Complex Frequency Research Articles

Vibration Characteristics of a Functionally Graded Viscoelastic Fluid-Conveying Pipe with Initial Geometric Defects under Thermal–Magnetic Coupling Fields

In this study, the Kevin–Voigt viscoelastic constitutive relationship is used to investigate the vibration characteristics and stability of a functionally graded viscoelastic(FGV) fluid-conveying pipe with initial geometric defects under thermal–magnetic coupling fields. First, the nonlinear dimensionless differential equations of motion are derived by applying Timoshenko beam theory. Second, by solving the equilibrium position of the system, the nonlinear term in the differential equations of motion is approximated as the sum of the longitudinal displacement at the current time and longitudinal displacement relative to the position, and the equations are linearized. Third, these equations are discretized using the Galerkin method and are numerically solved under simply supported conditions. Finally, the effects of dimensionless temperature field parameters, dimensionless magnetic field parameters, thermal–magnetic coupling, initial geometric defect types, and the power-law exponent on the complex frequency of the pipe are examined. Results show that increasing the magnetic field intensity enhances the critical velocity of first-order mode instability, whereas a heightened temperature variation reduces the critical velocity of first-order diverge instability. Under thermal–magnetic fields, when the magnetic field intensity and temperature difference are simultaneously increased, their effects on the complex frequency can partially offset each other. Increasing the initial geometric defect amplitude increases the imaginary parts of the complex frequencies; however, for different types of initial geometric defect tubes, it exhibits the most distinct influence only on a certain order.

Vibration control on coupled unit-plant structure of pumped storage power station during sudden load-up process

The versatile regulatory capacity of pumped storage power station (PSPS) stems from the reversible pumped turbine unit switching between multiple operating conditions. Nevertheless, the unit and plant structure experience heightened vibrations owing to the intricate interplay of hydraulic, electrical, and mechanical excitations during transition processes, and the vibration responses fluctuate as operating conditions shift, posing a significant challenge to the safety and high quality operation of power station. To tackle the practical engineering issue, this paper delves into the sudden load-up scenario in power generation situation of pumped turbine, leveraging a finite element model encompassing the coupled hydraulic-mechanical-electrical-structural system (HMES) of PSPS and a mathematical model of unit shaft system, the impacts of dynamic loads induced by various vibration source on the unit and plant structure during transient condition, are meticulously analyzed and discussed through numerical simulations. Additionally, the magnetorheological damper (MRD), is incorporated into the PSPS to explore the effectiveness of MRD in controlling transient vibration in the interconnected unit-plant structure. The results indicate that the system parameters and associated load excitations undergo rapid fluctuations during the load-up process, bringing about noticeable oscillations in vibration amplitudes of rotor and turbine. The floors and fan hood of plant are the most vulnerable areas in terms of structural strength, with associated displacement amplitudes being most noticeable. The incorporation of MRD proves to be highly effective in mitigating the unsteady vibrations in both the unit and the plant structure during load-up course, as well as optimizing the motion patterns of rotor and turbine, promoting a notable reduction in frequency amplitudes of spectrum. Moreover, the maximal transient displacement amplitude of unit is significantly diminished, with the rotor experiencing a decrease of approximately 79%, while the amplitude of turbine declines by 16%. The displacement fluctuation ranges of the plant structure are observably diminished, and the complex frequency components of vibration signal are efficiently controlled. The transient vibration characteristics of the coupled unit-plant structure and the damping behavior of MRD during the transition process are unveiled by the research findings in this paper, which can offer valuable insights for the stability assessment and the research on vibration management of HMES for PSPS under the unsteady operation conditions.

