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A high-resolution, temperature oscillation-based probe of physical aging in complex systems is introduced. The Fourier analysis of the measured responses allows one to extract high-order, aging-related nonlinearities that are not accessible via traditional temperature-jump and temperature-ramp procedures. To demonstrate the potential of this oscillatory approach, we analyze the periodic time evolution of glycerol's structural relaxation using shear rheology as a vehicle. Thereby, we access up to the sixth harmonic and detect aging fingerprints within a resolution range of three orders of magnitude for temperature amplitudes of up to 4 K. The even harmonics are present since aging is not symmetrical with respect to the direction of temperature change. The high-order aging coefficients obtained for glycerol are described reasonably well within the Tool–Narayanaswamy–Moynihan formalism. [ABSTRACT FROM AUTHOR]

A constraint satisfaction problem (CSP), \(\textsf {Max-CSP}(\mathcal {F})\) , is specified by a finite set of constraints \(\mathcal {F}\subseteq \lbrace [q]^k \rightarrow \lbrace 0,1\rbrace \rbrace\) for positive integers q and k. An instance of the problem on n variables is given by m applications of constraints from \(\mathcal {F}\) to subsequences of the n variables, and the goal is to find an assignment to the variables that satisfies the maximum number of constraints. In the (γ ,β)-approximation version of the problem for parameters 0 ≤ β ≤ γ ≤ 1, the goal is to distinguish instances where at least γ fraction of the constraints can be satisfied from instances where at most β fraction of the constraints can be satisfied. In this work, we consider the approximability of this problem in the context of sketching algorithms and give a dichotomy result. Specifically, for every family \(\mathcal {F}\) and every β < γ, we show that either a linear sketching algorithm solves the problem in polylogarithmic space or the problem is not solvable by any sketching algorithm in \(o(\sqrt {n})\) space. In particular, we give non-trivial approximation algorithms using polylogarithmic space for infinitely many constraint satisfaction problems. We also extend previously known lower bounds for general streaming algorithms to a wide variety of problems, and in particular the case of q=k=2, where we get a dichotomy, and the case when the satisfying assignments of the constraints of \(\mathcal {F}\) support a distribution on \([q]^k\) with uniform marginals. Prior to this work, other than sporadic examples, the only systematic classes of CSPs that were analyzed considered the setting of Boolean variables q = 2, binary constraints k =2, and singleton families \(|\mathcal {F}|=1\) and only considered the setting where constraints are placed on literals rather than variables. Our positive results show wide applicability of bias-based algorithms used previously by [47] and [41], which we extend to include richer norm estimation algorithms, by giving a systematic way to discover biases. Our negative results combine the Fourier analytic methods of [56], which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results. In particular, previous works used Fourier analysis over the Boolean cube to initiate their results and the results seemed particularly tailored to functions on Boolean literals (i.e., with negations). Our techniques surprisingly allow us to get to general q-ary CSPs without negations by appealing to the same Fourier analytic starting point over Boolean hypercubes. [ABSTRACT FROM AUTHOR]

Aiming at the problem of early inter-turn short circuit fault of axial flux stator coreless motor, a method for early inter-turn short circuit fault diagnosis and positioning of axial flux stator coreless motor based on the phase difference of zero sequence component and stator current component was proposed. Firstly, according to the characteristics of extremely small stator winding inductance, a mathematical model of inter-turn short circuit fault was established. Secondly, Fourier analysis of the short-circuit current, phase current and zero-sequence component before and after the fault was carried out, and the inter-turn short-circuit fault was identified by the change of the amplitude of the zero-sequence voltage fundamental wave.Finally, the fault phase was located by comparing the initial phase difference between the zero-sequence voltage fundamental wave and the stator three-phase current. The results show that the absolute value of the difference between initial phase of the phase current fundamental wave and the initial phase of the zero sequence voltage fundamental wave of the inter-turn short-circuit fault phase is approximately 180°, while the phase difference of the healthy phase is quite different from 180°. Based on the phase difference, the diagnosis and positioning of the early inter-turn short circuit fault of axial flux ironless motor can be realized, which provides some reference for the diagnosis of inter-turn short circuit fault of permanent magnet motor.

Abstract Transformer inrush current occurs due to the saturation of magnetic core. The magnetic characteristic of the core directly affects the inrush current waveform. Second harmonic and higher‐order harmonics are present in the inrush harmonic spectrum. A harmonic‐based method analysing the amplitude and phase of different harmonics is presented here. Based on the proposed method, the differences between the harmonic spectrum of new low‐loss and previous‐generation materials are investigated. Then, using the patterns of 1st to 10th harmonic phases, a novel method for inrush current detection is proposed. In the proposed method, possible patterns for the harmonic phases related to the inrush current are specified. The harmonic phases are compared with those specified patterns. In the case of matching, the inrush current condition is detected. To evaluate the theoretical principles, simulations are performed, also, the proposed method is applied to the field data to assess the practical performance, and results are presented.

