Time-averaged Spectrum Research Articles

High power impulse magnetron sputtering of Zn/Al target in an Ar and Ar/O2 atmosphere: The study of sputtering process and AZO films

Reactive high power impulse magnetron sputtering (R-HiPIMS) has been demonstrated as a promising technique for the ZnO:Al (AZO) thin film deposition at low temperature with improved electrical properties compared to the reactive direct current magnetron sputtering (R-dcMS). However, there are not enough studies about the HiPIMS process using Zn/Al target itself. Additionally, AZO films have not been deposited with the pulse duration times long enough to allow the discharge to develop into the self-sputtering mode. C-V-t characteristics and the time average plasma optical emission spectra were studied as a function of different sputtering parameters, such as frequency, average power, pulse duration time, and oxygen flow rate. AZO films were deposited on glass substrates without intentional heating by R-HiPIMS using 500 μs long pulses. Structural, electrical and optical properties of the AZO films were studied as a function of peak current. Obtained peak power densities are relatively low compared to other metals due to the strong argon gas rarefaction, however, it is possible to increase the peak power density above 0.5 kW/cm2 by increasing the time between pulses or the average power to reach the HiPIMS regime. If the pulse duration time is 500 μs, the sustained self-sputtering discharge can be observed when the peak power density is above 0.3 kW/cm2. The peak current is sensitive to the oxygen content in the sputtering atmosphere so that it can be used as a control parameter for the reactive sputtering. The lowest obtained resistivity of the AZO films is 1.0 × 10−3 Ωcm with the transmittance around 70% in the visible light range. From the XRD measurements, there is the indication of existing zincblende structural phase in the R-HiPIMS deposited AZO films using high oxygen partial pressure.

Multi-scale wake structures around the dune

The three-dimensional wake structures behind a barchan dune model are investigated by the high-speed particle image velocimetry (PIV) at the Reynolds number of 5530. The measured velocity fields are first evaluated by time-averaged flow patterns and power spectra analysis. Then the one-dimensional orthogonal wavelet analysis is applied to reveal multi-scale turbulent structures and their corresponding second order statistics in the dune wake. The instantaneous multi-scale structures suggest that the large-scale structure is responsible for the formation of separation region. The intermediate-scale structure tends to be more active at the boundary of separation region, which may be due to the secondary vortex movement caused by the interactions between the wake and main flow. The appearance of small-scale vortices at the downstream of separation region indicates the breakdown process of large-scale vortices. The Reynolds stress and kinetic energy distribution suggest that the large-scale structures dominate the generation of turbulence in the dune wake. The lower kinetic energy contained in intermediate- and small- scale structures is considered to be related to smaller-scale interactions that reflect energy cascading phenomenon. The Reynolds shear stresses distributions suggest that the intermediate-scale structures also make significance in the separated boundary layer. As for small-scale structure, it is worthy to note that a region of high Reynolds shear stresses with an opposite sign is observed around the dune crest. The cross-correlation function of multi-scale structures suggest the quasi-periodicity of large-scale structure. The intermediate-scale structures also show a certain periodicity, however, such structures tend to be more unstable and the strength of them reduces as they travel downstream. When decreasing to small-scale, the vortical structures decays quickly at the downstream with larger convective velocity. This may indicate the breakdown process of large-scale vortices and the quick dissipation of small-scale vortices.

