Search Results (79)

This study presents the Fourier–Gegenbauer integral Galerkin (FGIG) method, a new numerical framework that uniquely integrates Fourier series and Gegenbauer polynomials to solve the one-dimensional advection–diffusion (AD) equation with spatially symmetric periodic boundary conditions, achieving exponential convergence and reduced computational cost compared to traditional methods. The FGIG method uniquely combines Fourier series for spatial periodicity and Gegenbauer polynomials for temporal integration within a Galerkin framework, resulting in highly accurate numerical and semi-analytical solutions. Unlike traditional approaches, this method eliminates the need for time-stepping procedures by reformulating the problem as a system of integral equations, reducing error accumulation over long-time simulations and improving computational efficiency. Key contributions include exponential convergence rates for smooth solutions, robustness under oscillatory conditions, and an inherently parallelizable structure, enabling scalable computation for large-scale problems. Additionally, the method introduces a barycentric formulation of the shifted Gegenbauer–Gauss (SGG) quadrature to ensure high accuracy and stability for relatively low Péclet numbers. This approach simplifies calculations of integrals, making the method faster and more reliable for diverse problems. Numerical experiments presented validate the method’s superior performance over traditional techniques, such as finite difference, finite element, and spline-based methods, achieving near-machine precision with significantly fewer mesh points. These results demonstrate its potential for extending to higher-dimensional problems and diverse applications in computational mathematics and engineering. The method’s fusion of spectral precision and integral reformulation marks a significant advancement in numerical PDE solvers, offering a scalable, high-fidelity alternative to conventional time-stepping techniques. Full article

Gear transmission error (GTE) is a critical factor influencing the performance and service life of gear systems, as it directly contributes to vibration, noise generation, and premature wear. The present study introduces a combined theoretical and experimental approach to characterizing GTE in a single-stage spur gear system. A six-degree-of-freedom nonlinear dynamic model was formulated to capture coupled lateral–torsional vibrations, accounting for gear mesh stiffness, bearing and coupling characteristics, and a harmonic transmission error component representing manufacturing and assembly imperfections. Simulations and experiments were conducted under healthy and eccentricity-faulted conditions, where a controlled 890 g eccentric mass induced misalignment. Frequency domain inspection of faulty gear data showed pronounced sidebands flanking the gear mesh frequency near 200 Hz, as well as harmonics extending from 500 Hz up to 1200 Hz, in contrast with the healthy case dominated by peaks confined to 50–100 Hz. STFT analysis revealed dispersed spectral energy and localized high-intensity regions, reinforcing its role as an effective fault diagnostic tool. Experimental findings aligned with theoretical predictions, demonstrating that the integrated modelling and time–frequency framework is effective for early fault detection and performance evaluation of spur gear systems. Full article

Highly efficient shielding materials, transparent in the visible and IR ranges are becoming important in practice. This stimulates the development of cheap methods for creating transparent conductors with low sheet resistance and high optical transparency. This work presents a complex approach based on preliminary modeling of the shielding characteristics of two-layer sandwich structures based on irregular aluminum mesh (IAM) formed by the cracked template method. Experimentally measured spectral dependences of the transmission coefficient of single-layer IAM are used as a reference point for modeling. According to the simulation results, two types of sandwich structures were designed using IAM, with varying filling factors and a fixed PMMA layer thickness of 4 mm. The experimentally measured shielding characteristics of the sandwich structures in the range of 0.01–7 GHz are in good agreement with the calculated data. The obtained structures demonstrate a shielding efficiency of 55.96 dB and 65.55 dB at a frequency of 3.5 GHz (the average range of 5G communications). At the same time, their optical transparency at a wavelength of 550 nm are 84.07% and 75.78%, respectively. Our sandwich structures show electromagnetic shielding performance and uniform diffraction pattern. It gives them an advantage over structures based on regular meshes. The obtained results highlight the prospect of the proposed comprehensive approach for obtaining highly efficient, low-cost optically transparent shielding structures. Such materials are needed for modern wireless communication systems and metrology applications. Full article

The combined reducer consisting of spiral bevel gear pair and planetary gear train is widely used in the aerospace field, and its dynamic performance seriously affects the fatigue life of the gears. However, there has been little research on the dynamic performance analysis of the combined gear reducer. In this paper, the coupling multibody dynamic models of spiral bevel gear pair and planetary gear train with and without bearing modules are established based on ADAMS software, respectively, and the influence of bearings on the dynamic performance of the coupling system is studied, and the analysis results are verified by experiments. The results demonstrate that the flexible bearings in the coupled system will induce a pronounced shaft swing that amplifies the combined reducer vibration. Because of the displacement of the sun gear, the meshing force of the planetary gear train fluctuates periodically at low frequency, which increases the maximum dynamic meshing force and is not conducive to its fatigue life. This low-frequency fluctuation can be greatly reduced by introducing additional bearings. In addition, dynamic testing confirms vibration spectral components include obvious shaft rotation frequencies except gear meshing frequencies, verifying the modeling accuracy and analytical methodology. Full article

