Mode Amplitudes Research Articles

Spontaneous symmetry breaking in plasmon lattice lasers.

Spontaneous symmetry breaking (SSB) is key for our understanding of phase transitions and the spontaneous emergence of order. In this work, we report that, for a two-dimensional (2D) periodic metasurface with gain, SSB occurs in the lasing transition. We study diffractive hexagonal plasmon nanoparticle lattices, where the K-points in momentum space provide two modes that are degenerate in frequency and identically distributed in space. Using femtosecond pulses to energize the gain medium, we simultaneously capture single-shot real-space and Fourier-space images of laser emission. By combining Fourier and real space, we resolve the two order parameters for which symmetry breaking simultaneously occurs: spatial parity and U(1) (rotational) symmetry breaking, evident respectively as random relative mode amplitude and phase. The methodology reported in this work is generally applicable to 2D plasmonic and dielectric metasurfaces and opens numerous opportunities for the study of SSB and the emergence of spatial coherence in metaphotonics.

Phase and Amplitude Modes in the Anisotropic Dicke Model with Matter Interactions.

Phase and amplitude modes, also called polariton modes, are emergent phenomena that manifest across diverse physical systems, from condensed matter and particle physics to quantum optics. We study their behavior in an anisotropic Dicke model that includes collective matter interactions. We study the low-lying spectrum in the thermodynamic limit via the Holstein-Primakoff transformation and contrast the results with the semi-classical energy surface obtained via coherent states. We also explore the geometric phase for both boson and spin contours in the parameter space as a function of the phases in the system. We unveil novel phenomena due to the unique critical features provided by the interplay between the anisotropy and matter interactions. We expect our results to serve the observation of phase and amplitude modes in current quantum information platforms.

Impact of MoS2 Monolayers on the Thermoelastic Response of Silicon Heterostructures.

Understanding the thermoelastic response of a nanostructure is crucial for the choice of materials and interfaces in electronic devices with improved and tailored transport properties at the nanoscale. Here, we show how the deposition of a MoS2 monolayer can strongly modify the nanoscale thermoelastic dynamics of silicon substrates close to their interface. We demonstrate this by creating a transient grating with extreme ultraviolet light, using ultrashort free-electron laser pulses, whose ≈84 nm period is comparable to the size of elements typically used in nanodevices, such as electric contacts and nanowires. The thermoelastic response, featuring coherent acoustic waves and incoherent relaxation, is tangibly modified by the presence of monolayer MoS2. Namely, we observed a major reduction of the amplitude of the surface mode, which is almost suppressed, while the longitudinal mode is basically unperturbed, aside from a faster decay of the acoustic modulations. We interpret this behavior as a selective modification of the surface elasticity, and we discuss the conditions to observe such effect, which may be of immediate relevance for the design of Si-based nanoscale devices.

Low latency optical-based mode tracking with machine learning deployed on FPGAs on a tokamak.

Active feedback control in magnetic confinement fusion devices is desirable to mitigate plasma instabilities and enable robust operation. Optical high-speed cameras provide a powerful, non-invasive diagnostic and can be suitable for these applications. In this study, we process high-speed camera data, at rates exceeding 100 kfps, on in situ field-programmable gate array (FPGA) hardware to track magnetohydrodynamic (MHD) mode evolution and generate control signals in real time. Our system utilizes a convolutional neural network (CNN) model, which predicts the n = 1 MHD mode amplitude and phase using camera images with better accuracy than other tested non-deep-learning-based methods. By implementing this model directly within the standard FPGA readout hardware of the high-speed camera diagnostic, our mode tracking system achieves a total trigger-to-output latency of 17.6 μs and a throughput of up to 120 kfps. This study at the High Beta Tokamak-Extended Pulse (HBT-EP) experiment demonstrates an FPGA-based high-speed camera data acquisition and processing system, enabling application in real-time machine-learning-based tokamak diagnostic and control as well as potential applications in other scientific domains.