Detection of a Gamma-Ray Flare from the High-redshift Blazar DA 193

Abstract High-redshift (z > 2) blazars are the most powerful members of the blazar family. Yet, only a handful of them have both X-ray and γ-ray detection, thereby making it difficult to characterize the energetics of the most luminous jets. Here, we report, for the first time, the Fermi-Large Area Telescope detection of the significant γ-ray emission from the high-redshift blazar DA 193 (z = 2.363). Its time-averaged γ-ray spectrum is soft (γ-ray photon index = 2.9 ± 0.1), and together with a relatively flat hard X-ray spectrum (14–195 keV photon index = 1.5 ± 0.4), DA 193 presents a case to study a typical high-redshift blazar with inverse Compton peak being located at MeV energies. An intense GeV flare was observed from this object in the first week of 2018 January, a phenomenon rarely observed from high-redshift sources. What makes this event a rare one is the observation of an extremely hard γ-ray spectrum (photon index = 1.7 ± 0.2), which is somewhat unexpected because high-redshift blazars typically exhibit a steep falling spectrum at GeV energies. The results of our multifrequency campaign, including both space- (Fermi, NuSTAR, and Swift) and ground-based (Steward and Nordic Optical Telescope) observatories are presented, and this peculiar γ-ray flare is studied within the framework of a single-zone leptonic emission scenario.

Subgrid Parameterizations of the Eddy–Eddy, Eddy–Mean Field, Eddy–Topographic, Mean Field–Mean Field, and Mean Field–Topographic Interactions in Atmospheric Models

Abstract Parameterizations are developed for each of the subgrid turbulence interaction classes in fully three-dimensional global atmospheric flows over topography, typical of January and July climate states. Stochastic and deterministic parameterizations are developed for the eddy–eddy interactions and deterministic parameterizations for eddy–mean field, eddy–topographic, mean field–mean field, and mean field–topographic interactions. All parameterizations are calculated from the statistics of higher-resolution reference direct numerical simulations (DNSs) truncated into resolved and subgrid scales and employed without tuning coefficients. This parameterization framework is validated by performing large-eddy simulations (LESs) that closely agree with the reference DNSs in terms of time-averaged kinetic energy spectra, zonal jet structure, and nonzonal streamfunction fields. Both the DNSs and LESs are formulated in such a way that the usual problem of a long artificial dissipation range does not occur. Successful LESs are produced with truncation wavenumbers 31 and 15, using, respectively, only 11.9% and 1.3% of the DNS computational effort at truncation wavenumber 63. The lower-resolution LESs show that the parameterizations are successful even when the energy injection due to baroclinic instability is not completely resolved. The contribution of each of the parameterized interaction classes to the quality of the LES is identified. The best agreement is achieved when all subgrid components are included. There is a very high level of agreement between the LESs and DNSs with typical streamfunction pattern correlations of r = 0.962 for the nonzonal components and r = 0.999 for the total fields when the complete sets of parameterizations are used.

Implications of the Warm Corona and Relativistic Reflection Models for the Soft Excess in Mrk 509

Abstract We present the analysis of the first Nuclear Spectroscopic Telescope Array observations (∼220 ks), simultaneous with the last Suzaku observations (∼50 ks), of the active galactic nucleus of the bright Seyfert 1 galaxy Mrk 509. The time-averaged spectrum in the 1–79 keV X-ray band is dominated by a power-law continuum (Γ ∼ 1.8–1.9), a strong soft excess around 1 keV, and signatures of X-ray reflection in the form of Fe K emission (∼6.4 keV), an Fe K absorption edge (∼7.1 keV), and a Compton hump due to electron scattering (∼20–30 keV). We show that these data can be described by two very different prescriptions for the soft excess: a warm (kT ∼ 0.5–1 keV) and optically thick (τ ∼ 10–20) Comptonizing corona or a relativistically blurred ionized reflection spectrum from the inner regions of the accretion disk. While these two scenarios cannot be distinguished based on their fit statistics, we argue that the parameters required by the warm corona model are physically incompatible with the conditions of standard coronae. Detailed photoionization calculations show that even in the most favorable conditions, the warm corona should produce strong absorption in the observed spectrum. On the other hand, while the relativistic reflection model provides a satisfactory description of the data, it also requires extreme parameters, such as maximum black hole spin, a very low and compact hot corona, and a very high density for the inner accretion disk. Deeper observations of this source are thus necessary to confirm the presence of relativistic reflection and further understand the nature of its soft excess.