The aim of this work is to quantitatively assess the wavefront phase of keratoconic eyes measured by the ocular aberrometer t·eyede (based on WaveFront Phase Imaging Sensor), characterized by a lateral resolution of 8.6 µm without requiring any optical element to sample the wavefront information. We evaluated the parameters: root mean square error, Peak-to-Valley, and amplitude of the predominant frequency (Fourier Transform analysis) of a section of the High-Pass filter map in keratoconic and healthy cohorts. Furthermore, we have analyzed keratoconic eyes that presented dark–light bands in this map to assess their period and orientation with the Fourier Transform. There are significant statistical differences (p value < 0.001) between healthy and keratoconic eyes in the three parameters, demonstrating a tendency to increase with the severity of the disease. Otherwise, the quantification of the bands reveals that the width is independent of eye laterality and keratoconic stage as orientation, which tends to be oblique. In conclusion, the quantitative results obtained with t·eyede could help to diagnose and monitor the progression of keratoconus. [ABSTRACT FROM AUTHOR]

Due to its applications in signal analysis and image processing, the quaternionic Fourier analysis has received increasing attention. In particular, quaternionic Gabor frames (QGFs) attracted some mathematicians' interest. From the literatures, some results on QGFs are based on quaternionic Fourier orthonormal bases. But those used so-called quaternionic Fourier orthonormal bases have a gap that they are all incomplete. In this paper, we present a class of quaternionic Fourier orthonormal bases, and using them derive the corresponding Gabor orthonormal bases. [ABSTRACT FROM AUTHOR]

Tidally excited oscillations (TEOs) in Heartbeat Stars (HBSs) are an essential probe of the internal properties of the systems, but their potential has yet to be fully exploited. Based on the orbital parameters of TEO candidates from our previous works, we identify the pulsation phases and amplitudes of TEOs in 14 Kepler HBSs. Most pulsation phases of most systems can be explained by the dominant being l  = 2, m  = 0, or ±2 spherical harmonic, assuming that the spin and orbital axes are aligned, and the pulsations are adiabatic and standing waves. The largest deviation (>6σ) occurs in KIC 8459354, which can be explained by the spin-orbit misalignment, and KIC 5877364 has a similar scenario. For KIC 11122789, almost half of the harmonics show large deviations; we cautiously suggest that these harmonics may not be considered TEO candidates. A similar scenario also exists in KIC 6290740. This phases and mode identification approach can also be used inversely to verify the TEO candidates derived by the Fourier analysis. Furthermore, the harmonics with large deviations (>2σ) in KIC 4377638, KIC 5090937, and KIC 11403032 can be expected to be travelling waves rather than standing waves. In addition, we also suggest that the apsidal motion could cause large deviations in TEO phases from theoretical values. [ABSTRACT FROM AUTHOR]

In the general setting of long‐memory multivariate time series, the long‐memory characteristics are defined by two components. The long‐memory parameters describe the autocorrelation of each time series. And the long‐run covariance measures the coupling between time series, with general phase parameters. It is of interest to estimate the long‐memory, long‐run covariance and general phase parameters of time series generated by this wide class of models although they are not necessarily Gaussian nor stationary. This estimation is thus not directly possible using real wavelets decomposition or Fourier analysis. Our purpose is to define an inference approach based on a representation using quasi‐analytic wavelets. We first show that the covariance of the wavelet coefficients provides an adequate estimator of the covariance structure including the phase term. Consistent estimators based on a local Whittle approximation are then proposed. Simulations highlight a satisfactory behavior of the estimation on finite samples on multivariate fractional Brownian motions. An application on a real neuroscience dataset is presented, where long‐memory and brain connectivity are inferred. [ABSTRACT FROM AUTHOR]

An in‐depth study and analysis of the stability of one‐dimensional Linear System of PDEs via Caputo time fractional derivative (LSCFD) was presented. We proved some stability results for the LSCFD in different Hilbert spaces. Indeed, by using Fourier analysis method and the properties of the Mittag–Leffler Function (MLF), some polynomial stability results for LSCFD have been established. Finally, as an application, we used finite difference methods well suited to integer and fractional order derivatives, and performed some numerical experiments to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

This study is a continuation of pilot research on the relationships between seismic activity and changes in very low frequency (VLF) signals starting a few minutes or a few dozen minutes before an earthquake. These changes are recorded in the time and frequency domains and their duration can be influenced not only by the strongest earthquake but also by others that occur in a short time interval. This suggests that there are differences in these changes in cases of individual earthquakes and during the period of intense seismic activity (PISA). In a recent study, they were validated in the time domain by comparing the amplitude noise reductions during the PISA and before earthquakes that occurred in the analysed periods without intense seismic activity (PWISA). Here, we analyse the changes in the VLF signal amplitude in the frequency domain during the PISA and their differences are compared to the previously investigated relevant changes during PWISA. We observe the signal emitted by the ICV transmitter in Italy and received in Serbia from 26 October to 2 November 2016 when 907 earthquakes occurred in Central Italy. The study is based on analyses of the Fourier amplitude A F obtained by applying the fast Fourier transform (FFT) to the values of the ICV signal amplitude sampled at 0.1 s. The obtained results confirm the existence of one of the potential earthquake precursors observed during PWISA: significantly smaller values of A F for small wave periods (they can be smaller than 10 − 3 dB) than under quiet conditions (the expected values are larger than 10 − 2 dB). Exceptions were the values of A F for wave periods between 1.4 s and 2 s from a few days before the observed PISA to almost the end of that period. They were similar or higher than the values expected under quiet conditions. The mentioned decrease lasted throughout the observed longer period from 10 October to 10 November, with occasional normalisation. It was many times longer than the decreases in A F around the considered earthquakes during PWISA, which lasted up to several hours. In addition, no significant wave excitations were recorded at discrete small values of the wave periods during the PISA, as was the case for earthquakes during PWISA. These differences indicate the potential possibility of predicting the PISA if the corresponding earthquake precursors are recorded. Due to their importance for potential warning systems, they should be analysed in more detail in future statistical studies. [ABSTRACT FROM AUTHOR]

