Amplitude Spectrum Research Articles

Numerical simulation of flow around a transversely oscillating square cylinder at Re=22000

The study utilized OpenFOAM software, combined with the k-ω shear stress transport (SST) turbulence model and Arbitrary Lagrangian-Eulerian (ALE) dynamic mesh method, to investigate the influence of the oscillation amplitude on the flow dynamics around a square cylinder at Re = 2.2 × 104. It was found that various oscillation amplitudes affect the non-Gaussian characteristics of fluctuating pressure differently along the cylinder's surface: diminishing at the leading edge while intensifying at the trailing-edge corner. Concurrently, secondary recirculation bubbles near the cylinder's leading and trailing edges gradually diminish and eventually disappear with increasing oscillation amplitudes. Analysis of the amplitude spectrum of transverse velocity indicates the exclusive presence of odd-order harmonics along the central axis, while both odd and even-order harmonics are observed on either side of the central axis. Additionally, heightened oscillation amplitudes result in increased energy transfer from the cylinder to the fluid, with the energy density function predominantly exhibiting negative values and periodic variations occurring at twice the frequency of cylinder displacement or lift coefficient. As the oscillation amplitude increases, the vortex in the wake region transitions from a single-row to a double-row configuration. The research results provide important theoretical guidance for deepening the understanding of the flow characteristics around the oscillating square cylinder.

Photoacoustic Waveform Design for Optimal Parameter Estimation Based on Maximum Mutual Information

Waveform design is a potentially significant approach to improve the performance of an imaging or detection system. Photoacoustic imaging is a rapidly developing field in recent years; however, photoacoustic waveform design has not been extensively investigated. This paper considers the problem of photoacoustic waveform design for parameter estimation under constraints on input energy. The use of information theory is exploited to formulate and solve this optimal waveform design problem. The approach yields the optimal waveform power spectral density. Direct inverse Fourier transform of the optimal waveform frequency spectrum amplitude is proposed to obtain a real waveform in the time domain. Absorbers are assumed to be stochastic absorber ensembles with uncertain duration and location parameters. Simulation results show the relationship between absorber parameter distribution and the characteristics of optimal waveforms. Comparison of optimal waveforms for estimation, optimal waveforms for detection (signal-to-noise ratio) and other commonly used waveforms are also discussed. The symmetry properties of the forward and inverse Fourier Transforms are used to analyze the time and frequency properties and provide a heuristic view of how different goals affect the choice of waveform.

Rolling bearing fault diagnosis method based on SSA-IWT-EMD

Aiming at the problem of insufficient wavelet threshold noise reduction and unclear extraction of characteristic frequency of EMD decomposition, a rolling bearing fault diagnosis method based on SSA-IWT-EMD is proposed. Two adjustment factors are introduced to propose an improved threshold function (IWT), which overcomes the shortcomings of traditional soft and hard thresholds, and the sparrow search optimization algorithm (SSA) is used to globally optimize its parameters to achieve rolling bearing signal noise reduction. A comprehensive index P is proposed to select and reconstruct the components generated by empirical mode decomposition (EMD) to highlight the fault characteristic information of the signal. Envelope spectrum analysis is used to realize bearing fault diagnosis. Simulation and measurement results verify the effectiveness of the proposed method; at the same time, compared with the method of selecting components with a single index and the literature method, it is shown that the comprehensive index P and the proposed method have stronger noise reduction and feature extraction capabilities, and the envelope spectrum amplitude and frequency doubling components are more obvious, which can better realize the fault diagnosis of rolling bearings.

Implications of scattering for CMB foreground emission modelling

The extreme precision and accuracy of forthcoming observations of the cosmic microwave background (CMB) temperature and polarisation anisotropies, aiming to detect the tiny signatures of primordial gravitational waves or of light relic particles beyond the standard three light neutrinos, requires commensurate precision in the modelling of foreground Galactic emission that contaminates CMB observations. We evaluate the impact of second-order effects in Galactic foreground emission due to Thomson scattering off interstellar free electrons and to Rayleigh scattering off interstellar dust particles. We used existing sky survey data and models of the distribution of free electrons and dust within the Milky Way to estimate the amplitude and power spectra of the emission originating from radiation scattered either by free electrons or by dust grains at CMB frequencies. Both processes generate corrections to the total emission that are small compared to direct emission and are small enough not to pose problems for current-generation observations. However, B modes generated by Thomson scattering of incoming radiation off interstellar free electrons at CMB frequencies are within an order of magnitude compared to the sensitivity of the most advanced forthcoming CMB telescopes, and might require more precise evaluation in the future.