Early internal detection of magnetic tearing and implications for tokamak magnetohydrodynamic stability

Internal fluctuation measurements with Faraday-effect polarimetry in the DIII-D tokamak reveal the onset of a tearing mode with toroidal mode number n = 3 well before it is detected by the sensing coils external to the plasma. This mode appears before the n = 2, 1 modes and is first detected with internal measurements at a lower value of the ideal-wall kink beta limit than is indicated at the time of first detection by the sensing coils. When the mode is first detected, the linear resistive stability parameter, Δ′, indicates marginal stability and continues to do so until later when the mode amplitude begins increasing linearly with time—together suggesting a neoclassical origin for this mode.

A simple method improving acoustic mode identification capability based on genetic algorithms

This letter develops a simple approach of duct mode identification and reconstruction based on genetic algorithms, which can extend the azimuthal mode order range compared to the conventional method based on the (spatial) discrete Fourier transform. The underlying principle is reconstructing the dominant mode from the modal identification forward model through optimization by exploiting the sparsity of the mode amplitude vector. The performance is experimentally demonstrated for detections of one and two azimuthal modes under noisy conditions with nondominant modes. Overall, the proposed genetic-algorithm-based framework for solving acoustic inverse problems is beneficial to duct acoustic testing, particularly design evaluations of fan blades and acoustic liners for aeroengines.

Non-linear three-mode coupling of gravity modes in rotating slowly pulsating B stars

Context. Slowly pulsating B (SPB) stars display multi-periodic variability in the gravito-inertial mode regime with indications of non-linear resonances between modes. Several have undergone asteroseismic modeling in the past few years to infer their internal properties, but only in a linear setting. These stars rotate fast, so that rotation is typically included in the modeling by means of the traditional approximation of rotation (TAR). Aims. We aim to extend the set of tools available for asteroseismology, by describing time-independent (stationary) resonant non-linear coupling among three gravito-inertial modes within the TAR. Such coupling offers the opportunity to use mode amplitude ratios in the asteroseismic modeling process, instead of only relying on frequencies of linear eigenmodes, as has been done so far. Methods. Following observational detections, we derive expressions for the resonant stationary non-linear coupling between three gravito-inertial modes in rotating stars. We assess selection rules and stability domains for stationary solutions. We also predict non-linear frequencies and amplitude ratio observables that can be compared with their observed counterparts. Results. The non-linear frequency shifts of stationary couplings are negligible compared to typical frequency errors derived from observations. The theoretically predicted amplitude ratios of combination frequencies match with some of their observational counterparts in the SPB targets. Other, unexplained observed ratios could be linked to other saturation mechanisms, to interactions between different modes, or to different opacity gradients in the driving zone. Conclusions. For the purpose of asteroseismic modeling, our non-linear mode coupling formalism can explain some of the stationary amplitude ratios of observed resonant mode couplings in single SPB stars monitored during 4 years by the Kepler space telescope.

Revealing Novel Aspects of Light-Matter Coupling by Terahertz Two-Dimensional Coherent Spectroscopy: The Case of the Amplitude Mode in Superconductors.

Recently developed terahertz (THz) two-dimensional coherent spectroscopy (2DCS) is a powerful technique to obtain materials information in a fashion qualitatively different from other spectroscopies. Here, we utilized THz 2DCS to investigate the THz nonlinear response of conventional superconductor NbN. Using broadband THz pulses as light sources, we observed a third-order nonlinear signal whose spectral components are peaked at twice the superconducting gap energy 2Δ. With narrow-band THz pulses, a THz nonlinear signal was identified at the driving frequency Ω and exhibited a resonant enhancement at temperature when Ω=2Δ. General theoretical considerations show that such a resonance can arise only from a disorder-activated paramagnetic coupling between the light and the electronic current. This proves that the nonlinear THz response can access processes distinct from the diamagnetic Raman-like density fluctuations, which are believed to dominate the nonlinear response at optical frequencies in metals. Our numerical simulations reveal that, even for a small amount of disorder, the Ω=2Δ resonance is dominated by the superconducting amplitude mode over the entire investigated disorder range. This is in contrast to other resonances, whose amplitude-mode contribution depends on disorder. Our findings demonstrate the unique ability of THz 2DCS to explore collective excitations inaccessible in other spectroscopies.