AbstractThe convergence behavior of a two-dimensional (2D) transport method has been derived by Fourier analysis for single-group problems with isotropic sources. However, in real calculation, to pursue precision, a high-order scattering source is a common option, and its influence on convergence performance is worth investigating. No theoretical convergence study of a 2D transport method for multigroup problems with high-order scattering sources was previously performed, but it is important work that would complement existing studies. This study presents a Fourier analysis for solving multigroup problems with high-order scattering. First, the influences of the number of inner iterations for the multigroup isotropic scattering problem are analyzed. It is found that with an increase of the number of inner iterations, the spectral radius decreases and finally reaches an asymptotic value. When the scattering ratio is increased, more inner iterations are required to reach the asymptotic value. Then, the influences of high-order scattering are analyzed. The Fourier analysis results show that for high-order scattering source problems, the influence of the number of inner iterations is different from the isotropic scattering case. The influences of first-order scattering and second-order scattering are not the same. With an increase of first-order scattering, the spectral radius first decreases in the small optical thickness region and then increases in the large optical thickness region, which may lead to the divergence of iterations. If second-order scattering is not too large, an increase of second-order scattering decreases the spectral radius for all optical thickness regions. First-order scattering and second-order scattering that are too large may result in an unpredictable slope of the spectral radius for optical thicknesses between 10−1 and 1. [ABSTRACT FROM AUTHOR]

The study presents a bioindication complex and a technology of the experiment based on a submersible digital holographic camera with advanced monitoring capabilities for the study of plankton and its behavioral characteristics in situ. Additional mechanical and software options expand the capabilities of the digital holographic camera, thus making it possible to adapt the depth of the holographing scene to the parameters of the plankton habitat, perform automatic registration of the "zero" frame and automatic calibration, and carry out natural experiments with plankton photostimulation. The paper considers the results of a long-term digital holographic experiment on the biotesting of the water area in Arctic latitudes. It shows additional possibilities arising during the spectral processing of long time series of plankton parameters obtained during monitoring measurements by a submersible digital holographic camera. In particular, information on the rhythmic components of the ecosystem and behavioral characteristics of plankton, which can be used as a marker of the ecosystem well-being disturbance, is thus obtained. [ABSTRACT FROM AUTHOR]

Considering Africa's increasing electricity demands and the pivotal role of electricity in socioeconomic development, this study addresses a research gap in understanding the stochastic properties of per capita electricity consumption in African contexts. Through examining the integration properties of per capita electricity consumption across 19 African countries, the research determines whether 'shocks' yield transitory or permanent effects, aiding policy formulation and future demand forecasting. Annual electric power consumption data (1971 – 2014) (kWh per capita) from the WDI across 19 African countries are used. Our methodology starts with formally testing for cross-sectional dependence (CSD) using various tests to avoid potential size distortions. Subsequently, we employ the novel panel stationarity test of Nazlioglu and Karul (2017), a Fourier KPSS panel stationarity test. The robustness of the analysis is enriched by incorporating the Hadri and Kurozumi (2011) panel stationarity test and Nazlioglu et al. (2021) new panel stationary tests. The CSD test results reveal mutual dependency in electricity consumption among the sampled African countries, underscoring the need for a panel testing methodology that accommodates CSD. The results of the panel stationarity tests that allow CSD and structural breaks—specifically, the Nazlioglu and Karul (2017) test, which models structural breaks as a gradual process—reject the null hypothesis of trend stationarity for both single frequencies, i.e., k =1, and 2. Similarly, all new, complementary panel stationarity tests from Nazlioglu et al. (2021) reject the null hypothesis of stationarity for both frequencies. Collectively, the outcomes from various panel stationarity tests present strong evidence of nonstationary per capita electricity consumption within the sampled African countries. Additionally, the Nazlioglu and Karul panel stationarity test enables an analysis of the individual Fourier KPSS test for cross-sectional units in the panel. Of the 19 countries, only Togo does not reject the null hypothesis of stationarity for both frequencies. These individual country results align with the panel outcomes, providing compelling evidence for the nonstationarity of the per capita electricity consumption series across the investigated African nations. Accordingly, shocks to electricity consumption will have permanent effects, indicating that per capita electricity consumption will not return to its pre-shock equilibrium path. In this case, demand or consumption stabilizing policies will have long-run effects. [ABSTRACT FROM AUTHOR]