Photoionized emission and absorption features in the high-resolution X-ray spectra of NGC 3783

OurSwiftmonitoring program triggered two jointXMM-Newton,NuSTAR, and HST observations on 11 and 21 December 2016 targeting NGC 3783 because its soft X-ray continuum was heavily obscured. Consequently, emission features, including the O VIIradiative recombination continuum, stand out above the diminished continuum. We focus on the photoionized emission features in the December 2016 Reflection Grating Spectrometer (RGS) spectra, and compare them to the time-averaged RGS spectrum obtained in 2000–2001 when the continuum was unobscured. A two-phase photoionized plasma is required to account for the narrow emission features. These narrow emission features are weakly varying between 2000–2001 and December 2016. We also find a statistically significant broad emission component in the time-averaged RGS spectrum in 2000–2001. This broad emission component is significantly weaker in December 2016, suggesting that the obscurer is farther away than the X-ray broad-line region. In addition, by analyzing the archival high-resolution X-ray spectra, we find that nine photoionized absorption components with different ionization parameters and kinematics are required for the warm absorber in X-rays.

OUP accepted manuscript

Recent monitoring campaigns designed to map the accretion regime in AGN show major discrepancies with models where the optical/ultraviolet (UV) is produced by X-ray-illuminated, optically thick disc material within a few hundred gravitational radii. However, these campaigns only monitored X-rays below $10$ keV, whereas the bolometric luminosity for most of these AGN peaks above $50$ keV. We use data from the recent multiwavelength campaign by \cite{E17} on NGC 4151 - the only AGN bright enough to be monitored at higher energies with \textit{Swift} BAT. We develop a spectral-timing model with a hot corona, warm Comptonisation, and outer standard disc. This fits the time-averaged spectrum well, but completely fails to match the UV variability predicted from the X-ray lightcurve. However, it reveals that NGC 4151 had a bolometric luminosity around $1.4\%$ of the Eddington luminosity during this campaign, close to the luminosity at which AGN show a `changing-state' transition, where the broad optical lines disappear. Stellar mass black holes show a state transition at a similarly low Eddington fraction, which is broadly interpreted as the inner disc being replaced by an optically thin flow. We find that the UV lightcurve can instead be matched by reprocessing of the X-ray flux on size scales of the broad line region (BLR; $1.5-20$ light-days) and rule out there being optically thick material inwards of this, as expected if the thin disc is replaced by the flow below the inner radius of the BLR. These results emphasise the need for even longer-timescale, multiwavelength monitoring campaigns on variable AGN.

A protocol for quantifying cardiogenic oscillations in dynamic 129 Xe gas exchange spectroscopy: The effects of idiopathic pulmonary fibrosis.

The spectral parameters of hyperpolarized 129 Xe exchanging between airspaces, interstitial barrier, and red blood cells (RBCs) are sensitive to pulmonary pathophysiology. This study sought to evaluate whether the dynamics of 129 Xe spectroscopy provide additional insight, with particular focus on quantifying cardiogenic oscillations in the RBC resonance. 129 Xe spectra were dynamically acquired in eight healthy volunteers and nine subjects with idiopathic pulmonary fibrosis (IPF). 129 Xe FIDs were collected every 20ms (TE =0.932ms, 512 points, dwell time=32μs, flip angle ≈ 20°) during a 16s breathing maneuver. The FIDs were pre-processed using the spectral improvement by Fourier thresholding technique (SIFT) and fit in the time domain to determine the airspace, interstitial barrier, and RBC spectral parameters. The RBC and gas resonances were fit to a Lorentzian lineshape, while the barrier was fit to a Voigt lineshape to account for its greater structural heterogeneity. For each complex resonance the amplitude, chemical shift, linewidth(s), and phase were calculated. The time-averaged spectra confirmed that the RBC to barrier amplitude ratio (RBC:barrier ratio) and RBC chemical shift are both reduced in IPF subjects. Their temporal dynamics showed that all three 129 Xe resonances are affected by the breathing maneuver. Most notably, several RBC spectral parameters exhibited prominent oscillations at the cardiac frequency, and their peak-to-peak variation differed between IPF subjects and healthy volunteers. In the IPF cohort, oscillations were more prominent in the RBC amplitude (16.8±5.2 versus 9.7±2.9%; P=0.008), chemical shift (0.43±0.33 versus 0.083±0.05ppm; P<0.001), and phase (7.7±5.6 versus 1.4±0.8°; P<0.001). Dynamic 129 Xe spectroscopy is a simple and sensitive tool that probes the temporal variability of gas exchange and may prove useful in discerning the underlying causes of its impairment.