A spike is a spike: On the universality of spike features in four epilepsy models.

Frequency properties of the EEG characteristics of different seizure types including absence seizures have been described for various rodent models of epilepsy. However, little attention has been paid to the frequency properties of individual spike-wave complexes (SWCs), the constituting elements characterizing the different generalized seizure types. Knowledge of their properties is not only important for understanding the mechanisms underlying seizure generation but also for the identification of epileptiform activity in various seizure types. Here, we compared the frequency properties of SWCs in different epilepsy models. A software package was designed and used for the extraction and frequency analysis of SWCs from long-term EEG of four spontaneously seizing, chronic epilepsy models: a post-status epilepticus model of temporal lobe epilepsy, a lateral fluid percussion injury model of post-traumatic epilepsy, and two genetic models of absence epilepsy-GAERS and rats of the WAG/Rij strain. The SWCs within the generalized seizures were separated into fast (three-phasic spike) and slow (mostly containing the wave) components. Eight animals from each model were used (32 recordings, 104 510 SWCs in total). A limitation of our study is that the recordings were hardware-filtered (high-pass), which could affect the frequency composition of the EEG. We found that the three-phasic spike component was similar in all animal models both in time and frequency domains, their amplitude spectra showed a single expressed peak at 18-20 Hz. The slow component showed a much larger variability across the rat models. Despite differences in the morphology of the epileptiform activity in different models, the frequency composition of the spike component of single SWCs is identical and does not depend on the particular epilepsy model. This fact may be used for the development of universal algorithms for seizure detection applicable to different rat models of epilepsy. There is a large variety between people with epilepsy regarding the clinical manifestations and the electroencephalographic (EEG) phenomena accompanying the epileptic seizures. Here, we show that one of the EEG signs of epilepsy, an epileptic spike, is universal, since it has the same shape and frequency characteristics in different animal models of generalized epilepsies, despite differences in recording sites and location.

Wave patterns of the coupled nonlinear Schrödinger equations in photonic crystal fibers with four-wave mixing

Abstract In this paper, we examine the behavior of modulation instability within photonic crystals. The model employed is the coherent coupled nonlinear Schrödinger equation, incorporating weak birefringence and four-wave mixing, which arises at the edge of the optical mode. The linear analysis is used to derive the modulation instability spectrum. Throughout the modulation instability spectrum, we identify both stable and unstable modes, thereby confirming the breakdown of the plane wave. For certain four-wave mixing parameters, the amplitude of the modulation instability spectrum and its bandwidths expand, creating an opening for localized structures to emerge. Another aspect of this study has been demonstrated in normal and anomalous dispersion regimes where an increasing initial amplitude of the plane wave is fulfilled. Specifically, numerical simulations highlight the occurrence of Benjamin-Feir instability, where wave patterns emerge under the influence of four-wave mixing. Additionally, solitonic waves are generated, demonstrating the presence of Akhmediev breathers and other modulated structures, confirming that photonic crystals with four-wave mixing are conducive to these formations. The findings from this study could inform future research in the development of nonlinear photonic waveguides.

Curbing PBHs with PTAs

Sizeable primordial curvature perturbations needed to seed a population of primordial black holes (PBHs) will be accompanied by a scalar-induced gravitational wave signal that can be detectable by pulsar timing arrays (PTA). We derive conservative bounds on the amplitude of the scalar power spectrum at the PTA frequencies and estimate the implied constraints on the PBH abundance. We show that only a small fraction of dark matter can consist of stellar mass PBHs when the abundance is calculated using threshold statistics. The strength and the shape of the constraint depend on the shape of the power spectrum and the nature of the non-Gaussianities. We find that constraints on the PBH abundance arise in the mass range 0.1-103 M ⊙, with the sub-solar mass range being constrained only for narrow curvature power spectra. These constraints are softened when positive non-Gaussianity is introduced and can be eliminated when f NL ≳ 5. On the other hand, if the PBH abundance is computed via the theory of peaks, the PTA constraints on PBHs are significantly relaxed, signalling once more the theoretical uncertainties in assessing the PBH abundance.We further discuss how strong positive non-Gaussianites can allow for heavy PBHs to potentially seed supermassive BHs.