Background: A next generation tomosynthesis (NGT) system, capable of two‐dimensional source motion, detector motion in the perpendicular direction, and magnification tomosynthesis, was constructed to investigate different acquisition geometries. Existing position‐based geometric calibration methods proved ineffective when applied to the NGT geometries. Purpose: A line‐based iterative calibration method is developed to perform accurate geometric calibration for the NGT system. Methods: The proposed method calculates the system geometry through virtual line segments created by pairs of fiducials within a calibration phantom, by minimizing the error between the line equations computed from the true and estimated fiducial projection pairs. It further attempts to correct the 3D fiducial locations based on the initial geometric calibration. The method's performance was assessed via simulation and experimental setups with four distinct NGT geometries: X, T, XZ, and TZ. The X geometry resembles a conventional DBT acquisition along the chest wall. The T geometry forms a "T"‐shaped source path in mediolateral (ML) and posteroanterior (PA) directions. A descending detector motion is added to both X and T geometries to form the XZ and TZ geometries, respectively. Simulation studies were conducted to assess the robustness of the method to geometric perturbations and inaccuracies in fiducial locations. Experimental studies were performed to assess the impact of phantom magnification and the performance of the proposed method for various geometries, compared to the traditional position‐based method. Star patterns were evaluated for both qualitative and quantitative analyses; the Fourier spectral distortions (FSDs) graphs and the contrast transfer function (CTF) were extracted. The limit of spatial resolution (LSR) was measured at 5% modulation of the CTF. Results: The proposed method presented is highly robust to geometric perturbation and fiducial inaccuracies. After the line‐based iterative method, the mean distance between the true and estimated fiducial projections was [X, T, XZ, TZ]: [0.01, 0.01, 0.02, 0.01] mm. The impact of phantom magnification was observed; a contact‐mode acquisition of a calibration phantom successfully provided an accurate geometry for 1.85× magnification images of a star pattern, with the X geometry. The FSD graphs for the contact‐mode T geometry acquisition presented evidence of super‐resolution, with the LSR of [0°‐quadrant: 8.57, 90°‐quadrant: 8.47] lp/mm. Finally, a contact‐mode XZ geometry acquisition and a 1.50× magnification TZ geometry acquisition were reconstructed with three calibration methods—position‐based, line‐based, and iterative line‐based. As more advanced methods are applied, the CTF becomes more isotropic, the FSD graphs demonstrate less spectral leakage as super‐resolution is achieved, and the degree of blurring artifacts reduces significantly. Conclusions: This study introduces a robust calibration method tailored to the unique requirements of advanced tomosynthesis systems. By employing virtual line segments and iterative techniques, we ensure accurate geometric calibration while mitigating the limitations posed by the complex acquisition geometries of the NGT system. Our method's ability to handle various NGT configurations and its tolerance to fiducial misalignment make it a superior choice compared to traditional calibration techniques. [ABSTRACT FROM AUTHOR]

Transformer inrush current occurs due to the saturation of magnetic core. The magnetic characteristic of the core directly affects the inrush current waveform. Second harmonic and higher‐order harmonics are present in the inrush harmonic spectrum. A harmonic‐based method analysing the amplitude and phase of different harmonics is presented here. Based on the proposed method, the differences between the harmonic spectrum of new low‐loss and previous‐generation materials are investigated. Then, using the patterns of 1st to 10th harmonic phases, a novel method for inrush current detection is proposed. In the proposed method, possible patterns for the harmonic phases related to the inrush current are specified. The harmonic phases are compared with those specified patterns. In the case of matching, the inrush current condition is detected. To evaluate the theoretical principles, simulations are performed, also, the proposed method is applied to the field data to assess the practical performance, and results are presented. [ABSTRACT FROM AUTHOR]

A robust, in situ estimate of shear-wave velocity VS and the small-strain damping ratio DS (or equivalently, the quality factor QS) is crucial for the design of buildings and geotechnical systems subjected to vibrations or earthquake ground shaking. A promising technique for simultaneously obtaining both VS and DS relies on the Multichannel Analysis of Surface Waves (MASW) method. MASW can be used to extract the Rayleigh wave phase velocity and phase attenuation data from active-source seismic traces recorded along linear arrays. Then, these data can be inverted to obtain VS and DS profiles. This paper introduces two novel methodologies for extracting the phase velocity and attenuation data. These new approaches are based on an extension of the beamforming technique which can be combined with a modal filter to isolate different Rayleigh propagation modes. Thus, the techniques return reliable phase velocity and attenuation estimates even in the presence of a multimode wavefield, which is typical of complex stratigraphic conditions. The reliability and effectiveness of the proposed approaches are assessed on a suite of synthetic wavefields and on experimental data collected at the Garner Valley Downhole Array and Mirandola sites. The results reveal that, under proper modelling of wavefield conditions, accurate estimates of Rayleigh wave phase velocity and attenuation can be extracted from active-source MASW wavefields over a broad frequency range. Eventually, the estimation of soil mechanical parameters also requires a robust inversion procedure to map the experimental Rayleigh wave parameters into soil models describing VS and DS with depth. The simultaneous inversion of phase velocity and attenuation data is discussed in detail in the companion paper. [ABSTRACT FROM AUTHOR]

The transient Stokes magnetohydrodynamic (Stokes MHD) equations are thoroughly investigated in this paper using the variational subgrid multiscale stabilized finite element approach. In order to get the optimal order of convergence, appropriate stabilization parameter expressions have been derived using Fourier analysis. The theoretical convergence analysis of the subgrid algebraic stabilized numerical scheme is also presented in this study. The numerical studies on multiply-driven cavity flow establish the credibility of the variational algebraic subgrid multiscale stabilized finite element approach. Further, the theoretically determined convergence rate is numerically validated. For different Hartmann, Reynolds, and magnetic force inclination angle values, the flow fields are traced. [ABSTRACT FROM AUTHOR]