X-ray reverberation lags of the Fe–K line due to AGN disc winds

Short X-ray reverberation lags are seen across a broad Fe-K energy band in more than twenty active galactic nuclei (AGNs). This broad iron line feature in the lag spectrum is most significant in super-Eddington sources such as Ark 564 ($L/L_{\rm Edd}\sim 1$) and 1H 0707--495 ($L/L_{\rm Edd}\gtrsim 10$). The observed lag timescales correspond to very short distances of several $R_g/c$, so that they have been used to argue for extremely small `lamp-post' coronae close to the event horizon of rapidly spinning black holes. Here we show for the first time that these Fe-K short lags are more likely to arise from scattering in a highly-ionised wind, launched at $\sim 50\,R_g$, rotating and outflowing with a typical velocity of $0.2c$. We show that this model can simultaneously fit the time-averaged energy spectra and the short-timescale lag-energy spectra of both 1H 0707--495 and Ark 564. The Fe-K line in 1H 0707--495 has a strong P-Cygni-like profile, which requires that the wind solid angle is large and that our line of sight intercepts the wind. By contrast the lack of an absorption line in the energy spectrum of Ark 564 requires rather face-on geometry, while the weaker broad Fe-K emission in the energy and lag-energy spectra argue for a smaller solid angle of the wind. This is consistent with theoretical predictions that the winds get stronger when the sources are more super-Eddington, supporting the idea of AGN feedback via radiation pressure driven winds.

Spectral analysis of SXP59.0 during its 2017 outburst and properties of the soft excess in X-ray binary pulsars

We report the results provided by theXMM-Newtonobservation of the X-ray binary pulsar SXP59.0 during its most recent outburst in April 2017. The source was detected atfX(0.2–12 keV) = 8 × 10−11erg cm−2s−1, one of its highest flux levels reported to date. The measured pulse period wasPspin= 58.949(1) s, very similar to the periods measured in most of the previous observations. The pulsed emission was clearly detected over the whole energy range between 0.2 and 12 keV, but the pulse profile is energy dependent and the pulsed fraction increases as the energy increases. Although the time-averaged EPIC spectrum is dominated by a power-law component (with photon index Γ = 0.76 ± 0.01), the data show an evident soft excess, which can be described with the sum of a black-body and a hot thermal plasma component (with temperatureskTBB= 171+11−14eV andkTAPEC= 1.09+0.16−0.09keV, respectively). Moreover, the EPIC and RGS spectra show narrow emission lines due to N, O, Ne, Mg, and Fe. The phase-resolved spectral analysis of the EPIC data shows that the flux of the black-body component varies with the pulse phase, while the plasma component is almost constant. We show that the black-body component can be attributed to the reprocessing of the primary emission by the optically thick material at the inner edge of the accretion disc, while the hot plasma component is due to a diffuse gas far from the accretion region and the narrow emission lines of the RGS spectrum are most probably due to photoionized matter around the accreting source.

