Search Results (208)

The Dirac operator links harmonic analysis, physics and hypercomplex signal representations. However, most Dirac-based imaging methods remain integer order and lack spectral adaptability. In this paper, we propose a novel fractional Dirac framework for edge detection. Some fundamental properties are obtained, including square factorization, Liouville-type properties, and uncertainty principles with sharpened constants in a limiting case. Then, a numerically stable discrete realization is developed based on the quaternion Fourier transform. This realization yields an edge detector for both grayscale and RGB images. Experiments on benchmark datasets show that the proposed method produces coherent contours and competitive boundary-detection performance compared with classical gradient methods and recent transform-based detectors. Full article

The microstructure of metal matrix composites is inherently governed by fabrication routes and processing parameters, yet technological and physical constraints often prevent the realization of intended structural designs. In particle-reinforced composites produced via casting, interactions between the solidification front and inclusions frequently lead to agglomeration, segregation, and hence, a non-uniform distribution of the inclusions concentration. To mitigate these effects, post-processing techniques such as Friction Stir Processing offering particular promise for cast materials by refining microstructures and enhancing phase homogeneity. This study addresses these challenges by application of Fourier transform analysis to characterize stochastic inclusion distributions. Building on the Windows Washing method, we extend its application to heterogeneous media with varying inclusion concentrations. Through computer simulations and experimental analysis of real composites, we demonstrate that discrete Fourier transform can reveal hidden stochastic periodicity. The proposed framework provides a pathway toward improved predictive models and optimization strategies for metal matrix composites processing and performance. Full article

Hydrogen is a promising carbon-neutral fuel for future internal combustion engines due to its wide flammability range, high flame speed, and absence of carbon-based emissions. However, its high reactivity significantly increases susceptibility to abnormal combustion phenomena such as knock and pre-ignition, which can compromise engine efficiency, durability, and operational stability. Accurate detection and characterization of knock in hydrogen-fueled spark-ignition engines remain challenging due to the highly transient, broadband, and cycle-dependent nature of abnormal combustion-induced pressure oscillations. Conventional knock indicators based solely on time-domain pressure oscillations or fixed-band frequency analysis are limited in their ability to capture transient resonance behavior and cyclic variability. This study presents an integrated frequency- and time–frequency-domain methodology for knock detection using high-resolution in-cylinder pressure data acquired from a single-cylinder research engine operating under hydrogen port fuel injection (PFI). A discrete Fast Fourier Transform (DFFT) approach applied at stationary points of dynamically windowed pressure signals enables accurate identification of dominant resonance modes while minimizing spectral leakage. A Gaussian-based adaptive windowing strategy is introduced to capture combustion-driven cyclic variations more effectively. Short-Time Fourier Transform (STFT) and sum-based spectral analysis further provide detailed time–frequency localization of transient knock events. The proposed methodology demonstrates a clear separation between normal combustion and knock conditions, enabling reliable cycle-by-cycle identification of abnormal combustion events under varying operating conditions. The experimentally observed resonance frequencies are validated against theoretical predictions using Draper’s acoustic resonance equation, supporting the physical interpretation of knock-induced pressure oscillations. The results demonstrate that the proposed adaptive spectral methodology significantly improves knock detection accuracy compared to conventional indicators and provides a robust framework for advanced knock diagnostics, engine calibration, and combustion control in hydrogen-fueled engines. Full article

This study investigates the ecological footprint (EF) convergence dynamics of the “Big Ten Emerging Economies” (BTEs) over the period 1967–2024. Employing the Maximum Overlap Discrete Wavelet Transform (MODWT) in conjunction with the Fourier KPSS (FKPSS) stationarity test, the analysis decomposes the EF series into short-, medium-, and long-term frequency components, allowing the stochastic convergence hypothesis to be examined separately across multiple time horizons. The empirical results reveal that convergence is largely absent in the original series, with stochastic convergence detected only for India, Indonesia, and Türkiye at the aggregate level. Once the series are decomposed, convergence becomes considerably more visible. In the short run, convergence is supported for Argentina, Indonesia, Mexico, Poland, and Türkiye. The medium run emerges as the most robust convergence horizon, with all ten economies exhibiting stochastic convergence—a result that becomes visible only after accounting for nonlinear structural breaks through the Fourier framework. In the long run, convergence is supported for Argentina, Brazil, China, Korea, Poland, and South Africa, while India, Indonesia, Mexico, and Türkiye exhibit persistent divergence. No single country maintains convergence consistently across all time horizons, underscoring the heterogeneous and frequency-dependent nature of EF dynamics in major emerging economies. The robustness analysis based on the Fourier ADF and standard ADF tests supports the primary findings. These results contribute to the EF convergence literature by demonstrating that environmental convergence is a multi-layered and frequency-dependent phenomenon, and offer empirical insights relevant to the design of long-run sustainability policies for emerging economies. Full article