Monitoring of Amplitude Spectra of Betatron Oscillations in the JINR Booster Synchrotron

Methods of processing a digital signal obtained from a four-electrode transverse position sensor of ion bunches during acceleration in a synchrotron are discussed. A technique has been developed for reconstructing the amplitude spectrum of betatron oscillations of an ion bunch in the case of a sensor displacement relative to the initial position determined during calibration. The results obtained are used to reconstruct the amplitude spectrum of betatron oscillations of a bunch after injection of xenon ions into the JINR booster synchrotron.

Simulation of fatigue crack growth in aluminium alloy 7075-T7351 under spike overload and aircraft spectrum loading

The trend towards virtual testing and digital-twin assisted management means that the accurate and reliable simulation of fatigue crack propagation behaviour is more important than ever. Reliable but conservative approaches to support this are in widespread use in the aerospace industry. Nevertheless, the conservatism comes at a significant cost in terms of reduced structural life and an increased ongoing inspection requirement and, as such leads to questions about the economic burden of these approaches. Recent comparisons between blind predictions and test results revealed the extent of the issue for cracking in aluminium alloy 7075-T7351 coupons with configuration and loading representative of military transport aircraft wing skins. The current models were generally conservative by a factor of two or more in terms of crack propagation life. This suggested that there was significant scope to improve the modelling to better reflect all the complex contributing factors. The current work has investigated the issue of changes in the crack front constraint as the crack progresses from a state of high constraint (close to plane strain) to a lower constraint (approaching plane stress). This issue was investigated both experimentally and with the development of an improved analytical model. A test program was conducted on several specimens, loaded under constant-amplitude, constant-amplitude with spike-overloads and a variable amplitude spectrum. Crack-opening stress levels were measured at key points in the tests and the results were used to develop and evaluate improved modelling approaches. The improved model was generally able to predict crack growth within about ± 30 % of that demonstrated along with the correct form of the crack growth, which is a significant advance and will lead to reduced costs and increased safety.

Demodulation of vibration signals for bearing fault detection using a method based on filtering and absolute value

A method for amplitude demodulation of vibration signals is proposed in your study, the method is designed for diagnosis and fault detection. The approach of the method starts by calculating the absolute values of the vibration signal data to make them all positive. Then, a low-pass filtering is applied to obtain an exponential variation of the data on the spectrum of the demodulated amplitude signal. The proposed method is applied to signals from the database, and subsequently, these signals are demodulated using both the proposed method and the Hilbert transform. Both methods reveal high-amplitude peaks at the same frequency values in the demodulated amplitude spectrum.

Terahertz meta-biosensor for subtype detection and chemotherapy monitoring of glioma cells

Rapid and precise identification of glioma subtypes can assist surgeons in quickly determining patients’ conditions and developing treatment plans. However, current methods face challenges such as high cost and limited sensitivity, thereby significantly hindering diagnostic efficiency. In this paper, we proposed a spectral sensing strategy by introducing terahertz biosensors for glioma subtype recognition and therapeutic efficacy monitoring. Our findings demonstrated that both the resonance frequency and amplitude of the transmission spectra varied as the cell increased. The two-dimensional fingerprint diagram could help us rapidly recognize cell subtypes. Additionally, we conducted a theoretical analysis of the sensing performance. We confirmed that the high Q-factor (∼27.8) results from toroidal dipole resonance and examined the impact of dielectric loss and the refractive index of the analyte on the resonance dip. Furthermore, we applied the biosensor in therapeutic drug screening and showed that as the concentration of tubastatin A increased, the resonance frequency shifted from 183.1 GHz to 76.2 GHz. This result indicates that the toroidal dipole constructed by the metasurface enables ultrasensitive light-matter interactions that amplify subtle cellular changes to the resonance spectrum. The proposed THz meta-biosensor demonstrates significant potential for rapid intraoperative recognition of glioma cell subtypes and therapeutic efficacy monitoring.