Time-resolved PIV measurement of influence of upstream roughness on separated and reattached turbulent flows over a forward-facing step

This study reports an experimental investigation of the effects of upstream roughness on a low Reynolds number turbulent boundary layer over a forward-facing step. Two types of upstream roughness were investigated, including a transitionally rough 16-grit sandpaper (ks+ ≈ 69) and fully rough staggered cubes (ks+ ≈ 500). A two-dimensional two-component time-resolved particle image velocimetry (2D-2C TR-PIV) method was used to measure the time-averaged mean velocities, Reynolds stresses, temporal auto-correlations and frequency spectra of the flow field to quantify the influence of upstream roughness on the downstream evolution of the turbulence over the step. The results indicate that upstream roughness decreased the vortex shedding frequency. Roughness also decreased the reattachment length by enhancing the streamwise turbulence intensity level, reducing the magnitude of backflow and suppressing the vortex shedding frequency in comparison to the smooth wall. In the recirculation region, upstream roughness reduced the mean streamwise velocity only in the outer layer. The Reynolds stresses remained relatively unchanged by the sandpaper roughness but were significantly modified by the cube roughness. Downstream of the leading edge, the staggered cubes increased the streamwise Reynolds stress both near the wall and outside the shear layer but decreased the wall-normal Reynolds stress and Reynolds shear stress within the shear layer. These modifications are inversely proportional to distance in the recirculation region. The life times of the streamwise and wall-normal velocity fluctuations increase with streamwise distance and are much longer in the redevelopment region than in the recirculation region. Quadrant decomposition and joint probability density functions of the velocity fluctuations were also measured to characterize upstream roughness effects on the downstream evolution of the dominant motions producing the Reynolds shear stress.

Photoinduced valley and electron-hole symmetry breaking in α−T3 lattice: The role of a variable Berry phase

We consider $\alpha$-$T_3$ lattice illuminated by intense circularly polarized radiation in terahertz regime. We present quasienergy band structure, time-averaged energy spectrum and time-averaged density of states of $\alpha$-$T_3$ lattice by solving the Floquet Hamiltonian numerically. We obtain exact analytical expressions of the quasienergies at the Dirac points for all values of $\alpha$ and field strength. We find that the quasienergy band gaps at the Dirac point decrease with increase of $\alpha$. Approximate forms of quasienergy and band gaps at single and multi-photon resonant points are derived using rotating wave approximation. The expressions reveal a stark dependence of quasienergy on the Berry phase of the charge carrier. The quasi energy flat band remains unaltered in presence of radiation for dice lattice ($\alpha=1$). However, it acquires a dispersion in and around the Dirac and even-photon resonant points when $0<\alpha<1$. The valley degeneracy and electron-hole symmetry in the quasienergy spectrum are broken for $0<\alpha<1$. Unlike graphene, the mean energy follows closely the linear dispersion of the Dirac cones till near the single-photon resonant point in dice lattice. There are additional peaks in the time-averaged density of states at the Dirac point for $0 < \alpha \leq 1$.

Large-amplitude Rapid X-Ray Variability in the Narrow-line Seyfert 1 Galaxy PG 1404+226

Abstract We present the first results from a detailed analysis of a new, long (∼100 ks) XMM-Newton observation of the narrow-line Seyfert 1 galaxy PG 1404+226, which showed a large-amplitude, rapid X-ray variability by a factor of ∼7 in ∼10 ks with an exponential rise and a sharp fall in the count rate. We investigate the origin of the soft X-ray excess emission and rapid X-ray variability in the source through time-resolved spectroscopy and fractional rms spectral modeling. The strong soft X-ray excess below 1 keV observed in both the time-averaged and time-resolved spectra is described by the intrinsic disk Comptonization model as well as the relativistic reflection model where the emission is intense merely in the inner regions ( ) of an ionized accretion disk. We detected no significant UV variability, while the soft X-ray excess flux varies together with the primary power-law emission (as ), although with a smaller amplitude, as expected in the reflection scenario. The observed X-ray fractional rms spectrum is approximately constant with a drop at ∼0.6 keV and is described by a non-variable emission line component with the observed energy of ∼0.6 keV and two variable spectral components: a more variable primary power-law emission and a less variable soft excess emission. Our results suggest the “lamppost geometry” for the primary X-ray-emitting hot corona, which illuminates the innermost accretion disk due to strong gravity and gives rise to the soft X-ray excess emission.