We develop a high-order space-time spectral method for nonlinear convection–diffusion equations with a Riemann–Liouville time-fractional derivative and a spectrally defined space-fractional Laplacian. The spatial discretization uses a Fourier spectral method that diagonalizes the fractional Laplacian under periodic boundary conditions. The temporal discretization employs a Petrov–Galerkin method based on generalized Jacobi functions which capture the initial singularity exactly. The nonlinear convection term is treated pseudo-spectrally, and the resulting algebraic system is solved with a damped Newton iteration. Rigorous error analysis proves exponential convergence in both space and time. Numerical experiments for various fractional orders confirm the spectral accuracy. Simulations of the fractional Burgers equation demonstrate that increasing the viscosity enhances diffusion and stabilizes the solution, while a nonlinear coefficient that significantly exceeds the viscosity leads to error growth over long time intervals. The method provides an efficient and accurate tool for simulating anomalous transport phenomena. Full article

The electromagnetic scattering problem for dielectric objects involves a linear integral equation that relates the total field to the scattered field inside the object. Numerical solution methods require discretization by choosing a suitable set of basis functions. An optimal choice of the expansion functions not only achieves numerical efficiency but also allows the correct subspaces to be spanned. We resort to the spectral decomposition of the pertinent operator to investigate such optimal functions. A one-dimensional (1D) geometry (i.e., scattering by a homogenous dielectric slab) is considered because it allows us to derive some analytical results and simple closed-form solutions to be used in the numerical verifications. Then, the spectral decomposition is performed numerically. The analysis of the eigenvalues and the eigenfunctions allows for predicting the required number once the maximum slab permittivity is given. In turn, the corresponding maximum number of Fourier harmonics can also be established, as they provide the basis to expand the eigenfunctions. Full article

This paper proposes disturbance detection algorithms to mitigate the oscillations in smartphone camera module actuators induced by external shocks (e.g., drop events). Smartphone camera modules operate under volumetric constraints with inter-component trade-offs. Specifically, the limited space leads to insufficient performance because actuators are unstable under external disturbances. To optimize actuator function, we define the dynamic model of a voice coil motor (VCM) actuator, a controller model, and a shock disturbance model and perform worst-case operational analysis with MATLAB/Simulink (R2015a) simulations. Moreover, we propose two disturbance detection techniques: a phase-based detection algorithm that statistically analyzes the phase difference between the control input and the position feedback signal to detect disturbances and a frequency-based detection algorithm that uses discrete Fourier transform (DFT) to identify the characteristic spectral component of disturbances at 500 Hz. According to the simulation results, both methods reduce recovery time upon disturbance. Furthermore, the frequency-based algorithm achieves faster recovery performance than the phase-based detection algorithm. The phase-based detection method offers low computational complexity but increased processing latency, while the frequency-based detection method requires more memory capacity. The proposed techniques are anticipated to improve the recovery time of smartphone camera modules under disturbances, thereby enhancing system robustness and contributing to a more stable user imaging experience by mitigating image blur. Full article

The current paper studies the global shell layer of the Finite Ring Continuum framework in the symmetry-complete regime realized here by framed finite fields, ${\mathbb{F}}_{\mathsf{p}}(\mathsf{t};0,1,e_{\mathsf{t}})$, with $\mathsf{p}=4\mathsf{t}+1$. We show that a single symmetry-complete shell carries a unified finite Euclidean datum for which its continuum comparison interpretation reproduces the familiar structural roles of e, $\pi$, and i of a one-phase step with an exponential kernel, a half-period, and a quarter-turn, respectively. In the same shell, the orbital geometry is generated by additive meridian action and multiplicative phase action from that same frame datum. The resulting orbital shell has a canonical spherical completion, combinatorially equivalent to the two-sphere, with labels depending on the chosen frame, but the shell type fixed up to isomorphism. Arbitrary finite-precision approximation on this external spherical comparison object is then obtained within every fixed symmetry-complete shell by the scale-periodic framed-rational refinement generated by the same frame datum. The Fourier formalism is developed strictly as a discrete Fourier transform over the shell ring, with conventional continuum Fourier language becoming a continuum large-$\mathsf{p}$ comparison case of that shell formalism. Full article