Unsupervised clustering of mining-induced microseismicity provides insights into source mechanisms

Microseismic source mechanisms in underground mines can provide information about the rock mass response to mining. Conventional approaches to such studies rely upon moment tensor solutions that are susceptible to modeling assumptions and need reliable information about source locations and high-resolution velocity models. We propose the application of unsupervised clustering to group microseismic events into different classes directly from the waveform data such that the events in a specific class have similar source mechanisms. Our method has three main steps, first using spectral decomposition to separate the source terms from the path-receiver contributions in the observed amplitude spectra of events occurring in spatially dense clusters. Second, reducing the number of features from the source spectra using independent component analysis (ICA). Third, applying a Gaussian mixture model (GMM) to the reduced feature matrix to obtain event clusters. To test our method, we generate synthetic waveform data using the receiver network and the recorded microseismic event locations in an underground potash mine in Saskatchewan. Results show the ability of our method to separate events into different classes corresponding to differences in source mechanisms. Application to field data recorded in the mine during February 2021 successfully discriminates between blasts and microseismic events. The data recorded between 1 March and 30 June 2021 that contain microseismic events only are divided into two dominant classes. Using known moment tensors (MT) of some of these events for labeling, we interpret one of the two classes as having dominant double-couple mechanisms as compared to the other which most likely corresponds to the linear dipole-tensile mechanisms. Our method, combined with some expert knowledge such as MT of some larger magnitude events, can offer an assessment of source types of large microseismic populations as often encountered in induced seismicity.

A Dual-Stream Deep Learning-Based Acoustic Denoising Model to Enhance Underwater Information Perception

Estimating the line spectra of ship-radiated noise is a crucial remote sensing technique for detecting and recognizing underwater acoustic targets. Improving the signal-to-noise ratio (SNR) makes the low-frequency components of the target signal more prominent. This enhancement aids in the detection of underwater acoustic signals using sonar. Based on the characteristics of low-frequency narrow-band line spectra signals in underwater target radiated noise, we propose a dual-stream deep learning network with frequency characteristics transformation (DS_FCTNet) for line spectra estimation. The dual streams predict amplitude and phase masks separately and use an information exchange module to swap learn features between the amplitude and phase spectra, aiding in better phase information reconstruction and signal denoising. Additionally, a frequency characteristics transformation module is employed to extract convolutional features between channels, obtaining global correlations of the amplitude spectrum and enhancing the ability to learn target signal features. Through experimental analysis on ShipsEar, a dataset of underwater acoustic signals by hydrophones deployed in shallow water, the effectiveness and rationality of different modules within DS_FCTNet are verified.Under low SNR conditions and with unknown ship types, the proposed DS_FCTNet model exhibits the best line spectrum enhancement compared to methods such as SEGAN and DPT_FSNet. Specifically, SDR and SSNR are improved by 14.77 dB and 13.58 dB, respectively, enabling the detection of weaker target signals and laying the foundation for target localization and recognition applications.

Nonlinear effect on stable state and snap-through bistability of square composite laminate

Bistable structures with the elastic instability caused by buckling are confirmed to perform significantly in micro-electromechanical systems, metamaterials, energy harvester, vibration isolation and morphing structures. The target of this paper is to explore the dynamic responses of cross-ply bistable composite laminate, focusing on the nonlinear effect of the single- and double-well vibration. Both theoretical and finite element (FE) methods are employed to simulate the nonlinear vibration and dynamic snap-through of bistable composite laminate under the foundation excitation at the center. In the theoretical model, the governing equations are established via Lagrange's equation based on the first-order shear deformation theory, von Karman nonlinear strain-displacement relation and Rayleigh-Ritz method. The fourth-order Runge-Kutta method is adopted to solve the governing equations, and the numerical results are validated by FE model. Subsequently, the details of the dynamic responses are analyzed to identify the nonlinear effects in the form of bifurcation diagram, phase portrait, time history, Poincare maps and amplitude spectrum. The dynamic responses are examined for a series of excitation parameters in both time and frequency domain. Through fixed frequency and frequency sweep tests, the nonlinear phenomenon of the single- and double-well vibrations are analyzed including superharmonic resonance, stiffness softening, hysteresis phenomenon, various periodic and chaotic vibration. The diverse responses to external inputs contribute significantly to efficiently predicting mechanical behaviors in real-world conditions, thereby offering indispensable theoretical support for structural design applications.