Predicting the linear response of self-gravitating stellar spheres and discs with LinearResponse.jl

ABSTRACT We present LinearResponse.jl, an efficient, versatile public library written in julia to compute the linear response of self-gravitating (three-dimensional spherically symmetric) stellar spheres and (two-dimensional axisymmetric razor-thin) discs. LinearResponse.jl can scan the whole complex frequency plane, probing unstable, neutral and (weakly) damped modes. Given a potential model and a distribution function, this numerical toolbox estimates the modal frequencies as well as the shapes of individual modes. The libraries are validated against a combination of previous results for the spherical isochrone model and Mestel discs, and new simulations for the spherical Plummer model. Beyond linear response theory, the realm of applications of LinearResponse.jl also extends to the kinetic theory of self-gravitating systems through a modular interface.

Two-dimensional control of a biphoton joint spectrum.

Control over the joint spectral amplitude of a photon pair has proved highly desirable for many quantum applications, since it contains the spectral quantum correlations, and has crucial effects on the indistinguishability of photons, as well as promising emerging applications involving complex quantum functions and frequency encoding of qudits. Until today, this has been achieved by engineering a single degree of freedom, either by custom poling nonlinear crystal or by shaping the pump pulse. We present a combined approach where two degrees of freedom, the phase-matching function, and the pump spectrum, are controlled. This approach enables the two-dimensional control of the joint spectral amplitude, generating a variety of spectrally encoded quantum states - including frequency uncorrelated states, frequency-bin Bell states, and biphoton qudit states. In addition, the joint spectral amplitude is controlled by photon bunching and anti-bunching, reflecting the symmetry of the phase-matching function.

Modal propagation analysis with participation factors of complex frequency variables

This paper proposes the use of participation factors of complex frequency variables to study the propagation of oscillations in power systems. The method combines the recently proposed concept of complex frequency with modal participation analysis to derive a novel metric that locates the sources of oscillations in the system and tracks their spatial propagation. The proposed approach allows isolating the variables more sensitive to oscillations, bus voltage or frequency, thus facilitating the selection of corrective actions. The validity of the theoretical results and the scalability of the method are supported with extensive simulations performed for test networks of various sizes and with both conventional and inverter-based generation.

IR and Raman markers of the interactions between MoS2 and pyrimidine bases

Changes in vibrational spectra are among the most important manifestations of the interaction between transition metal dichalcogenides and nucleic acid bases (NAB). Infrared and Raman spectra were calculated using the DFT/M06-2X method for the most stable stacked and covalently bonded complexes of pyrimidine bases with MoS2. Obtained spectra were analyzed to determine the spectral markers of the interactions between the pyrimidine bases and MoS2. We found that interaction with MoS2 leads to significant changes in both frequencies and intensities of NAB vibrations. The correlation between the changes and interaction energies of the NAB molecules with MoS2 was demonstrated. In general, changes in the vibrational frequencies in complexes with covalent bonds are significantly greater than ones in stacked ones. For the bonded complexes, the most significant changes are observed for those fragments of the NAB molecules that are directly involved in the formation of the covalent bonds. Calculations predict the decrease of the IR intensity and Raman activities of the NAB molecules in the spectra of stacked complexes and their increase in the spectra of covalently bonded complexes.

A comparative analysis of damping models for the vibratory properties of a bent beam

Much of Eric Unger's career was devoted to the study of dissipation mechanisms. This paper will explore the effect of various ways that damping effects have been incorporated in the solution of equations of motion. The analytical model of an L-shaped beam, cantilvered at one end and loaded at its free end by a force that is transverse to the plane of the bent beam, is the basis for the study. Equations of motion that account for coupling of flexure and torsion are created by merging the Ritz series method and the method of Lagrange multipliers. Energy is dissipated by a dashpot transversely mounted at the corner. An “exact” solution of the equations of motion using state-space modal analysis provides the reference for approximate methods including proportional damping, modal decoupling, and structural damping. Impulse response and complex frequency response at various levels of damping will be addressed.