While superdeterministic and fractal spacetime models offer compelling alternative perspectives on quantum foundations, the simulation and validation of effective wave dynamics in such non-differentiable, deterministic settings remain computationally and theoretically challenging. To address this, a framework built around the Fractional Nonlinear Klein–Gordon Equation (FNKGE), defined through the spectral fractional Laplacian, was developed. This equation was solved and benchmarked through a comparative study between Physics-Informed Neural Networks (PINNs) with Fourier features and Physics-Informed Graph Neural Networks (PI-GNNs). Additionally, detection patterns were simulated via deterministic agents, and theoretical links between fractal geometry, computational irreducibility, and deviations from statistical independence were formalized. Regarding the computational evaluation, superior accuracy was achieved by the PI-GNNs, yielding a mean relative error of $0.5\%$ ($\overline{ϵ}=0.005$), alongside faster convergence and a more well-conditioned Hessian spectrum compared to PINNs. Crucially, a continuous power-law decay ($S\left(k_y\right)\sim k_y^{-1.8}$) was revealed by the spectral analysis of the simulated detection patterns, confirming the emergence of classical optical caustics rather than discrete quantum-interference peaks. Furthermore, a modified dispersion relation that accurately predicts linear instability regimes was derived, and specific boundary artifacts in non-periodic domains were identified. Taken together, the FNKGE is validated by these results as a viable effective model for fractal wave phenomenology and as a robust benchmark for physics-informed learning architectures. Full article

In order to improve the accuracy of multi-tone parameter estimation, we propose a scheme derived from a novel spectral scenario based on all-phase Fast Fourier Transform (apFFT)/all-phase discrete-time Fourier Transform (apDTFT). This scheme is constructed based on the following architecture. Firstly, we theoretically extend the original discrete apFFT analysis to the proposed continuous apDTFT analysis, so that two excellent spectral properties (suppression of spectral leakage and phase invariance) hold across the entire frequency axis. Secondly, on the basis of apFFT/apDTFT, we design a single-tone interpolator and its improved version with frequency-shift iteration. Thirdly, we derive a multi-tone harmonic estimator, which can further reduce the mutual spectral interference under the apFFT-/apDTFT-based spectral scenario. Both numerical and experimental results demonstrate that, even with one fewer sample, the proposed apFFT-/apDTFT-based estimator achieves higher accuracy across individual harmonics and inter-harmonics than the FFT-/DTFT-based estimator. Full article

The weak-field, quasi-static regime of gravity is commonly described by the Newton–Poisson equation as an effective response law. We construct this response within a cost-first discrete variational framework. The Recognition Composition Law (RCL) uniquely selects a reciprocal closure cost within the restricted quadratic symmetric composition class; together with the discrete ledger axioms AX1–AX5 (including conservation) and standard DEC refinement, the Newton–Poisson baseline is then recovered in the instantaneous-closure limit. Conditional on Assumption AS1 (scale-free latency) and Assumption AS2 (causal frequency–wavenumber ansatz), allowing finite equilibration introduces fractional memory into the response, yielding a scale-free modification of the source–potential relation characterized by a power-law kernel $w_{\ker }\left(k\right)=1+C{(k_0/k)}^{\alpha }$ in Fourier space. The kernel exponent $\alpha =\frac{1}{2}(1-{\phi }^{-1})\approx 0.191$, where $\phi =(1+\sqrt{5})/2$, is derived from self-similarity of the discrete ledger closure; the amplitude $C={\phi }^{-2}\approx 0.382$ is identified as a hypothesis from a three-channel factorization argument. We evaluate this quasi-static kernel-motivated response against SPARC galaxy rotation curves under a strict global-only protocol (fixed $M/L=1$, no per-galaxy tuning, conservative ${\sigma }_{\mathrm{tot}}$), using a controlled multiplicative surrogate for the full nonlocal disk operator implied by the kernel. In this deliberately over-constrained setting, the surrogate interface achieves $\mathrm{median}({\chi }^2/N)=3.06$ over 147 galaxies (2933 points), outperforming a strict global-only NFW benchmark and remaining less efficient than MOND under identical constraints. The analysis is restricted to the non-relativistic, quasi-static sector and should be read as a falsifier-oriented galactic-regime consistency check of the scaling window, not as a relativistic completion or a claim of Solar System viability without additional UV regularization/screening. Full article

Transonic buffet is a critical self-sustained shock/boundary-layer instability limiting the flight envelope of modern transport aircraft. This study investigates the interaction between shock buffet and forced wing motion on the Airbus XRF-1 wind tunnel model, using unsteady Reynolds-Averaged Navier–Stokes (URANS) simulations with the DLR TAU code. The investigation is carried out in deep buffet condition ($\mathrm{Ma}=0.84$, $\alpha =4.5^{\circ }$, $\mathrm{Re}=25\times {10}^6$) and validated against wind tunnel data at the same flow condition. The buffet flow is superimposed with forced wing motions derived from a symmetric wing eigenmode at $\mathrm{Sr}=0.164$. Two different amplitudes scaled with the half-span s are considered: $A_{tip}=0.0025·s$ and $0.01·s$. The baseline no-forcing URANS captures the buffet flow quite well with only small deviations in the standard deviation of the surface pressure coefficient $c_{p,rms}$. A special variant of the Discrete Fourier Transformation for the whole wing upper surface $c_p$ distribution revealed that the typical buffet frequencies are also matched. The analysis of the forced simulations revealed a strong influence of the local wing motion on the increase of $c_{p,rms}$. The spectral content showed a shift and damping or amplification of different buffet modes, which is relevant for the interaction of motion induced and buffed induced aerodynamic forces. Full article