General solution for linear 2D anisotropic surface gravity water waves on uniform current

Measuring and modeling ocean waves is a routine task for oceanographers and marine engineers. Accounting for current effects on waves is less common; however, such effects can be non-trivial, particularly for strong currents. Recent research has also found that currents are increasing with global temperatures. Thus, accounting for currents is of potential importance to a growing subset of real-world environments. One significant impact of currents is their modification of dispersion. It is known that, in contrast to dispersion without current, wave–current dispersion is multivalued and anisotropic, meaning it varies with direction and can yield multiple solutions for the same frequency. Strictly speaking, a complete analysis ought to account for all dispersion solutions. This study presents a general wave field solution for linear steady-state two-dimensional surface gravity waves on current. In contrast to existing formulations, it accounts for the complete set of dispersion solutions. The multiple solutions correspond to linearly independent (same frequency) spatial modes with no analogy in models without current. To fully determine the complete temporal and spatial features of a wave field, one must determine the amplitudes of all spatial modes. This can be achieved through the solution of an inverse problem, provided one has sufficient initial conditions. The significance of accounting for all spatial modes is demonstrated through examples. It is shown that a single time-series measurement is insufficient for determining the spatial features of a monochromatic (single frequency) wave. Rather, additional spatial information must be introduced to render the problem well-posed. The theory and methodology presented can be used to improve wave models and measurements.

Harmonic Source Depth Estimation by a Single Hydrophone under Unknown Seabed Geoacoustic Property

The passive estimation of harmonic sound source depth is of great significance for underwater target localization and identification. Passive source depth estimation using a single hydrophone with an unknown seabed geoacoustic property is a crucial challenge. To address this issue, a harmonic sound source depth estimation algorithm, seabed independent depth estimation (SIDE) algorithm, is proposed. This algorithm combines the estimated mode depth functions, modal amplitudes, and the sign of each modal to estimate the sound source depth. The performance of the SIDE algorithm is analyzed by simulations. Results show that the SIDE is insensitive to the initial range of the sound source, the source depth, the hydrophone depth, the source velocity, and the type of the seabed. Finally, the effectiveness of the SIDE algorithm is verified by the SWellEX-96 data.

Vibration control of thin shallow paraboloidal shells with light-activated shape memory polymers

With the applications of thin-walled paraboloidal shell structure in aviation, aerospace and communication systems, smart-structure based active vibration control becomes essential to improve the performance of thin-walled parabolic structures. Light-activated shape memory polymer (LaSMP) is a novel actuator material that exhibits dynamic Young's modulus and strain properties under ultraviolet (UV) light exposures, which can be used for non-contact vibration control. This study focuses on investigating the vibration control performance of a shallow parabolic thin shell, with simply supported boundary conditions, with laminated LaSMP patches. Based on the LaSMP strain model, the vibration control effect of LaSMP patch on the thin shell is discussed. A finite element model of the simply supported parabolic thin shell is developed to obtain the natural frequencies. The modal expansion method is employed to investigate the vibration control of the shallow parabolic thin shell laminated with LaSMPs, and independent modal responses are calculated. According to the different control mode, the effects of LaSMP actuators on vibration control of shallow paraboloid shell are studied in three cases with varying actuation position and coverage area of LaSMP actuators. The results indicate that LaSMP can control the vibration of the thin shell by reducing the vibration amplitude and the final vibration control effect is determined by the mode shape, the initial LaSMP strain, and the location and area covered by LaSMP actuators. By establishing the model between the LaSMP actuator force and the attenuations in modal amplitude, this study provides an analytical tool for the application of LaSMPs in vibration control of flexible structures.

Extraction and evaluation of cable forces of a cable-stayed bridge based on amplitude and phase estimation method

In order to identify the time-varying frequency and amplitude of structural vibration based on the bridge structural health monitoring data and obtain the cable force of cable-stayed bridges in real time, a spectrum analysis method based on amplitude and phase estimation (APES) was proposed in this study. The amplitude spectrum of the acceleration data is first calculated by the APES method, the real-time spectrogram of the cable is obtained by the sliding window method. Then the modal frequency and amplitude are automatically extracted from the real-time spectrum by using a frequency extrusion post-processing technique, which can be regarded as the average value of the instantaneous frequency and amplitude respectively. Next, the fundamental frequency of the cable is extracted by using an automatic identification method, and the performance of the proposed method is verified. Finally, real-time scoring of cable forces and structural condition assessment is achieved with consideration of the moderation index model as well as the material strength. The results show that the APES method can use shorter calculation samples than the traditional Fast Fourier Transform (FFT) to obtain higher resolution and more accurate amplitude, which provides a theoretical basis for the real-time identification of fundamental frequency based on short-term monitoring data. The frequency extrusion post-processing-algorithm can reduce the spectrum recognition delay and improve timeliness of the cable force evaluation. The time-varying cable force with an interval of 10 s can be used to reflect the health status of the cable in time. The research results can provide technical support for the real-time extraction of cable force of long-span cable-stayed bridges, and can also provide an effective basis for component condition evaluation and bridge maintenance decision-making.