A physical model for the spectral-timing properties of accreting black holes

We develop new techniques to deconvolve the radial structure of the X-ray emission region in the bright low/hard state of the black hole Cygnus X-1 using both spectral and timing data in the 3-35~keV range. The spectrum at these energies is dominated by Comptonisation rather than the disc, but there is a complex pattern in the time lags between different energy bands and differences in the normalisation and shape in the power spectra of these bands, which clearly shows that the Comptonisation is not produced from a single, homogeneous region. We use a physically based model of density fluctuations propagating through a spectrally inhomogeneous flow, setting the spectral components by jointly fitting to the time-averaged and Fourier resolved spectra. The predicted variability in any band is modelled analytically in Fourier space so it can be fit directly to the observed power spectra and lags. We find that the best fit model picks out three distinct radii in the flow, each with a distinct Compton spectrum. The variability and luminosity produced at these radii is enhanced, while propagation of fluctuations from larger radii is suppressed. We associate these radii with the disc truncation, the inner edge of the flow, and (more speculatively) the jet launch radius. These distinct radii are most evident where the source is close to a transition between the low/hard and high/soft states. We suggest that the smoother power spectra seen at lower luminosities imply that the source structure is simpler away from the transition.

The nature of X-ray spectral variability in SWIFT J2127.4+5654

We study the flux-flux plots (FFPs) of the Seyfert galaxy SWIFT J2127.4+5654 which was observed simultaneously by XMM-Newton and NuSTAR. The 0.7-2 keV FFPs show a non-linear behaviour, while they are well fitted by a straight line, in the $\sim 2-40$ keV range. Without any additional modelling, this result strongly suggests that neither absorption nor spectral slope variations can contribute significantly to the observed variability above 2 keV (on time scales $\lesssim$5 days, at least). The FFP method is capable of separating the variable and the constant X-ray spectral components in this source. We found that the low-, average- and high-flux spectra of the variable components are consistent with a power law varying in normalisation only plus a relativistic reflection component varying simultaneously with the continuum. At low energies, we identify an additional variable component, consistent with a neutral absorber with a variable covering fraction. We also detect two spectral components whose fluxes remain constant over the duration of the observations. These components can be well described by a blackbody emission of $kT_{\rm BB}\sim 0.18\, \rm keV$, dominating at soft X-rays, and a reflection component from neutral material. The spectral model resulting from the FFP analysis can fit well the energy spectra of the source. We suggest that a combined study of FFPs and energy spectra in the case of X-ray bright and variable Seyferts can identify, unambiguously, the various spectral components, and can lift the degeneracy that is often observed within different models fitting equally well time-averaged spectra of these objects.

A Systematic Spectral-timing Analysis of Kilohertz Quasi-periodic Oscillations in the Rossi X-Ray Timing Explorer Archive

Kilohertz quasi-periodic oscillations or kHz QPOs occur on the orbital timescale of the inner accretion flow and may carry signatures of the physics of strong gravity (c$^{2}$ ~ GM/R) and possibly clues to constraining the neutron star equation of state (EOS). Both the timing behavior of kHz QPOs and the time-averaged spectra of these systems have been studied extensively, yet no model completely describes all the properties of kHz QPOs. Here, we present a systematic study of spectral-timing products of kHz QPOs from low-mass X-ray binary systems using archival Rossi X-ray Timing Explorer/Proportional Counter Array data. For the lower kHz QPOs in fourteen objects and the upper kHz QPOs in six, we were able to obtain correlated time-lags as a function of QPO frequency and energy, as well as energy-dependent covariance spectra and intrinsic coherence. For the lower kHz QPOs, we find a monotonic decrease in lags with increasing energy, rising covariance to ~12 keV, and near unity coherence at all energies. For the upper kHz QPOs, we find near zero lags, rising covariance to ~12 keV, and less well-constrained coherence at all energies. These results suggest that while kHz QPOs are likely produced by similar mechanisms across the population of LMXBs, the lower kHz QPOs are likely produced by a different mechanism than upper kHz QPOs

Pressure characteristics of hydrodynamic cavitation reactor due to the combination of Venturi tubes with multi-orifice plates