This paper conducts the analytical investigation on the buckling of cylindrical shells with axially variable elastic modulus subjected to axial compressive load for the first time. First, it proves that the axially distributed elastic modulus can be expressed as the combination of constant and variable component. Then, governing differential equations for buckling analysis are derived and exactly solved by the combined perturbation method and Fourier analysis. Accordingly, the closed analytical solutions for the cylinder with arbitrarily variable elastic modulus are obtained, which reveal the explicit relations among buckling load, shell sizes and elastic modulus functions. Based on the presented analytical formulas, four types of elastic modulus variations for shell material which are uniform, periodic, linear and combined are studied in detail, and the results are also well verified. The derived analytical solutions in this paper can serve as benchmarks for buckling analyses of thin-walled cylinders with elastic modulus variations resulted from design, material manufacturing process, material imperfections and so on. [ABSTRACT FROM AUTHOR]

The results of a Fourier analysis of high-precision Kepler photometry of 75 double-mode RR Lyrae (RRd) stars observed during NASA's K2 Mission (2014-18) are presented. Seventy-two of the stars are 'classical' RRd (cRRd) stars lying along a well-defined curve in the Petersen diagram and showing no evidence of Blazhko modulations. The remaining three stars are 'anomalous' RRd (aRRd) stars that lie well below the cRRd curve in the Petersen diagram. These stars have larger fundamental-mode amplitudes than first-overtone amplitudes and exhibit Blazhko variations. Period-amplitude relations for the individual pulsation components of the cRRd stars are examined, as well as correlations involving Fourier phase-difference and amplitude-ratio parameters that characterize the light curves for the two radial modes. A simple statistical model relating the fundamental (P 0) and first-overtone (P 1) periods to [Fe/H] provides insight into the functional form of the Petersen diagram. A calibration equation for estimating [Fe/H]phot abundances of 'classical' RRd stars is derived by inverting the model and using 211 field and 57 globular cluster cRRd stars with spectroscopic metallicities to estimate the model coefficients. The equation is used to obtain [Fe/H]phot for the full sample of 72 K2 cRRd stars and for 2130 cRRd stars observed by the ESA Gaia Mission. Of the 49 K2 cRRd stars that are in the Gaia DR3 catalogue only five were found to be correctly classified, the remainder having been misclassified 'RRc' or 'RRab'. [ABSTRACT FROM AUTHOR]

In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type of discretization and problem. The presented framework is crucial in practice since it allows one to know a priori the answer to questions such as what is the size of the patch to use within these relaxations, the size of the overlap, or even the optimal values for the weights involved in the smoother. Results are shown for a class of additive and restricted additive Schwarz relaxations used within a multigrid framework applied to high-order finite-element discretizations and saddle point problems, which are two of the contexts in which these types of relaxations are widely used. [ABSTRACT FROM AUTHOR]

The creation of an explicit finite difference scheme with the express purpose of resolving initial boundary value issues with linear and semi-linear variable-order temporal fractional properties is presented in this study. The rationale behind the utilization of the Caputo derivative in this scheme stems from its known importance in fractional calculus, an area of study that has attracted significant interest in the mathematical sciences and physics. Because of its special capacity to accurately represent physical memory and inheritance, the Caputo derivative is a relevant and appropriate option for representing the fractional features present in the issues this study attempts to address. Moreover, a detailed Fourier analysis of the explicit finite difference scheme's stability is shown, demonstrating its conditional stability. Finally, certain numerical example solutions are reviewed and MATLAB-based graphic presentations are made. [ABSTRACT FROM AUTHOR]

This work presents a post-data analysis procedure, namely, proper orthogonal decomposition (POD)–dynamic mode decomposition (DMD)–discrete Fourier transform analysis, for evaluating the dominant features of the flow fields from both energetic and dynamic perspectives. The large-eddy simulation (LES) was first employed to reproduce the flow field surrounding three types of building layouts. Subsequently, both POD and DMD were conducted according to LES simulation results. The extracted modes were classified into three types based on the POD and DMD: Type-1 mode: energetically and dynamically significant mode, Type-2 mode: energetically significant and dynamically insignificant mode, and Type-3 mode: energetically insignificant and dynamically significant mode. The findings indicate that Type-1 mode governs the primary velocity field and the predominant vortex patterns observed at the rear of the building arrays, as the reduction of inter-building widths leads to a shorter flow separation region. Type-2 mode is characterized by the presence of small-scale vortices and the high turbulent kinetic energy region, which periodically triggers pollutant increase in the vicinity of structures. Type-3 mode demonstrates a minimal energetic influence on the flow field; nevertheless, it significantly contributes to the consistent build-up of pollutants within the far-wake region. The present study also investigates the predominant coherent structures of flow fields concerning various building layouts and highlights the influence of passage widths on the efficiency of pollutant removal. This comprehensive analysis enables a systematic exploration of flow patterns within various building layouts, offering potential solutions for pollutant dispersion challenges in metropolitan areas. [ABSTRACT FROM AUTHOR]

We study the homogeneously precessing domain (HPD) in superfluid 3 He-B in a regular continuous-wave nuclear magnetic resonance (CW NMR) experiment. Using Fourier analysis of CW NMR time traces, we identify several oscillation modes with frequency monotonically increasing with the frequency shift of the HPD. Some of these modes are localized near the cell walls, while others are localized in bulk liquid and can be interpreted as oscillations of ϑ -solitons. We also observe chaotic motion of the HPD in a certain range of temperatures and frequency shifts. [ABSTRACT FROM AUTHOR]