Interaction of ultrasonic guided waves with interfacial debonding in a stiffened composite plate under variable temperature and operational conditions

Stiffeners play a vital role in strengthening thin panels in a wide range of engineering constructions by reducing additional structural weight. However, these structures are vulnerable to issues such as interlayer delamination or skin-stiffener interfacial debonding due to high stress levels developed from external environmental conditions and operational loadings. In contrast, ultrasonic-guided wave (UGW) techniques exhibit an efficient and precise approach for monitoring discontinuities or damages in composite structures. There is a lack of research on understanding the characteristics of the interaction between UGW and interfacial debonding when in-plane edge loading and environmental factors are simultaneously taken into account. Therefore, this study is motivated by the need to develop a multiphysics numerical model which employs a commercially available finite element software, COMSOL Multiphysics®, to simulate UGW propagation in a stiffened composite plate with debonding at the plate-stiffener interface through a piezoelectric transducer under the combined influence of in-plane edge load and hygrothermal environment. The stiffened plate and piezoelectric patches are modelled with the tetrahedral element, and the bottom surface of the attached stiffener has a through-width 0.1 mm deep groove simulated for debonding. The developed FE model is validated against the results of the conducted experiments and those found in the available literature through the correlation coefficient. Further, the study conducts a comprehensive parametric investigation on stiffened cross-ply (0/90/0) laminated plates, considering variations in debonding size, in-plane load, and hygrothermal load intensity through the excitation of A0 mode. The acquired response is processed to compare the peak amplitude of various modes and energy of the waveform. Additionally, statistical indices such as normalised correlation moment (NCM) and variance of the continuous wavelet transform (CWT) peak are estimated to understand the impact of various parameters on waveform. The results show that the presence of a 90° lamina in the cross-ply laminate generates a low amplitude S0 mode in the scattered response. Moreover, a mode conversion from A0 to S0 mode is observed due to perfect bonding between the plate and the stiffener, providing insights into the bonding state in the panel. Furthermore, it is found that the magnitude of the in-plane loading marginally affects the peak amplitude of various modes in the scattered response. Additionally, when temperature intensity rises, the energy and amplitude of the UGW signals acquired through piezoelectric patches positioned in a direct line with the actuator gradually increase. The NCM value enhances with debonding regardless of exposed hygrothermal condition and reduces with increasing temperature intensity. In addition, the variance of the CWT peak reduces with debonding. The findings of this research are expected to be helpful for the development of efficient algorithms for detecting damages for structural health monitoring of stiffened composite panels.

Intervention Hypothesis for Training with Whole-Body Vibration to Improve Physical Fitness Levels: An Umbrella Review.

Whole-body vibration (WBV) is a training modality, and it seems to be a safe and efficient exercise especially to improve different aspects of physical fitness in different populations. The protocols for WBV are still not standardized. The difficulty in comparing the data confuses the real efficacy of this instrument. Consequently, the objective of this umbrella review is to analyze the protocols previously adopted and eventually to propose a standard operating procedure for WBV training. Systematic review and meta-analysis of randomized controlled trials on WBV were searched on the electronic databases PubMed, Web of Science, and Scopus until 18 March 2024. A quality assessment of the studies included has been performed. A total of 20 studies were included in this umbrella review and frequency, magnitude, and amplitude intensity data were recorded. Detailed information about the protocols (static or dynamic exercises, barefoot or with shoes, intensity duration, weekly frequency, and vibration characteristics) was also collected. WBV presents widely different protocols. Consequently, a standard operating procedure has not been proposed for WBV training. A hypothesis of intervention was instead written in which parameters for frequency, amplitude, acceleration, and training mode were proposed.