Characterization and analysis of attenuation anisotropy in viscoelastic vertical transverse isotropic media

AbstractDue to the intrinsic attenuation of the earth, the study of wave propagation characteristics, considering seismic attenuation plays an important role in high‐precision reservoir prediction. Therefore, we investigate the propagation and reflection characteristics of seismic waves in viscoelastic vertical transverse isotropic media in the complex frequency domain. Specifically, we analyse the response characteristics of velocity, propagation vector and attenuation vector with respect to viscosity media with different attenuation intensities. Furthermore, based on the quasi‐Zoeppritz equation, the variation of reflection coefficient amplitude with offset at different attenuation angles and different attenuation intensities is studied. We also compare the trends in the amplitude variation of reflection coefficients with offset in elastic isotropic, elastic anisotropic and viscoelastic anisotropic media. Due to the complexity of the exact reflection coefficient expression, we first propose the approximate expression of the attenuation–anisotropy parameters and then derive the approximate expression of the reflection coefficient. The numerical simulation results show that the approximate expression of the reflection coefficient is still accurate, even in media with strong anisotropy. Finally, the accuracy evaluations of the reflection coefficient formulas using four typical theory models demonstrate that the approximate reflection coefficient formulas are highly accurate in both weak and strong anisotropic media.

Waveform shaping in photonic time-crystals

This paper reports on the waveform shaped by a finite duration photonic time-crystal with its permittivity and permeability periodically varying in time. A Gaussian-modulated sinusoidal pulse is incident onto this photonic time-crystal to evaluate the backward- and forward-scattering waveforms. An analytical formulation, utilizing a cascade of temporal transfer matrices and the inverse fast Fourier transform, was employed to conduct time-domain waveform computations. Interestingly, the dispersion diagram of the temporal unit cell, which displays a momentum gap characterized by a complex effective angular frequency, plays a crucial role in shaping the incident waveform. Specifically, the presence of momentum gaps in the spectrum of the incident pulse determines the frequencies of the generated oscillation modes.

THE USE OF TWO FREQUENCY VARIABLES IN THE DISTRIBUTED CIRCUITS SYNTHESIS.

One of the approaches to the design of filters from segments of non-uniform lines is the use of NLs connected by a quadrupole between the generator and the load. In this case, the required characteristic of selectivity is achieved by changing the wave resistance of the line according to a certain law. However, the input op of the NL loaded with an active resistance cannot be purely reactive at real frequencies, so the reflection coefficient cannot be equal to unity at any of them. Therefore, it is fundamentally impossible to obtain a significant attenuation at least at one point outside the passband of the filter. Only by choosing a certain class of complex loads can significant attenuation be achieved outside the passband. Another principle of filter construction is based on the use of the simplest heterogeneous lines that perform the functions of resonators. The necessary selective characteristic of the filter is achieved by selecting the parameters of resonators and communication circuits. This method of building filters is more rational. In addition, in the process of synthesis, you can use ideas and techniques characteristic of circles from segments of uniform lines. It is shown that in the synthesis of distributed circuits based on transmission lines, complex functions of two frequency variables should be used, which allows the construction arbitrary circuit functions and fully cover the classes of physically realized transfer functions. A description of the elements "inductance" and "capacitance" in the class of functions of two complex frequency variables was obtained, which allows synthesizing circuits using the ideas and methods of Richards’s circuit theory.

Control/physical systems co-design with spectral temporal logic specifications and its applications to MEMS

‘Co-design’ problems try to simultaneously design the physical and control components to improve the overall system performance. However, existing co-design paradigms cannot deal with complex frequency temporal domain specifications. In this paper, we investigate the co-design problem for a class of linear parameter-varying (LPV) systems with frequency temporal domain specifications. Firstly, the frequency temporal domain specifications are written in a formal language called spectral temporal logic (STL). Secondly, the satisfaction conditions of the spectral temporal logic specifications have been transformed into non-linear matrices inequality forms with necessary and sufficient conditions. Thirdly, the co-design problem is transformed into a non-convex optimisation problem with mixed-integer linear matrix inequalities (MILMIs) constraints, and then an iterative algorithm is proposed to solve the co-design problem with semidefinite programming (SDP). Finally, the performance of the algorithm and the expressiveness of spectral temporal logic are illustrated with the applications to micro-electromechanical systems (MEMS).