Externally excited synchronous machines (EESMs) are a rare-earth-free solution for traction applications. However, variable field excitation and magnetic coupling increase control complexity. Efficient validation of the resulting control functionalities can be carried out using hardware-in-the-loop (HIL) testing, which requires high-fidelity real-time simulation models. This paper presents a semi-analytical, discrete-time EESM model tailored for HIL applications. Nonlinear magnetic saturation and magnetic coupling are captured using an inverted flux–current characteristic combined with a rotating coordinate transformation, which improves resource utilization. Spatial harmonics are included through a Fourier decomposition of the angle-dependent inverse characteristics. Additionally, different loss mechanisms are considered to accurately represent the physical behavior of the machine. The model is parameterized using finite element analysis (FEA) results from a 100$\mathrm{k}$$\mathrm{W}$ salient-pole EESM. It is implemented on a field-programmable gate array to achieve real-time capability at a simulation frequency of $2.5$$\mathrm{M}$$\mathrm{Hz}$. Validation results for the typical operating range show deviations below $0.1$% compared to detailed FEA results, demonstrating accurate real-time simulation of the electromagnetic behavior. Full article

This study introduces a modified computational scheme for handling linear and nonlinear fractal time-dependent partial differential equations. The method is constructed using three different stages that provide third-order accuracy in the fractal time variable. The stability of the approach is examined using scalar fractal models and Fourier analysis, while convergence is established for coupled convection–diffusion systems. The numerical algorithm is applied to analyze the mixed convective flow of a Carreau–Yasuda non-Newtonian fluid over stationary and oscillating plates under the influence of viscous dissipation and magnetic field effects. For spatial discretization, the incompressible continuity equation is handled by a first-order difference scheme, whereas higher-order compact schemes are implemented for the momentum, thermal, and concentration equations. The numerical findings show that increasing the Weissenberg number and magnetic field inclination reduces the velocity distribution. An accuracy assessment against existing numerical techniques demonstrates that the present method yields smaller computational errors, particularly when central difference schemes are used in space. In addition, a surrogate machine learning model is developed to predict the skin friction coefficient and local Nusselt number using Reynolds, Weissenberg, Prandtl, and Eckert numbers as input features. The predictive capability of the model is validated through Parity plots, bar charts for sensitivity analysis, scatter visualization, and Taylor Diagrams, confirming strong agreement with the numerical results. Full article

The Korteweg–de Vries (KdV) equation is a foundational model in geophysical fluid dynamics (GFD), governing the propagation of long internal and surface gravity waves in stratified and shallow ocean environments where the interplay between nonlinear steepening and frequency-dependent dispersion gives rise to solitons. Although the analytical tractability of the KdV equation through inverse scattering is well established, systematic numerical exploration of multi-soliton interactions remains valuable for benchmarking solvers, probing conservation properties under varied oceanic initial conditions, and building intuition for more complex ocean wave phenomena. This article presents sangkuriang, an open-source Python library that solves the KdV equation using Fourier pseudo-spectral spatial discretization and adaptive eighth-order Runge–Kutta time integration. The implementation leverages just-in-time (JIT) compilation to achieve research-grade computational efficiency on standard hardware, making it readily accessible for coastal and ocean engineering applications, including idealized modeling of internal solitary waves on continental shelves, rapid parameter studies for solitary wave propagation in stratified basins, and pedagogical investigations of nonlinear dispersive wave dynamics. The solver is validated through four progressively complex idealized scenarios motivated by oceanic wave dynamics: isolated soliton propagation, symmetric interactions, overtaking collisions, and three-body interactions. High-fidelity conservation of mass, momentum, and energy is demonstrated, with relative errors remaining below $\mathcal{O}\left({10}^{-4}\right)$ across all test cases. Measured soliton velocities align with theoretical predictions within 5%, confirming the capture of the amplitude-dependent dispersion characteristic of oceanic solitary waves. Complementary diagnostics, including spectral entropy and recurrence quantification analysis (RQA), verify that the numerical solutions preserve the regular phase-space structure characteristic of integrable Hamiltonian systems. These results establish sangkuriang as a robust, lightweight platform for reproducible numerical investigation of idealized nonlinear dispersive wave dynamics relevant to coastal and ocean engineering applications. Full article