In this paper, we perform a Floquet-based linear stability analysis of the centrifugal parametric resonance phenomenon in a Taylor–Couette system subjected to a time-quasiperiodic forcing where both the inner and outer cylinders are oscillating with the same amplitude and different angular velocities given respectively by $\varOmega _0 \cos (\omega _1t)$ and $\varOmega _0 \cos (\omega _2t)$ . In this context, the frequencies $\omega _1$ and $\omega _2$ are incommensurate, where the ratio $\omega _2/\omega _1$ is irrational. Taking into account non-axisymmetric disturbances, a new set of partial differential equations is derived and solved using the spectral method along with the Runge–Kutta numerical scheme. The obtained results in this framework show that this forcing triggers new and numerous reversing and non-reversing Taylor vortex flows arising via either synchronous or period-doubling bifurcations. A rich and complex dynamics is found owing to strong mode competition between these modes that alters significantly the topology of the marginal stability curves. The latter exhibit a multitude of small and condensed parabolas, giving rise to several codimension-two bifurcation points, discontinuities and cusp points in the stability diagrams. Furthermore, a proper tuning of the frequency ratio leads to a significant control of both the instability threshold and the axisymmetric nature of the primary bifurcation. Moreover, using a local quasi-steady analysis when the cylinders are slowly oscillating, intermittent instabilities are detected, characterised by spike-like behaviour in the stability diagrams with several successive growths, dampings and periods of quietness. In this limit case, the inner cylinder drive becomes the responsible forcing of the Taylor vortices’ formation where the calculated critical instability parameters correspond to those of the inner oscillating cylinder case with fixed outer cylinder. The potentially unstable regions between the cylinders are determined on the basis of the Rayleigh discriminant, where an excellent agreement with the linear stability analysis results is pointed out.

This study proposes a fiber chromatic confocal method with a 2D spectral demodulation to improve the axial resolution, which is achieved by the cross-dispersion of an echelle grating and prism. A chromatic confocal axial response model is derived based on confocal imaging and grating diffraction theories. The model parameters are fitted using calibration data, thereby facilitating the decoding, intensity correction, and reconstruction of the spectrogram to convert the 2D spectral peak accurately into the measured position. Experimental results show the axial resolution of 0.1μm for the fiber probe with a measurement range of 3mm, doubling the performance of conventional 1D spectral demodulation methods. This improvement demonstrates the applicability of the proposed method for high-precision measurement requirements, such as the assembly and testing of aeroengines.

Non-rapid eye movement (NREM) sleep is characterized by the interaction of multiple oscillations essential for memory consolidation, alongside a dynamic arrhythmic 1/f scale-free background that may also contribute to its functions. Recent spectral parametrization methods, such as FOOOF (Fitting-One-and-Over-f) and IRASA, enable the dissociation of rhythmic and arrhythmic components in the spectral domain; however, they do not resolve these processes in the time domain. Instantaneous measures of frequency, amplitude, and phase-amplitude coupling are thus still confounded by fluctuations in arrhythmic activity. This limitation represents a significant pitfall for studies of NREM sleep, often relying on instantaneous estimates to investigate the coupling of specific oscillations. To address this limitation, we introduce 'Rhythms & Background' (RnB), a novel wavelet-based methodology designed to dynamically denoise time-series data of arrhythmic interference. This enables the extraction of purely rhythmic time series, suitable for enhanced time-domain analyses of sleep rhythms. We first validate RnB through simulations, demonstrating its robust performance in accurately estimating spectral profiles of individual and multiple oscillations across a range of arrhythmic conditions. We then apply RnB to publicly available intracranial EEG sleep recordings, showing that it provides an improved spectral and time-domain representation of hallmark NREM rhythms. Finally, we demonstrate that RnB significantly enhances the assessment of phase-amplitude coupling between cardinal NREM oscillations, outperforming traditional methods that conflate rhythmic and arrhythmic components. This methodological advance offers a substantial improvement in the analysis of sleep oscillations, providing greater precision in the study of rhythmic activity critical to NREM sleep functions.Significance statement The Rhythms and Background (RnB) algorithm introduces a novel approach to signal processing in electrophysiology by disentangling rhythmic activity from the arrhythmic background at the time-series level. RnB denoise brain rhythms from arrhythmic interference in both the time and spectral domains, providing clearer insights into cerebral oscillatory processes. This breakthrough has direct applications in studying brain connectivity and oscillatory dynamics during sleep. Additionally, its application in clinical populations where pathological changes in arrhythmic activity are common, such as neurodevelopmental and neurodegenerative disorders, will help to better understand abnormal oscillatory processes. By improving the accuracy of rhythmic signal analysis, RnB opens new avenues for understanding brain function and dysfunction in research and clinical settings.