Among unmanned surface vehicle (USV) components, underwater thrusters are pivotal in their mission execution integrity. Yet, these thrusters directly interact with marine environments, making them perpetually susceptible to malfunctions. To diagnose thruster faults, a non-invasive and cost-effective vibration-based methodology that does not require altering existing systems is employed. However, the vibration data collected within the hull is influenced by propeller-fluid interactions, hull damping, and structural resonant frequencies, resulting in noise and unpredictability. Furthermore, to differentiate faults not only at fixed rotational speeds but also over the entire range of a thruster's rotational speeds, traditional frequency analysis based on the Fourier transform cannot be utilized. Hence, Continuous Wavelet Transform (CWT), known for attributions encapsulating physical characteristics in both time-frequency domain nuances, was applied to address these complications and transform vibration data into a scalogram. CWT results are diagnosed using a Vision Transformer (ViT) classifier known for its global context awareness in image processing. The effectiveness of this diagnosis approach was verified through experiments using a USV designed for field experiments. Seven cases with different fault types and severity were diagnosed and yielded average accuracy of 0.9855 and 0.9908 at different vibration points, respectively. [ABSTRACT FROM AUTHOR]

A three-phase multilevel inverter (MLI), synthesized with 31 levels in regard to its output voltage, is used to provide the AC supply to a three-phase, squirrel cage induction motor. The gating angles required for the 30 power switches on the MLI are optimized using both the genetic algorithm (GA) and the grey wolf optimizer (GWO), in which the optimal angles are determined through solving the trigonometric equations taken from Fourier analysis to target the minimum total harmonic distortion (THD) at the MLI output. A simulation model and an experimental prototype are developed for performance analysis and validation. The results demonstrate that the MLI is effectively able to produce 31 levels of three-phase AC output voltage, with the THD not exceeding 5% when loaded with a resistive load and a three-phase induction motor. The voltage and current are measured and recorded for different loads and operating conditions, including the amount of energy consumed by the load. The results of the frequency analysis demonstrate that most of the triple harmonics, which can harm the efficiency of the inverter, are cancelled. [ABSTRACT FROM AUTHOR]

The warp is a well-known undulation of the Milky Way disc. Its structure has been widely studied, but only since Gaia DR2 has it been possible to reveal its kinematic signature beyond the solar neighbourhood. In this work, we present an analysis of the warp traced by Classical Cepheids by means of a Fourier decomposition of their height (Z) and, for the first time, of their vertical velocity (Vz). We find a clear but complex signal that in both variables reveals an asymmetrical warp. In Z , we find the warp to be almost symmetric in amplitude at the disc's outskirts, with the two extremes never being diametrically opposed at any radius and the line of nodes presenting a twist in the direction of stellar rotation for R > 11 kpc. For Vz , in addition to the usual m  = 1 mode, an m  = 2 mode is needed to represent the kinematic signal of the warp, reflecting its azimuthal asymmetry. The line of maximum vertical velocity is similarly twisted as the line of nodes and trails behind by ≈25°. We develop a new formalism to derive the pattern speed and change in amplitude with time |$\dot{A}$| of each Fourier mode at each radius, via a joint analysis of the Fourier decomposition in Z and Vz. By applying it to the Cepheids we find, for the m  = 1 mode, a constant pattern speed in the direction of stellar rotation of 9.2 ± 3.1 km s−1 kpc−1, a negligible |$\dot{A}$| up to R ≈ 14 kpc and a slight increase at larger radii, in agreement with previous works. [ABSTRACT FROM AUTHOR]

Continuing our earlier work in Nam et al. (One-step replica symmetry breaking of random regular NAE-SAT I, arXiv:2011.14270, 2020), we study the random regular k-nae-sat model in the condensation regime. In Nam et al. (2020), the (1rsb) properties of the model were established with positive probability. In this paper, we improve the result to probability arbitrarily close to one. To do so, we introduce a new framework which is the synthesis of two approaches: the small subgraph conditioning and a variance decomposition technique using Doob martingales and discrete Fourier analysis. The main challenge is a delicate integration of the two methods to overcome the difficulty arising from applying the moment method to an unbounded state space. [ABSTRACT FROM AUTHOR]

For site characterization, the elliptic particle motion of Rayleigh waves and its frequency dependence is a well-known property that aroused less interest than the frequency dependence of the phase velocity. More than 50 yr ago, ellipticity was already recognized as providing information independent from phase velocity, despite the difficulties inherent to its accurate and precise measurement. Several techniques were developed during the last two decades to extract the ellipticity curve from ambient vibration recordings, with a single three-component (3C) station, with pairs of 3C stations and more recently with 3C arrays. The latter has the advantage over the other approaches that the sign of the ellipticity can be retrieved. Moreover, higher order mode separation is possible under certain conditions. Nevertheless, Rayleigh Three-component BeamForming (RTBF) proposed by Wathelet et al. encounters difficulties in the presence of significant levels of incoherent noise when the true ellipticity is vanishing or when it has a high absolute value. In this work, the analytical expressions of the beam power for a single source wavefield are revised under more realistic assumptions for the incoherent noise azimuthal distribution. The proposed model also includes an asymmetric distribution of the incoherent noise between vertical and horizontal components, which was not the case in the original publication. Switching from ellipticity to angular ellipticity drastically simplifies the formalism. Moreover, it naturally leads to a new steering matrix (all-component ellipticity steering) which solves the limitation around zero and infinity observed for RTBF. Interestingly, the accuracy of the ellipticity is no longer influenced by the absolute level of incoherent noise but by the difference between the incoherent noise ratio on vertical and horizontal components. A method based on the second derivative of the beam power versus the radial wavenumber is finally proposed to experimentally measure the noise ratio difference, which allows experimental values to be corrected. The methodology is compared with classical vertical beamforming and RTBF for a synthetic case and three experimental data sets. [ABSTRACT FROM AUTHOR]

