hollowness ratio, mass ratio, taper ratio, and viscosity coefficient on the stability and critical spinning speed of the fluid–structure interaction system. The results show that for a viscoelastic tapered rotor with the internal flow, the rotor experiences a stability evolution of “stable-first mode divergence-stable-first mode flutter-first mode divergence-first mode flutter.” The dynamic behavior of the rotor system depends strongly on the mass ratio, hollowness ratio, taper ratio, flow velocity, and viscoelasticity of the material.

Extended Discrete-State Event-Driven Hardware-in-the-Loop Simulation for Power Electronic Systems Based on Virtual-Time-Ratio Regulation

This paper proposes an extended discrete-state event-driven (EDSED) controller hardware-in-the-loop (CHIL) method for power electronic systems, employing virtual time ratio (VTR) regulation to achieve CHIL function. Specifically, the proposed VTR in CHIL simulation is introduced to define the time ratio at which the mathematical model of the power circuit runs in the simulator. Additionally, by adjusting different VTRs, the data interaction between the simulator and controller is modified and employed as an event to trigger both simulation and control calculations, ensuring a precise correlation between simulation data and control information. The proposed EDSED CHIL simulation method is validated through CHIL and full hardware experiments involving a power electronic transformer and a multi-port power router. This paper offers an effective CHIL solution for testing control strategies and codes in power electronic systems characterized by complex coupling and high frequency.

A Study on the Readability of American English Textbooks and Korean English Textbooks Comparing Syntactic Complexity and Conjunction Frequency in Sentence Structures

A Study on the Readability of American English Textbooks and Korean English Textbooks Comparing Syntactic Complexity and Conjunction Frequency in Sentence Structures

Attempts for increasing Astyanax altiparanae spawning rates and percentage of responsive oocytes

In this study, we aimed to propose changes in the protocol of cultured Astyanax altiparanae hypophysation to increase the maximum ovulation rate of 60% registered previously. To that two consecutive experiments were conducted. In the first experiment, three carp pituitary homogenate (CPH) doses (3, 6, and 9 mg/kg) were administered in a single injection, while in the second experiment, the 6 mg/kg CPH dose was tested either in single or double injections. In the first experiment, a single injection of 3 mg/kg CPH did not induce final oocyte maturation or spawning, while a dose of 6 mg/kg CPH resulted in an increase in the plasma level of prostaglandin (PGF2α) at ovulation. The single higher dose of 9 mg/kg CPH did not improve reproductive performance and even though anticipated the resumption of meiosis it was detrimental to the spawning rate. In the second experiment, the dose of 6 mg/kg CPH fractionated into two injections led to a higher spawning rate, spawning volume per female body mass, frequency of post-ovulatory complexes, and PGF2α concentration at ovulation compared to the single injection. The most effective treatment remained the 6 mg/kg of CPH fractionated into two injections, but still providing very low proportion of ovulated females (∼40 %). Overall, this study indicates that the spawning protocols for this species need to be improved to induce ovulation in a larger number of females and be more potent in those females that respond positively.

Estimation of limit cycle amplitude after onset threshold of thermoacoustic Stirling engine

This study estimates the amplitude saturation process of spontaneous pressure oscillations in the thermoacoustic Stirling engine, which harnesses a stack-screen regenerator, after the engine onset. To observe spontaneous initiations leading to finite amplitudes of sound in the engine, the engine is studied experimentally to see how the acoustic pressure fluctuates in the time domain. To describe this, the nonlinear effects of the flow resistance of the stacked-screen regenerators, empirically proposed as an effective radius reff whose size decreases with increasing Reynolds number, are incorporated into the framework of Rott’s linear thermoacoustic theory for depicting the evolution of oscillations from initiation to a steady state. The numerical calculations are based on the coupling between pressure oscillations and the imaginary part of a complex angular frequency which is obtained numerically from the characteristic equation derived from the transfer matrices modeling the engine. For the scenarios of steady oscillations, the measured results are elucidated with calculations by consciously adjusting r0 which is involved in reff and estimates the threshold of thermoacoustic instability. By plotting with the adjusted r0, the measured stability limits expressly agree with the stability curve calculated from Rott’s theory. This work improves Rott’s frequency-domain theory to the temporal description of the thermoacoustic Stirling engine, from start-up to limit cycle oscillation.