The minimum-frequency property of complex trace analysis

A waveform has the property of minimum frequency if its instantaneous frequency equals the Hilbert transform of its instantaneous bandwidth plus the spectral low-cut frequency. Minimum frequency is characterized by an amplitude spectrum that is maximally skewed toward the low frequencies. The associated property of maximum frequency is characterized by an amplitude spectrum that is maximally skewed toward the high frequencies. Minimum and maximum frequency are the time-domain counterparts of the spectral properties of minimum and maximum delay. Many waveforms have the property of minimum frequency, such as the Ricker wavelet. Waveforms that have the property of maximum frequency include Klauder wavelets that emphasize high frequencies. Impulsive wavelets can have both minimum frequency and minimum delay. The properties of minimum and maximum frequency suggest time-variant measures to estimate the spectral low-cut and high-cut frequencies of seismic traces and produce an instantaneous frequency attribute that is free of spikes. The property of minimum frequency has long been known but remains unfamiliar to geophysics. It is explained in the context of complex trace analysis illustrated with seismic wavelets and traces.

The September 6, 2021 MW 5.4 Tofalaria earthquake at a weakly active segment of the Main Sayan fault (Eastern Siberia)

We study in detail the Mw 5.4 September 6, 2021 Tofalaria earthquake occurred in a mountain area of the Eastern Sayan which is characterized by a low level of seismic activity. An interest in the seismic event is caused, on the one hand, by poor knowledge about stress-strain field of the crust in the considered region, and, on the other hand, by its relation to the NW segment of the ancient Main Sayan fault – a structural boundary between the Sayan-Baikal fold belt and the tectonically stable Siberian platform. Seismic moment tensors and hypocentral depths of the mainshock and its largest aftershock (Mw 4.6) are inverted from intermediate-period surface wave amplitude spectra calculated at the stations located at teleseismic distances. Integral source parameters of the mainshock, characterizing its spatio-temporal development, are also estimated and the fault plane is determined. Epicenters of 31 aftershocks with M ≥ 1.8, occurred up to the end of 2021, are constrained from body waves recorded at regional seismic stations. The obtained results show that the Tofalaria earthquake occurred under the influence of the SW-NE compression, which is observed in Western Mongolia. Focal mechanism of the largest aftershock and the NE elongation of the aftershock epicentral field (22 km) indicate stress redistribution after the mainshock in a local crustal volume, bordered by small-scale faults.

Correlation between zeta potential and electron paramagnetic resonance of thulium, europium co-doped yttria based suspensions

The formation of advanced ceramic components with homogeneous microstructure and functional characteristics demands a suitable control of particle dispersion. Thus, the characterization of particle stability as immersed in a liquid medium is important. The present paper reports an approach to evaluate the stability of europium, thulium co-doped yttria (YET) nanoparticles by a correlation between zeta potential and Electron Paramagnetic Resonance (EPR) techniques. Based on results, YET suspensions exhibited high stability apart from pH 10, while their isoelectric point presented a slight variation from pHIEP 8.5 to 9.2 according to thulium content 0 and 2 at.%, respectively. The peak-to-peak amplitude of EPR spectra of the YET suspensions increased as pH shifted toward alkaline condition, following zeta potential curves features. The present achievements are very useful parameters to form stable suspensions based on rare-earth oxides and to advance toward new materials for radiation dosimetry.

Ultrasonic Assessment of Liver Fibrosis Using One-Dimensional Convolutional Neural Networks Based on Frequency Spectra of Radiofrequency Signals with Deep Learning Segmentation of Liver Regions in B-Mode Images: A Feasibility Study.