Active control of Alfvén eigenmodes by external magnetic perturbations with different spatial spectra

Alfvén eigenmodes have been suppressed and excited in tokamak plasmas by (just) modifying the poloidal spectra of externally applied static magnetic perturbations. This effect is observed experimentally when toroidal spectra of n = 2, n = 4 as well as a mixed spectrum of n = 2 and n = 4 is applied. Under the n = 2 magnetic perturbations, the modes are excited or suppressed by modifying the coil phasing between the upper and the lower set of coils. Regardless of the absolute rotation, an even parity for the n = 4 perturbation is observed to reduce the amplitude of the Alfvénic instabilities, while an odd parity amplifies it. To combine the stabilizing (and destabilizing) effect of n = 2 and n = 4, a mixed spectrum is applied, finding similar reduction (and amplification) trends. However, the impact on the mode amplitude is more subtle, due to the reduced coil current required for a mixed spectrum. The signal level on the fast-ion loss detector is sensitive to the applied poloidal spectrum, which is consistent with Hamiltonian full-orbit modelling of an edge resonant transport layer activated by the 3D perturbative fields. An internal redistribution of the fast-ion population is induced, modifying the phase-space gradients driving the Alfvénic instabilities, and ultimately determining their existence. The calculated edge resonant layers for both n = 2 and n = 4 toroidal spectra are consistent with the observed suppressed and excited phases. Moreover, hybrid kinetic-magnetohydrodynamic (MHD) simulations reveal that this edge resonant transport layer overlaps in phase-space with the population responsible for the fast-ion drive. The results presented here may help to control fast-ion driven Alfvénic instabilities in future burning plasmas with a significant fusion born alpha particle population.

Difference between Upshear- and Downshear-Propagating Waves Associated with the Development of Squall Lines

Abstract During the development of squall lines, low-frequency gravity waves exhibit contrasting behaviors behind and ahead of the system, corresponding to its low-level upshear and downshear sides, respectively. This study employed idealized numerical simulations to investigate how low-level shear and tilted convective heating influence waves during two distinct stages of squall-line evolution. In the initial stage, low-level shear speeds up upshear waves, while it has contrasting effects on the amplitudes of different wave modes, distinguishing it from the Doppler effect. Downshear deep tropospheric downdraft (n = 1 wave) exhibits larger amplitudes, resulting in strengthened low-level inflow and upper-level outflow. However, n = 2 wave with low-level ascent and high-level descent has higher amplitude upshear and exhibits a higher altitude of peak w values downshear, leading to the development of a more extensive upshear low-level cloud deck and a higher altitude of downshear cloud deck. In the mature stage, as the convective updraft greatly tilts rearward (upshear), stronger n = 1 waves occur behind the system, while downshear-propagating n = 2 waves exhibit larger amplitudes. These varying wave behaviors subsequently contribute to the storm-relative circulation pattern. Ahead of the squall line, stronger n = 2 waves and weaker n = 1 waves produce intense outflow concentrated at higher altitudes, along with moderate midlevel inflow and weak low-level inflow. Conversely, behind the system, the remarkable high pressure in the upper troposphere and wake low are attributed to more intense n = 1 waves. Additionally, the cloud anvil features greater width and depth rearward and is situated at higher altitudes ahead of the system due to the joint effects of n = 1 and n = 2 waves. Significance Statement Squall lines are a significant source of high-impact weather events, and their development has been partially explained through linear wave dynamics. While the recurrent generation of waves during squall-line evolution has been found, the differentiation of wave behavior behind and ahead of the system, as well as its implications for storm circulation, has remained unclear. This study employs idealized simulations to reveal that during different stages of convection, low-level shear and the tilting of convective heating exert contrasting effects on wave behaviors. Moreover, various wave modes exhibit distinct responses to specific factors, and their combined effect elucidates the structural discrepancies observed both rearward and forward of the convective updraft. These findings could allow a step toward a better understanding of the intricate interaction between waves and convections.