Identifying Informative Nodes in Attributed Spatial Sensor Networks Using Attention for Symbolic Abstraction in a GNN-based Modeling Approach

Modeling complex data, e.g. time series as well as network-based data, is a prominent area of research. In this paper, we focus on a combination of both, analyzing network-based spatial sensor data which is attributed with high frequency time series information. We apply a symbolic representation and an attention-based local abstraction approach, to enhance interpretability on the respective complex high frequency time series data. For this, we aim at identifying informative measurements captured by the respective nodes of the sensor network. To do so, we demonstrate the efficacy of the Symbolic Fourier Approximation (SFA) and the attention-based symbolic abstraction method to localize relevant node sensor-information, by using a transformer architecture as an encoder for a graph neural network. In our experiments, we compare two seismological datasets to their previous state-of-the-art model, demonstrating the advantages and benefits of our presented approach.

May myocardial work predict the risk of cardiomyopathy in patients with premature ventricular complex?

Background An increased premature ventricular complex (PVC) frequency is related to an increased risk of cardiomyopathy. Changes in myocardial work (MW) parameters in patients with PVC may be a predictor of the development of cardiomyopathy. Methods The study included 56 patients with PVC and 50 healthy volunteers as a control group. A comprehensive echocardiographic examination was done. A speckle tracking echocardiography was used to obtain the left ventricle (LV) global longitudinal strain (GLS). A bull’s eye plot of the global MW index and the global work efficiency of 17 left ventricle segments with MW component values were generated. Results Global work index (GWI), global constructive work (GCW), and global work efficiency (GWE) were significantly lower in the patient group (2377.84 ± 216.52 vs.1818.30 ± 283.73, 2734.00 ± 208.90 vs. 2283.73 ± 321.65, 92.48 ± 2.85 vs. 87.75 ± 3.87, respectively, all p values <0.001). Global wasted work (GWW) was significantly higher in the patient group (216.80 ± 26.86 vs. 302.13 ± 41.81, p < 0.001) Patients were compared according to the origin of PVCs. GWI, GCW, GWE were significantly lower and GWW was significantly higher in patients with PVC originating from the right ventricle or the epicardial region (p < 0.001). Conclusions Compared to healthy individuals, patients with PVC had lower GCW, GWI, GWE values and a higher GWW value than healthy individuals, similar to cardiomyopathy patients. Therefore, the detoriation in MW parameter in patients with PVC may be a predictor of cardiomyopathy development.

Exact conditions for quasi-normal modes of extremal M5-branes and exact WKB analysis

We study the quasi-normal modes (QNMs) of a massless scalar perturbation to the extremal M5-branes metric by using the exact WKB analysis. The exact WKB analysis provides two exact QNMs conditions depending on the argument of the complex frequency of the perturbation. The exact conditions show that the discontinuity of the perturbative part of the QNMs leads the non-perturbative part of themselves. We also find a new example of the Seiberg-Witten/gravity correspondence, which helps us to compute the QNMs from our conditions.

Fault Diagnosis of Rolling Bearings in VMD and GWO-ELM

Strong noise, nonlinearity, and complex frequency are the remarkable symbols of vibration signals when rolling bearing failure. So a new method that improved the accuracy of rolling bearing fault diagnosis is proposed based on variational mode decomposition (VMD) and grey wolf algorithm optimized extreme learning machine (GWO-ELM). The bearing vibration signal is decomposed by VMD, and decomposed Intrinsic Mode Component (IMF) is used for fuzzy entropy calculation to construct a multi-scale complexity eigenvector. The fault pattern recognition is carried out in the extreme learning machine afterward. The parameter selection problem in VMD and fuzzy entropy algorithm is analysed through the experimental fault data of the rolling bearing, and the noise robustness of the experimental data is verified. Through fault data of rolling bearings on site, the comparison of the results shows that the GWO-ELM model can effectively identify the abnormal conditions, and has a faster training and learning speed in diagnosing the faults.