The early detection of liver fibrosis is of significant importance. Deep learning analysis of ultrasound backscattered radiofrequency (RF) signals is emerging for tissue characterization as the RF signals carry abundant information related to tissue microstructures. However, the existing methods only used the time-domain information of the RF signals for liver fibrosis assessment, and the liver region of interest (ROI) is outlined manually. In this study, we proposed an approach for liver fibrosis assessment using deep learning models on ultrasound RF signals. The proposed method consisted of two-dimensional (2D) convolutional neural networks (CNNs) for automatic liver ROI segmentation from reconstructed B-mode ultrasound images and one-dimensional (1D) CNNs for liver fibrosis stage classification based on the frequency spectra (amplitude, phase, and power) of the segmented ROI signals. The Fourier transform was used to obtain the three kinds of frequency spectra. Two classical 2D CNNs were employed for liver ROI segmentation: U-Net and Attention U-Net. ROI spectrum signals were normalized and augmented using a sliding window technique. Ultrasound RF signals collected (with a 3-MHz transducer) from 613 participants (Group A) were included for liver ROI segmentation and those from 237 participants (Group B) for liver fibrosis stage classification, with a liver biopsy as the reference standard (Fibrosis stage: F0 = 27, F1 = 49, F2 = 51, F3 = 49, F4 = 61). In the test set of Group A, U-Net and Attention U-Net yielded Dice similarity coefficients of 95.05% and 94.68%, respectively. In the test set of Group B, the 1D CNN performed the best when using ROI phase spectrum signals to evaluate liver fibrosis stages ≥F1 (area under the receive operating characteristic curve, AUC: 0.957; accuracy: 89.19%; sensitivity: 85.17%; specificity: 93.75%), ≥F2 (AUC: 0.808; accuracy: 83.34%; sensitivity: 87.50%; specificity: 78.57%), and ≥F4 (AUC: 0.876; accuracy: 85.71%; sensitivity: 77.78%; specificity: 94.12%), and when using the power spectrum signals to evaluate ≥F3 (AUC: 0.729; accuracy: 77.14%; sensitivity: 77.27%; specificity: 76.92%). The experimental results demonstrated the feasibility of both the 2D and 1D CNNs in liver parenchyma detection and liver fibrosis characterization. The proposed methods have provided a new strategy for liver fibrosis assessment based on ultrasound RF signals, especially for early fibrosis detection. The findings of this study shed light on deep learning analysis of ultrasound RF signals in the frequency domain with automatic ROI segmentation.

Blind spectral inversion of seismic data

AbstractReflectivity inversion is a key step in reservoir prediction. Conventional sparse‐spike deconvolution assumes that the reflectivity (reflection coefficient series) is sparse and solves for the reflection coefficients by an L1‐norm inversion process. Spectral inversion is an alternative to sparse‐spike deconvolution, which is based on the odd–even decomposition algorithm and can accurately identify thin layers and reduce the wavelet tuning effect without using constraints from logging data, from horizon interpretations or from an initial model of the reflectivity. In seismic processing, an error exists in wavelet extraction because of complex geological structures, resulting in the low accuracy of deconvolution and inversion. Blind deconvolution is an effective method for solving the problem mentioned above, which comprises seismic wavelet and reflectivity sequence, assuming that the wavelets that affect some subsets of the seismic data are approximately the same. Therefore, we combined blind deconvolution with spectral inversion to propose blind spectral inversion. Given an initial wavelet, we can calculate the reflectivity based on spectral inversion and update the wavelet for the next iteration. During the update processing, we add the smoothness of the wavelet amplitude spectrum as a regularization term, thus reducing the wavelet oscillation in the time domain, increasing the similarity between inverted and initial wavelets, and improving the stability of the solution. The blind spectral inversion method inherits the wavelet robustness of blind deconvolution and high resolution of spectral inversion, which is suitable for reflectivity inversion. Applications to synthetic and field seismic datasets demonstrate that the blind spectral inversion method can accurately calculate the reflectivity even when there is an error in wavelet extraction.

Investigation into NSAW excitation and modulation utilizing the grating mask technique

Narrowband surface acoustic wave (NSAW) method is a promising ultrasonic detection technique, with its laser-induced excitation technology offering the advantages of non-contact and flexible regulation. This paper proposes an NSAW excitation and modulation system based on the grating mask method to detect the nonlinear characteristics of the spectra caused by the variation in material surface properties. According to Doyer’s sharp line excitation theory, a strip line source array excitation model formed by superposition principle is established, and the effects of duty ratios of the masks on NSAW spectra amplitude characteristics are interpreted. An NSAW excitation and B-scan experimental system that can realize line source spacing changes is developed, and the effects of cylindrical lens height and masks with different duty ratios on NSAW spectra modulation are studied. The experimental results show that the amplitude ratios (the ratio of the double frequency amplitude to the second harmonic amplitude) are consistent with the results of the Doyer superimposed strip line source array excitation model in which the excitation light source energy is evenly distributed. The second-order nonlinear coefficients extracted from the experimental spectra can effectively characterize the surface properties of 6061 aluminum alloy at different annealing temperatures.