Theoretical and experimental investigation on the sound absorption performance of ultra-thin curled acoustic metasurface

A simplified model of the absorption coefficient of traditional Helmholtz resonators (THR) was established, and the influence of different geometric parameters on the absorption coefficient of THR was analyzed. To realize the low-frequency broadband acoustic structure design, an accurate theoretical model for the sound absorption coefficient of the curled acoustic metasurface (CAM) unit was established. Based on the complex frequency plane method (CFPM), the CAM units with perfect sound absorption at four discrete frequencies were designed. The low-frequency broadband acoustic metasurfaces in parallel under decoupled and coupled conditions were studied, and the thickness is only 12 mm. The high efficiency of sound absorption above 0.8 was achieved in the frequency range of 758 Hz–940 Hz. The experiment verifies the efficient sound absorption effect of the CAM unit and the broadband sound absorption effect under coupled conditions. The research in this paper has a certain potential applications for low-frequency broadband noise control technology.

Boundary correlators and the Schwarzian mode

The effective low temperature dynamics of near-extremal black holes is governed by the quantum fluctuations of the Schwarzian mode of JT gravity. Utilizing as a proxy a planar charged black hole in asymptotically Anti-de-Sitter spacetime, we investigate the effects of these fluctuations on a probe scalar field. The corresponding holographic real-time boundary correlators are computed following a holographic renormalization procedure, using the dubbed gravitational Schwinger-Keldysh geometry (grSK) and known exact results of boundary correlators from the near-horizon region. This analysis gives rise to a retarded Green’s function that decays as a power law for late Lorentzian times. Its analytic structure indicates the presence of a branch cut in the complex frequency domain at finite temperature. These features are a non-perturbative hallmark that prevails as long as the planar transverse space is kept compact.

Non-generic bound states in the continuum in waveguides with lateral leakage channels.

For optical waveguides with a layered background which itself is a slab waveguide, a guided mode is a bound state in the continuum (BIC), if it coexists with slab modes propagating outwards in the lateral direction; i.e., there are lateral leakage channels. It is known that generic BICs in optical waveguides with lateral leakage channels are robust in the sense that they still exist if the waveguide is perturbed arbitrarily. However, the theory is not applicable to non-generic BICs which can be defined precisely. Near a BIC, the waveguide supports resonant and leaky modes with a complex frequency and a complex propagation constant, respectively. In this paper, we develop a perturbation theory to show that the resonant and leaky modes near a non-generic BIC have an ultra-high Q factor and ultra-low leakage loss, respectively. Recently, many authors studied merging-BICs in periodic structures through tuning structural parameters. It has been shown that resonant modes near a merging-BIC have an ultra-high Q factor. However, the existing studies on merging-BICs are concerned with specific examples and specific parameters. Moreover, we analyze an arbitrary structural perturbation given by δF(r) to waveguides supporting a non-generic BIC, where F(r) is the perturbation profile and δ is the amplitude, and show that the perturbed waveguide has two BICs for δ > 0 (or δ < 0) and no BIC for δ < 0 (or δ > 0). This implies that a non-generic BIC can be regarded as a merging-BIC (for almost any perturbation profile F) when δ is considered as a parameter. Our study indicates that non-generic BICs have interesting special properties that are useful in applications.

Hybrid CPU-GPU solution to regularized divergence-free curl-curl equations for electromagnetic inversion problems

The Curl-Curl equation is the foundation of time-harmonic electromagnetic (EM) problems in geophysics. The efficiency of its solution is key to EM simulations, accounting for over 95% of the computation cost in geophysical inversions for magnetotelluric or controlled-source EM problems. However, most published EM inversion codes are still central processing unit (CPU)-based and cannot utilize recent computational developments on the graphic processing units (GPUs). Based on a previously proposed divergence-free algorithm developed on CPUs, this study demonstrates the current limits of the CPU-based inversion procedure. To exploit the high throughput capability of GPUs, we propose a hybrid CPU-GPU framework to solve forward and adjoint problems required for EM inversions. The large sparse linear systems arising from the staggered-grid finite difference approximation of the Curl-Curl equation are solved with a mixed-precision Krylov subspace solver implemented on a GPU. The algorithm is then tested in EM forward and adjoint calculations, with real-world three-dimensional numerical examples. Test results show promising 30× kernel-level speed-ups over the conventional CPU algorithm. This approach may further take the complex frequency domain EM inversions onto the next, practical stage on small affordable GPU platforms.