PO-05-137 ECG MORPHOLOGY IS A DETERMINANT OF SURVIVAL IN PULSELESS ELECTRICAL ACTIVITY

Sudden cardiac arrest (SCA) due to pulseless electrical activity (PEA) has a poor prognosis and identification of cases with a higher likelihood of survival could facilitate the resuscitation process. In PEA, QRS frequency and morphology can vary significantly. To investigate if the frequency and morphology of the QRS can predict survival outcomes in PEA. The study population is drawn from two prospective, community-based studies of out-of-hospital SCA in the U.S.: Oregon SUDS from the Portland, OR metro area (Pop. approx. 1 million; since 2002) and Ventura PRESTO from Ventura County CA (Pop. approx. 850,000, since 2015). In the present study, we included SCA cases resuscitated by EMS that had EMS recording of the ECG available, and PEA was the presenting rhythm. We analyzed QRS frequency, regularity, and width of the presenting PEA rhythm in a subset of 347 PEA-SCA cases (34 survivors and 313 non-survivors). The mean age of the subjects was 70.3±15.5 years and 60.2% were male. The prevalence of QRS frequency >60 bpm was 23.1% and QRS width <120 ms was 32.6%. Females were more likely to have a narrow QRS complex than males (39.9% vs. 27.8%; p=0.02) but there was no sex difference in the QRS frequency. Those with QRS frequency >60 bpm had a higher survival rate than those with QRS frequency <60 bpm (17.5% vs. 7.5%: p=0.02). In addition, cases with QRS width <120 ms had a higher survival rate in comparison to cases with QRS width >120 ms (17.7% vs. 6.0%; p=0.001). Cases with both narrow QRS complex (<120 ms) and fast frequency (>60 bpm) had the highest survival rate (10/38, 26.3%). There was no difference in the survival rate between regular and irregular rhythms. PEAs with electrical activity >60 bpm and narrow QRS complex were associated with higher survival. These results suggest that resuscitation efforts are most likely to be beneficial in PEA-SCA cases that present with a narrow and fast QRS pattern.

A spectral force representation and its physical implication for vortex shedding past a stationary or an oscillating circular cylinder at low Reynolds number

Vortex shedding is an ubiquitous phenomenon behind a bluff body (such as circular cylinder) and becomes more complicated when the body is also in oscillation. It is apparent that periodic behavior must be accompanied by the time-varying force, such as lift and drag (coefficients) with known distinguished cases (say, at Re=200) of low-frequency modulation (LFM), sub-harmonic synchronization (SHS), and normal harmonic synchronization (NHS). In a classical analysis, the force spectrum is often analyzed by the Fourier transform or some more recent methods, and typically, a quite complex frequency spectrum is obtained owing to the inherent nonlinearity in the flow system. In the present study, we extend the principal frequency analysis [Lu et al., “An EMD-based principal frequency analysis with applications to nonlinear mechanics,” Mech. Syst. Signal Process. 150, 107300 (2021)] to the principal spectrum analysis (PSA) with both its amplitude and phase in a composite functional form and provide a spectral representation (SR) of the force coefficients only in terms of the characteristic frequencies. In particular, we consider the unsteady laminar flow past a stationary circular cylinder or an oscillating circular cylinder (with frequency f0), while the resulting vortex shedding frequency is denoted by fVS. The spectral representation via the proposed PSA can reveal nonlinear interactions of the two characteristic frequencies (f0 and fVS) in influencing the force coefficients and distinguish direct and interactive modes in which f0 and fVS interact with each other. As a matter of fact, the successively shed vortices are not identical in the strength (amplitude) nor in the phase function. The spectral representation further enables us to identify complicated vorticity activity near around the bluff body: the periodicity of the strength of the shed vortices and the phase shift in the successive vortex shedding—all at the integer multiples of the greatest common-divisor (gcd) of the (two) characteristic frequencies. The gcd frequency of ⟨f0, fVS⟩ is identified as the genuine (slow, long-term) frequency of the entire vortex shedding process in contrast to the (fast, short-term) vortex shedding frequency. It turns out in this scheme of classification by the PSA-SR that all the distinguished types of the above-mentioned LFM, SHS, and NHS can be considered to be gcd-frequency synchronization.

Applications of Fourier series and Fourier Transform in Electrical and Electronics Devices