A model of umbral oscillations inherited from subphotospheric fast-body modes

Recently, complex horizontal patterns of umbral oscillations have been reported, but their physical nature and origin are still not fully understood. Here we show that the two-dimensional patterns of umbral oscillations of slow waves are inherited from the subphotospheric fast-body modes. Using a simple analytic model, we successfully reproduced the temporal evolution of oscillation patterns with a finite number of fast-body modes. In this model, the radial apparent propagation of the pattern is associated with the appropriate combination of the amplitudes in radial modes. We also find that the oscillation patterns are dependent on the oscillation period. This result indicates that there is a cutoff radial mode, which is a unique characteristic of the model of fast-body modes. In principle, both internal and external sources can excite these fast-body modes and produce horizontal patterns of umbral oscillations.

Data-driven modeling of equatorial atmospheric waves: The role of moisture and nonlinearity on global-scale instabilities and propagation speeds.

The equatorial region of the Earth's atmosphere serves as both a significant locus for phenomena, including the Madden-Julian Oscillation (MJO), and a source of formidable complexity. This complexity arises from the intricate interplay between nonlinearity and thermodynamic processes, particularly those involving moisture. In this study, we employ a normal mode decomposition of atmospheric reanalysis ERA-5 datasets to investigate the influence of nonlinearity and moisture on amplitude growth, propagation speed, and mode coupling associated with equatorially trapped waves. We focus our analysis on global-scale baroclinic Kelvin and Rossby waves, recognized as crucial components contributing to the variability of the MJO. We examine the dependence of wave amplitudes on the background moisture field in the equatorial region, as measured by total column water vapor. Our analysis demonstrates the crucial role of moisture in exciting these waves. We further investigate the dependence of the propagation speed of the waves on their amplitudes and the background moisture field. Our analysis reveals a robust correlation between the phase speed of the normal modes and their corresponding amplitude, whereas a weaker correlation is found between the eigenmodes' phase speed and the moisture field. Hence, our findings suggest that moisture plays a role in exciting the global-scale Rossby-Kelvin structure of the MJO. In this context, the propagation speed of the eigenmodes is mainly influenced by their amplitudes, underscoring the significant role of nonlinearity in wave propagation.

Time analysis for aero-engine acoustic modes exploiting block sparsity

Acoustic Mode Analysis (AMA) for aero-engines can offer valuable insights for the design of silent engines as well as for fault diagnosis. Commonly, this is done in the (spatial) Fourier domain, necessitating the use of multiple uniformly spaced microphones to ensure adequate resolution. Recent works show that sub-Nyquist estimation is feasible using sparse reconstruction frameworks, although such modelling generally introduces an estimation bias that has to be compensated for. Moreover, there is a growing interest in monitoring mode amplitude over continuous time, as it can offer crucial insights for diagnosing operational conditions. In this work, we introduce a Block Orthogonal Matching Pursuit (BOMP) method for continuous time mode analysis, exploiting the underlying structural sparsity of the signal model. Specifically, the (pseudo) ℓ0−norm penalty is employed to induce sparsity in the wavenumber domain, whereas a block structure is imposed as a constraint to monitor the amplitude variation in the time domain. The effectiveness of the BOMP is evaluated using both numerical simulations and experimental measurements, indicating the proposed method’s preferable performance as compared to the classic Least Absolute Shrinkage and Selection Operator (LASSO) and Orthogonal Matching Pursuit (OMP) methods.

Linear and Nonlinear Electro-optic Response of MHPOCBC

This study investigated the linear and second-order electro-optic responses in chiral smectic liquid crystal 4-(1-methylheptyloxycarbonyl) phenyl 4-octylcarbonyloxybiphenyl-4-carboxylate (MHPOCBC). The result revealed a single Debye-type relaxation in the linear electro-optic frequency dispersion, with a relaxation frequency extending up to one hundred kHz. Conversely, the second-order electro-optic response exhibited intricate temperature-dependence, accurately depicted by a phenomenological Landau theory around the SmA–SmCa* phase transition point. Notably, in the SmCa* phase, critical slowing down of the amplitude mode occurred near the transition to the SmA phase, while at lower temperatures of the SmCa* phase, a distinct low-frequency relaxation mode emerged. Furthermore, the relaxation frequency of the antiferroelectric Goldstone mode in the SmCA* phase remained constant across the entire temperature range. These findings should significantly contribute to the understanding of dynamic behaviors in chiral smectic liquid crystals, shedding light on their complex phase transitions and electro-optic properties.