Faster Gastrointestinal Transit, Reduced Small Intestinal Smooth Muscle Tone and Dysmotility in the Nlgn3R451C Mouse Model of Autism.

Individuals with autism often experience gastrointestinal issues but the cause is unknown. Many gene mutations that modify neuronal synapse function are associated with autism and therefore may impact the enteric nervous system that regulates gastrointestinal function. A missense mutation in the Nlgn3 gene encoding the cell adhesion protein Neuroligin-3 was identified in two brothers with autism who both experienced severe gastrointestinal dysfunction. Mice expressing this mutation (Nlgn3R451C mice) are a well-studied preclinical model of autism and show autism-relevant characteristics, including impaired social interaction and communication, as well as repetitive behaviour. We previously showed colonic dysmotility in response to GABAergic inhibition and increased myenteric neuronal numbers in the small intestine in Nlgn3R451C mice bred on a mixed genetic background. Here, we show that gut dysfunction is a persistent phenotype of the Nlgn3 R451C mutation in mice backcrossed onto a C57BL/6 background. We report that Nlgn3R451C mice show a 30.9% faster gastrointestinal transit (p = 0.0004) in vivo and have 6% longer small intestines (p = 0.04) compared to wild-types due to a reduction in smooth muscle tone. In Nlgn3R451C mice, we observed a decrease in resting jejunal diameter (proximal jejunum: 10.6% decrease, p = 0.02; mid: 9.8%, p = 0.04; distal: 11.5%, p = 0.009) and neurally regulated dysmotility as well as shorter durations of contractile complexes (mid: 25.6% reduction in duration, p = 0.009; distal: 30.5%, p = 0.004) in the ileum. In Nlgn3R451C mouse colons, short contractions were inhibited to a greater extent (57.2% by the GABAA antagonist, gabazine, compared to 40.6% in wild-type mice (p = 0.007). The inhibition of nitric oxide synthesis decreased the frequency of contractile complexes in the jejunum (WT p = 0.0006, Nlgn3R451C p = 0.002), but not the ileum, in both wild-type and Nlgn3R451C mice. These findings demonstrate that changes in enteric nervous system function contribute to gastrointestinal dysmotility in mice expressing the autism-associated R451C missense mutation in the Neuroligin-3 protein.

Compensating losses in polariton propagation with synthesized complex frequency excitation.

Surface plasmon polaritons and phonon polaritons offer a means of surpassing the diffraction limit of conventional optics and facilitate efficient energy storage, local field enhancement and highsensitivity sensing, benefiting from their subwavelength confinement of light. Unfortunately, losses severely limit the propagation decay length, thus restricting the practical use of polaritons. While optimizing the fabrication technique can help circumvent the scattering loss of imperfect structures, the intrinsic absorption channel leading to heat production cannot be eliminated. Here, we utilize synthetic optical excitation of complex frequency with virtual gain, synthesized by combining the measurements made at multiple real frequencies, to compensate losses in the propagations of phonon polaritons with dramatically enhanced propagation distance. The concept of synthetic complex frequency excitation represents a viable solution to the loss problem for various applications including photonic circuits, waveguiding and plasmonic/phononic structured illumination microscopy.

Utility of electrocardiogram to predict the occurrence of the no-reflow phenomenon in patients undergoing primary percutaneous coronary intervention (PPCI): a systematic review and meta-analysis.