The pressure characteristics in the throats of Venturi tube and behind triangular multi-orifice plates were experimentally investigated by a pressure data acquisition system of SINOCERA-YE6263, and the effect of throat length of Venturi tube, different geometric parameters of multi-orifice plate and their combinations on the time-averaged pressure, cavitation number, and pressure frequency spectrum, correlation function calculated by FFT were analyzed. The experimental results showed that the throat length of L/R = 40 made for improving the fluctuation energy and promoting the uniform energy distribution, appropriately decreasing the size and increasing the number of orifice could accelerate the uniform distribution of the fluctuation energy in frequency domain. In the combination reactors, the cavitation number behind multi-orifice plates was lower and the fluctuation of correlation function was more intense.

Quasi ~500-year Cycle Signals in Solar Activity

Direct observations of solar activity are available for the past four century, so some proxies reflecting solar activity such as 14C, 10Be and geomagnetic variations are used to reconstruct solar activity in the past. In this present paper, the authors use rectified wavelet power transform and time-averaged wavelet power spectrum to investigate long-term fluctuations of the reconstructed solar activity series. Results show obvious a quasi ~500-year cycle exists in the past solar activity. Three reconstructed solar activity series from 14C variations confirm the periodic signals.

Comparison of forcing functions in magnetohydrodynamics

Results are presented of direct numerical simulations of incompressible, homogeneous magnetohydrodynamic turbulence without a mean magnetic field, subject to different mechanical forcing functions commonly used in the literature. Specifically, the forces are negative damping (which uses the large-scale velocity field as a forcing function), a nonhelical random force, and a nonhelical static sinusoidal force (analogous to helical ABC forcing). The time evolution of the three ideal invariants (energy, magnetic helicity and cross helicity), the time-averaged energy spectra, the energy ratios and the dissipation ratios are examined. All three forcing functions produce qualitatively similar steady states with regards to the time evolution of the energy and magnetic helicity. However, differences in the cross helicity evolution are observed, particularly in the case of the static sinusoidal method of energy injection. Indeed, an ensemble of sinusoidally-forced simulations with identical parameters shows significant variations in the cross helicity over long time periods, casting some doubt on the validity of the principle of ergodicity in systems in which the injection of helicity cannot be controlled. Cross helicity can unexpectedly enter the system through the forcing function and must be carefully monitored.

Continuous Wavelet Transform Analysis of Surface Electromyography for Muscle Fatigue Assessment on the Elbow Joint Motion

Studying muscle fatigue plays an important role in preventing the risks associated with musculoskeletal disorders. The effect of elbow-joint angle on time-frequency parameters during a repetitive motion provides valuable information in finding the most accurate position of the angle causing muscle fatigue. Therefore, the purpose of this study is to analyze the effect of muscle fatigue on the spectral and time-frequency domain parameters derived from electromyography (EMG) signals using the Continuous Wavelet Transform (CWT). Four male participants were recruited to perform a repetitive motion (flexion and extension movements) from a non-fatigue to fatigue condition. EMG signals were recorded from the biceps muscle. The recorded EMG signals were then analyzed offline using the complex Morlet wavelet. The time-frequency domain data were analyzed using the time-averaged wavelet spectrum (TAWS) and the Scale-Average Wavelet Power (SAWP) parameters. The spectral domain data were analyzed using the Instantaneous Mean Frequency (IMNF) and the Instantaneous Mean Power Spectrum (IMNP) parameters. The index of muscle fatigue was observed by calculating the increase of the IMNP and the decrease of the IMNF parameters. After performing a repetitive motion from non-fatigue to fatigue condition, the average of the IMNF value decreased by 15.69% and the average of the IMNP values increased by 84%, respectively. This study suggests that the reliable frequency band to detect muscle fatigue is 31.10-36.19Hz with linear regression parameters of 0.979mV^2Hz^(-1) and 0.0095mV^2Hz^(-1) for R^2 and slope, respectively.