We study the singularity formation of a quasi-exact 1D model proposed by Hou and Li (2008 Commun. Pure Appl. Math. 61 661–97). This model is based on an approximation of the axisymmetric Navier–Stokes equations in the r direction. The solution of the 1D model can be used to construct an exact solution of the original 3D Euler and Navier–Stokes equations if the initial angular velocity, angular vorticity, and angular stream function are linear in r. This model shares many intrinsic properties similar to those of the 3D Euler and Navier–Stokes equations. It captures the competition between advection and vortex stretching as in the 1D De Gregorio (De Gregorio 1990 J. Stat. Phys. 59 1251–63; De Gregorio 1996 Math. Methods Appl. Sci. 19 1233–55) model. We show that the inviscid model with weakened advection and smooth initial data or the original 1D model with Hölder continuous data develops a self-similar blowup. We also show that the viscous model with weakened advection and smooth initial data develops a finite time blowup. To obtain sharp estimates for the nonlocal terms, we perform an exact computation for the low-frequency Fourier modes and extract damping in leading order estimates for the high-frequency modes using singularly weighted norms in the energy estimates. The analysis for the viscous case is more subtle since the viscous terms produce some instability if we just use singular weights. We establish the blowup analysis for the viscous model by carefully designing an energy norm that combines a singularly weighted energy norm and a sum of high-order Sobolev norms. [ABSTRACT FROM AUTHOR]

In this paper, we propose and demonstrate a new method for measuring the trap frequency from the fluorescence dynamics of an ion, initiated using fast trap-center displacement. Here, we observe the coherently excited motion of an ion in a harmonic trap using time-resolved fluorescence detection. Furthermore, Fourier analysis of the ion fluorescence signal was used to determine the trap frequency of an ion with high precision and reproducibility. The results show that our proposed method can be an alternative way to determine trap frequencies in an ion trap experiment. [ABSTRACT FROM AUTHOR]

In part I of the article, we demonstrated that a variant of the dynamic mode decomposition (DMD) algorithm based on variable projection optimization, called optimized DMD (OPT-DMD), enables a robust identification of the dominant spatiotemporally coherent modes underlying the data across various test cases representing different physical parameters in an E × B simulation configuration. We emphasized that the OPT-DMD significantly improves the analysis of complex plasma processes, revealing information that cannot be derived using conventionally employed analyses such as the fast Fourier transform. As the OPT-DMD can be constrained to produce stable reduced-order models (ROMs) by construction, in this paper, we extend the application of the OPT-DMD and investigate the capabilities of the linear ROM from this algorithm toward forecasting in time of the plasma dynamics in configurations representative of the radial-azimuthal and axial-azimuthal cross-sections of a Hall thruster and over a range of simulation parameters in each test case. The predictive capacity of the OPT-DMD ROM is assessed primarily in terms of short-term dynamics forecast or, in other words, for large ratios of training-to-test data. However, the utility of the ROM for long-term dynamics forecasting is also presented for an example case in the radial-azimuthal configuration. The model's predictive performance is heterogeneous across various test cases. Nonetheless, a remarkable predictiveness is observed in the test cases that do not exhibit highly transient behaviors. Moreover, in all investigated cases, the error between the ground-truth and the reconstructed data from the OPT-DMD ROM remains bounded over time within both the training and the test window. As a result, despite its limitation in terms of generalized applicability to all plasma conditions, the OPT-DMD is proven as a reliable method to develop low computational cost and highly predictive data-driven ROMs in systems with a quasi-periodic global evolution of the plasma state. [ABSTRACT FROM AUTHOR]

This article, titled "Approximation of Periodic Functions of High Generalized Smoothness by Fourier Sums," discusses the conditions under which Fourier sums provide the best approximation for periodic functions with high generalized smoothness. The article presents necessary and sufficient conditions for the generator of a generalized derivative, and explores the cases where the best order of approximation is not achieved by partial Fourier sums or de la Vallée-Poussin means. The article also introduces Theorem 1, which provides a criterion for determining when Fourier sums provide the best approximation. The authors conclude that the quality of approximation by partial Fourier sums depends on the scale of generators and the behavior of the function and its derivative. The article was published in Mathematical Notes in 2024 and was written by N. V. Laktionova and K. V. Runovskii. [Extracted from the article]

This work is conducted to improve the electrochemical performance of PANI with the incorporation of spinel‐type transition metal oxide, that is, 1 wt.% of nickel ferrite (NiFe2O4) (NF). The addition of NiFe2O4 into the PANI matrix is accomplished via in situ oxidative polymerization approach at a very low temperature (0‐5°C). It is observed that the various valence states of NiFe2O4 in the electrolytic ions considerably increase due to formation of a well‐interconnected conducting network with PANI. The requisite interaction of PANI/NiFe2O4 is verified by Raman analysis and Fourier Transform Infrared Spectroscopy (FTIR). PANI1:1/NF1 ratio of the composite facilitates strong conducting route improving delocalization of the electrons in the polymeric chain resulting in extra stability of the system. It is observed that NF nanoparticles fills the gaps in the polymeric matrix rendering to attain highest specific capacitance of 758 F g−1 of the PANI 1:1/NF1 electrode cell as compared to bare PANI1:1 (677 F g−1), PANI1:2 (500 F g−1), NF (253 F g−1) and other PANI1:2/NF2 (686 F g−1) samples at 10mV/s. The PANI1:1 device also shows energy density ~ 54 W kg−1 at 0.3 mA/cm2 with corresponding power density at ~1705 W kg−1, and the cyclic stability ~97% after 10,000 GCD cycles. The said device also exhibits a lower charge transfer resistance (Rct) 0.35 Ω as compared to other fabricated devices. NiFe2O4 acts as a 'superhighway' for charge transportation between PANI, which is beneficial for supercapacitors. [ABSTRACT FROM AUTHOR]