Abstract: Fourier series are of great importance in both theoretical and ap­ plied mathematics. For orthonormal families of complex­valued functions Fourier Series are sums of the φn that can approximate periodic, complex­valued functions with arbitrary precision. This paper will focus on the Fourier Series of the complex exponentials. Of the many possi­ ble methods of estimating complex­valued functions, Fourier series are especially attractive because uniform convergence of the Fourier series (as more terms are added) is guaranteed for continuous, bounded functions. Furthermore, the Fourier coefficients are designed to minimize the square of the error from the actual function. Finally, complex exponentials are relatively simple to deal with and ubiquitous in physical phenomena. This paper first defines generalized Fourier series, with an emphasis on the se­ ries with complex exponentials. Then, important properties of Fourier series are described and proved, and their relevance is explained. A com­plete example is then given, and the paper concludes by briefly mentioning some of the applications of Fourier series and the generalization of Fourier series, Fourier transforms. In the mid­eighteenth century, physical problems such as the conduction pat­ terns of heat and the study of vibrations and oscillations led to the study of Fourier series. Of central interest was the problem of how arbitrary real­valued functions could be represented by sums of simpler functions. As we shall see later, a Fourier series is an infinite sum of trigonometric functions that can be used to model real­valued, periodic functions. We shall begin by giving a brief description of the trigonometric polynomials,and especially of their relation to the complex exponentials. The Fourier series, the founding principle behind the field of Fourier analysis, is an infinite expansion of function in terms sine’s and cosines. Fourier transform provides a continuous complex frequency of a function. It is useful in the study of frequency response of a filter, solution PDE, Discrete Fourier transform and FFT in the signals analysis. The advent of Fourier transformation method has greatly extended our ability to implement Fourier methods on digital multimedia visualization system. It covers the mathematical foundations of Digital signal processing (DSP), classical sound, synthesis algorithms and multi-time frequency domain analysis associated musical sound. In this paper, we are analysis of square wave in terms of Fourier component, may occur in electric circuits designed to handle sharply rising pulses and how to convert analog to digital system by using Fourier transform and its applications in electronics and digital multimedia visualization signal process of communication system.

Following the Higgs mode across the BCS-BEC crossover in two dimensions

Although substantial effort has been dedicated to analyzing the Higgs (amplitude) mode in superconducting systems, there are relatively few studies of the Higgs peak's dispersion and width, quantities which are observable in spectroscopic measurements. These properties can be obtained from the location of the pole of the amplitude (Higgs) susceptibility in the lower half plane of complex frequency. We analyze the behavior of the Higgs mode in a two-dimensional neutral fermionic superfluid at $T=0$ throughout the crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) behavior. This occurs when the dressed chemical potential $\ensuremath{\mu}$ changes sign from positive to negative. For $\ensuremath{\mu}&gt;0$, we find a pole in the Higgs susceptibility in the lower half plane of frequency and demonstrate that it leads to a well-defined peak in spectroscopic probes. For $\ensuremath{\mu}&lt;0$, the pole still exists but is ``hidden,'' not giving rise to a peak in spectroscopic probes. Extending this analysis to a charged superconductor, we find that the Higgs mode is unaffected by the long-range Coulomb interaction.

Plasmonic volcano-like fiber-optic probe for Raman enhancement.

Light-matter interaction is a fascinating topic extensively studied from classical theory, based on Maxwell's equations, to quantum optics. In this study, we introduce a novel, to the best of our knowledge, silver volcano-like fiber-optic probe (sensor 1) for surface-enhanced Raman scattering (SERS). We employ the emerging quasi-normal mode (QNM) method to rigorously calculate the Purcell factor for lossy open system responses, characterized by complex frequencies. This calculation quantifies the modification of the radiation rate from the excited state e to ground state g. Furthermore, we use and extend a quantum mechanical description of the Raman process, based on the Lindblad master equation, to calculate the SERS spectrum for the plasmonic structure. A common and well-established SERS probe, modified by a monolayer silver nanoparticle array, serves as a reference sensor (sensor 2) for quantitatively predicting the SERS performance of sensor 1 using quantum formalism. The predictions show excellent consistency with experimental results. In addition, we employ the FDTD (finite-difference time-domain) solver for a rough estimate of the all-fiber Raman response of both sensors, revealing a reasonable range of SERS performance differences compared to experimental results. This research suggests potential applications in real-time, remote detection of biological species and in vivo diagnostics. Simultaneously, the developed FDTD and quantum optics models pave the way for analyzing the response of emitters near arbitrarily shaped plasmonic structures.

Chiral spectral singularities spawning from quasi-bound states in the continuum in PT-symmetric dielectric metasurfaces

We investigate the chiral spectral singularities, i.e., laser threshold modes, in PT-symmetric dielectric metasurfaces originating from quasi-bound states in the continuum. The poles, referred to as the quasi-bound states in the continuum, of scattering matrix can move to the upper complex frequency plane from the lower half-plane by increasing the balanced gain and loss. The maximal intrinsic optical chirality of laser threshold mode has been theoretically demonstrated via the large transmission circular dichroism spectra. Our work paves the way for studying the enhanced optical chirality in non-Hermitian nanophotonics empowered by quasi-bound states in the continuum, together with various intriguing applications, such as chiral coherent perfect absorber and laser.