Ecological flow management is important for maintaining ecosystem stability and promoting sustainable development. Dynamic ecological flow regulation depends on precise real-time monitoring of water levels and flow velocities. To address challenges in ecological flow monitoring, including maintenance difficulties and insufficient accuracy, an improved DSC-YOLOv8n-seg model is proposed for dynamic multi-parameter sensing, achieving more efficient object detection and semantic segmentation. Compared with traditional affine transformation-edge detection, this approach enables joint recognition of water level lines and staff gauge characters, achieving an average recognition error of ±1.2 cm, with a model accuracy of 93.1%, recall rate of 94.5%, and mAP50:95 of 93.9%. A deep learning-based spectral principal direction recognition method was also employed to calculate the surface water flow velocity, which demonstrated stable and efficient performance, achieving a relative error of 0.005 m/s for the surface velocity. Experimental results confirm that it can effectively address issues such as environmental interference, exhibiting enhanced robustness in low-light and nighttime scenarios. The proposed method provides efficient and accurate identification for dynamic water level monitoring and for real-time detection of river surface flow velocities to improve ecological flow management.

Optimal control of a rumor spreading model in online social networks based on a spectral method and pufferfish optimizer

Comprehensive characterization of keratin extracted from patients with androgenetic alopecia and healthy individuals through multimolecular spectroscopy and structural analysis.

Contour line-based image pattern recognition technique for the interpretation of fluorescence excitation-emission matrix map: qualitation and quantitation.

Distributed fiber-optic sensing has become an indispensable tool for large-scale structural and environmental monitoring, where spectral interrogation of backscattering light enables high-precision quantitative measurement of external perturbations. Conventional spectral analysis methods, typically based on frequency-domain serial interrogation or time-to-frequency mapping, face inherent trade-offs between measurement speed, dynamic strain measurement range, and system complexity. Here, we present a distributed frequency comb enabled spectrum-correlation reflectometry as a universal spectral analysis framework that leverages optical frequency comb for parallel multi-frequency interrogation, which is experimentally demonstrated in a phase-sensitive optical time-domain reflectometry (φ-OTDR) system. This method eliminates the need for large frequency scans, achieving more than tenfold improvement in measurement speed over the state-of-the-art spectral analysis methods. Compared to existing phase-demodulated φ-OTDR systems, this method enables vibration amplitude monitoring with a dynamic strain measurement range expanded by more than an order of magnitude, while intrinsically circumventing phase unwrapping issues and interference fading. This work establishes a new paradigm for distributed spectral analysis, providing a flexible and robust platform for a wide range of sensing technologies, including Rayleigh and Brillouin-based schemes, which may have significant impact for geophysics, seismology, civil engineering, and other fields.

Multi-task decoding from electroencephalogram (EEG) signals is valuable for brain-computer interface (BCI) applications in naturalistic settings. Most existing studies focus on decoding distinctly different tasks, leaving the diversity of cognitive responses elicited by a single stimulus underexplored. We introduced a novel experimental paradigm where a common visual stimulus elicits five distinct cognitive processes: single reach, interception reach, sequence reach, attention reach, and inhibition reach. EEG signatures were analyzed using temporal and spectral methods. A regularized linear discriminant analysis (RLDA) classifier was employed for decoding, utilizing both temporal and event-related spectral perturbation (ERSP) features. Significant neural activation differences (p < 0.05) were observed across tasks and brain regions. The RLDA classifier achieved high decoding accuracy: 91.72% ± 6.10% for classifying the five cognitive states using ERSP features. Furthermore, for the sequence reach task, temporal features enabled classification of normal versus catch trials with 77.96% ± 7.03% accuracy. All these results demonstrate the potential for EEG-based BCI applications to distinguish diverse cognitive states elicited by identical stimuli, offering new insights for improving the naturalness and intelligence of BCI systems. Future work will focus on enhancing decoding performance and extending this research to online applications.

An efficient spectral element method for dynamic analysis of fluid-conveying pipes under base and pulsation excitations

A multi-domain spectral collocation method for PDEs in curved domains with holes

Movement fluency metrics during multi-phase sit-to-walk and reach-to-grasp: Test-retest reliability and agreement between laboratory-based and portable 3D motion analysis systems.

Spectral Restoration Method of Disordered Dispersion Microspectrometer Based on the Nonlinear Characteristics of the Camera

An efficient structural vibration damage evaluation method based on the spectral element method

DG-TSEM: A discontinuous Galerkin tetrahedral spectral element method for elastic wave propagation in complex geological models

Individual micron-sized coal aerosol particle for quantitative analysis based on hollow laser trapping-LIBS and machine learning.

The overlapping spectral element method

Influence of grain size distribution type on statistical moments of ultrasonic attenuations and phase velocities in random polycrystals.

Angular-spatial hp-adaptivity for radiative transfer with discontinuous Galerkin spectral element methods

Long-term empirical radiation detector calibration for airborne geophysical surveying.