In the present study, poly(N‐Isopropylacrylacrylamide‐co‐N‐tertiarybutylacrylamide‐co‐hydroxyethylcrylamide) (NIPAM‐co‐NTBA‐co‐HEAAm) hydrogels are prepared with variation of molar ratio of hydrophilic HEAAm and hydrophobic NTBA. The prepared hydrogels are characterized with elemental analysis and Fourier transform infrared (FTIR) spectroscopy. The thermodynamics of swelling properties of poly(NIPAM‐co‐NTBA‐co‐HEAAm) hydrogels have also been discussed. The experimental C/N ratios are comparable with the theoretical value. The enthalpy change of mixing ∆Hmix, entropy change of mixing ∆Smix, free energy change of mixing ∆Gmix are determined for swelling of hydrogels at 25 °C. The value of total free energy of hydrogel swelling is found to be negative which confirms the lower critical solution temperature (LCST) exhibited in all hydrogels and the volume change transition shows the thermoresponsive behavior. The values of ∆Smix increase and ∆Gmix decrease with increasing amount of hydrophobic NTBA content in the hydrogels. The values of free energy change of elasticity (∆Gel) are found to be increased with increasing the hydrophobic NTBA content followed by decrease in swelling percentage. Also, the transition temperature of the hydrogel is found to be decreased with increasing the hydrophobic NTBA. [ABSTRACT FROM AUTHOR]

Background Efficient infection control during carbapenem-resistant Enterobacterales outbreaks demands rapid and simple techniques for outbreak investigations. WGS, the current gold standard for outbreak identification, is expensive, time-consuming and requires a high level of expertise. Fourier-transform infrared (FTIR) spectroscopy (IR Biotyper) is a rapid typing method based on infrared radiation applied to samples, which provides a highly specific absorption spectrum. Objectives To investigate an outbreak of OXA-48-producing Escherichia coli in real-time using FTIR and subsequently compare the results with WGS. Methods Twenty-one isolates were collected during a nosocomial outbreak, and identification and antibiotic susceptibilities were confirmed by VITEK®2. FTIR was conducted for all isolates, and nine representative isolates were sequenced. Results FTIR was able to correctly determine the clonal relatedness of the isolates and to identify the outbreak cluster, as confirmed by WGS. By WGS, isolates in the main FTIR cluster belonged to the same MLST type and core-genome MLST type, and they harboured similar plasmids and resistance genes, whereas the singletons external to the FTIR cluster had different genetic content. Conclusions FTIR can operate as a rapid, efficient and reliable first-line tool for outbreak investigations during a real-time ongoing E. coli outbreak, which can contribute to limiting the spread of pathogens. [ABSTRACT FROM AUTHOR]

In the present paper, the unique solvability of the direct and inverse source problems for the pseudo-parabolic equation involving the bi-ordinal Hilfer fractional derivative and 2D Landau Hamiltonian operator is considered. Applying the Fourier analysis for the operator Landau Hamiltonian, the theorems of uniqueness and existence of solutions to direct and inverse source problems are proved. In the investigation of the inverse source problem, we have used the value of unknown function at the final time in order to find the right-hand side of the equation. It is also presented the stability result of the inverse problem. [ABSTRACT FROM AUTHOR]

The recent discovery of barred spiral galaxies in the early Universe (z > 2) poses questions of how these structures form and how they influence galaxy evolution in the early Universe. In this study, we investigate the morphology and kinematics of the far-infrared (FIR) continuum and [C  ii ] emission in BRI1335-0417 at z ≈ 4.4 from ALMA observations. The variations in position angle and ellipticity of the isophotes show the characteristic signature of a barred galaxy. The bar, |$3.3^{+0.2}_{-0.2}$| kpc long in radius and bridging the previously identified two-armed spiral, is evident in both [C  ii ] and FIR images, driving the galaxy's rapid evolution by channelling gas towards the nucleus. Fourier analysis of the [C  ii ] velocity field reveals an unambiguous kinematic m  = 2 mode with a line-of-sight velocity amplitude of up to ∼30–40 km s−1; a plausible explanation is the disc's vertical bending mode triggered by external perturbation, which presumably induced the high star formation rate and the bar/spiral structure. The bar identified in [C  ii ] and FIR images of the gas-rich disc galaxy (≳ 70 per cent of the total mass within radius R ≈ 2.2 disc scale lengths) suggests a new perspective of early bar formation in high redshift gas-rich galaxies – a gravitationally unstable gas-rich disc creating a star-forming gaseous bar, rather than a stellar bar emerging from a pre-existing stellar disc. This may explain the prevalent bar-like structures seen in FIR images of high-redshift submillimeter galaxies. [ABSTRACT FROM AUTHOR]