The no-reflow phenomenon affects about one out of five patients undergoing Primary Percutaneous Coronary Intervention (PPCI). As the prolonged no-reflow phenomenon is linked with unfavorable outcomes, making early recognition is crucial for effective management and improved clinical outcomes in these patients. Our review study aimed to determine whether electrocardiogram (ECG) findings before PCI could serve as predictors for the occurrence of the no-reflow phenomenon. We systematically searched MEDLINE, Scopus, and Embase to identify relevant studies. The random-effect model using inverse variance and Mantel-Haenszel methods were used to pool the standardized mean differences (SMD) and odds ratios (OR), respectively. Sixteen eligible articles (1,473 cases and 4,264 controls) were included in this study. Based on our meta-analysis of baseline ECG findings, the no-reflow group compared to the control group significantly had a higher frequency of fragmented QRS complexes (fQRS) (OR (95% CI): 1.35 (0.32-2.38), P-value = 0.01), and Q-waves (OR (95% CI): 1.97 (1.01-2.94), P-value <0.001). Also, a longer QRS duration (QRSD) (SMD (95% CI): 0.72 (0.21, 1.23), p-value <0.001) and R wave peak time (RWPT) (SMD (95% CI): 1.36 (0.8, 1.93), P < 0.001) were seen in the no-reflow group. The two groups had no significant difference regarding P wave peak time (PWPT), and P wave maximum duration (Pmax) on baseline ECG. Our findings suggest that prolonged QRSD, delayed RWPT, higher fQRS prevalence, and the presence of a Q wave on baseline ECG may predict the occurrence of the no-reflow phenomenon in patients undergoing PPCI.

Taxonomy of Power Converter Control Schemes Based on the Complex Frequency Concept

This paper proposes a taxonomy of power converter control schemes based on the recently proposed concept of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">complex frequency</i> . This quantity captures local frequency variations due to the change of both the phase angle and amplitude of bus voltages and current injections. The paper derives the analytical expressions of the link between complex power variations and complex frequency of each converter controller as well as the identification of critical control parameters. The main contribution of this work is to provide a general framework that allows classifying converters synchronization mechanisms and controllers. This framework also allows comparing converters with synchronous machines. To validate the theoretical results, extensive simulations are performed using a modified version of the WSCC 9-bus system. Examples of how the theoretical formulations of the paper can be used to improve power converter control in power system applications are showcased.

Patterns of ganglion cell complex defects and association with functional status in glaucoma patients and suspects

Aims/Purpose: To evaluate the frequency and patterns of ganglion cell complex (GCC) defects by spectral‐domain, high‐resolution optical coherence tomography (OCT) in POAG patients and suspects. Secondary endpoint was to analyse and compare the peripapillary retinal nerve fibre layer (RNFL) and GCC thickness as well as the visual field parameters among each GCC defect pattern.Methods: This was a cross‐sectional study and included 220 patients with POAG and suspects. The OCT printouts were analysed by two examiners who carefully searched for GCC defects and in common agreement stratified them into 10 different patterns. GCC thickness, retinal nerve fibre layer (RNFL) thickness were determined for every participant from the exams; mean deviation (MD) and pattern standard deviation (PSD) values were retrieved from automated perimetry exams for every patient. The structural and functional variables were compared among the groups.Results: The sample comprised 91 eyes of 47 patients. The most frequent GCC defect pattern was the minimal (39.1%). It affected more women than man at a rate of 1.4 and was associated with early disease (p &lt; 0.001). The least frequent were inferior and superior confined (2.2% and 1.1% respectively); both were associated with moderate disease (MD = 10.0 dB, p &lt; 0.001). The temporal raphe sign was observed in 5.5% of eyes and was associated with early disease (MD = −5.0 db).Conclusions: In this cohort of Brazilians patients with POAG and suspects, the minimal pattern was the most prevalent GCC defect and was noticed in eyes with early disease. Clinicians should pay special attention to this defect when evaluation eyes with suspicious looking optic disc and POAG patients with early disease.