Direct numerical simulations (DNSs) of the T106A low-pressure turbine were conducted for various turbulence intensities and length scales to investigate their effects on flow behaviour and transition. A source-term formulation of the synthetic eddy method (SEM) was implemented in the Nektar++ spectral/hp element framework to introduce anisotropic turbulence into the flow field. A single sponge layer was imposed, which covers the inflow and outflow regions just downstream and upstream of the inflow and outflow boundaries, respectively, to avoid acoustic wave reflections on the boundary conditions. Additionally, in the T106A model, mixed polynomial orders were utilized, as Nektar++ allows different polynomial orders for adjacent elements. A lower polynomial order was employed in the outflow region to further assist the sponge layer by coarsening the mesh and diffusing the turbulence near the outflow boundary. Thus, this study contributes to the development of a more robust and efficient model for high-fidelity simulations of turbine blades by enhancing stability and producing a more accurate flow field. The main findings are compared with experimental and DNS data, showing good agreement and providing new insights into the influence of turbulence length scales on flow separation, transition, wake behaviour, and loss profiles. Full article

The Central Depression of the Junggar Basin relies heavily on Permian lacustrine mudstone for deep-seated hydrocarbon sealing. This research investigated how the fluorescence parameters of caprock samples responded to the leakage of palaeo-oil zones based on measurements from SEM, Rock-Eval, and X-ray diffraction analysis. First, two sets of control experiments were conducted to establish the proper grain-size range of 100–140 mesh for testing caprock samples in the research area using quantitative fluorescence technology. Subsequently, based on the examination of the rock pyrolysis parameters and the fluorescence parameters against TOC values, the conjecture was formed that the quantitative fluorescence technology test results were mostly unaffected by the primary hydrocarbons. Lastly, four fluorescence parameters were used to assess seal integrity: quantitative grain fluorescence intensity of the extract (QGF E intensity, the meaning of QGF is the same in this study), QGF spectral peaks (QGF λmax), the ratio of QGF intensity to fluorescence intensity at 300 nm on the QGF spectrum (QGF index), and total scanning fluorescence spectral ratio R₁ (TSF R₁). The Permian caprock can effectively seal hydrocarbons as evidenced by the decrease of QGF E intensity and QGF index values with depth. When hydraulic fracturing causes caprock failure, it can lead to complete leakage of hydrocarbons from the palaeo-oil zones. As the depth becomes shallower, the QGF E intensity value increases, the QGF index value decreases. Due to the differences in the migration pathways of hydrocarbons in the caprock, those leaked from the Permian palaeo-oil zone into the well PD1 caprock are mainly condensate and light–normal crude oil, while the hydrocarbons from the Carboniferous palaeo-oil zone into the well MS1 caprock consist predominantly of light–normal crude oil and medium–heavy crude oil. Full article

Achieving high-order accuracy in finite difference/spectral methods for space-time fractional differential equations often relies on very restrictive and usually unrealistic smoothness assumptions in the spatial and/or temporal domains. For spatial discretization, spectral methods using smooth basis functions are commonly employed. However, spatial–fractional derivatives pose challenges, as they often lack guaranteed spatial smoothness, requiring non-smooth basis functions. In the temporal domain, finite difference schemes on uniformly graded meshes are commonly employed; however, achieving accuracy remains challenging for non-smooth solutions. In this paper, an efficient algorithm is adopted to improve the accuracy of finite difference/Pertrov–Galerkin spectral schemes for a time-space fractional reaction–diffusion equation, with a hyper-singular integral fractional Laplacian and non-smooth solutions in both time and space domains. The Pertrov–Galerkin spectral method is adapted using non-smooth generalized basis functions to discretize the spatial variable, and the L1 scheme on a non-uniform graded mesh is used to approximate the Caputo fractional derivative. The unconditional stability and convergence are established. The rate of convergence is $O\left(N^{\mu -\gamma }+K^{-min\{\rho \beta ,2-\beta \}}\right),$ achieved without requiring additional regularity assumptions on the solution. Finally, numerical results are provided to validate our theoretical findings. Full article

The primary atomization of planar liquid sheets near nozzle exits plays a critical role in the study of pressure-swirl atomizers, yet its intrinsic destabilization and breakup mechanisms remain insufficiently characterized due to the multi-scale nature of gas–liquid interactions, significantly limiting the predictive capacity of current widely adopted atomization models. This study utilizes three-dimensional direct numerical simulations (DNSs) with adaptive mesh refinement and the Volume-of-Fluid (VOF) method to examine the instability and disintegration of a spatially developing planar liquid sheet under operating conditions representative of aero-engine combustors (thickness $h=100 \mathsf{\mu }\mathrm{m}$, $We=2544$, $Re=886$). Adaptive grid resolution (minimum cell size $2.5 \mathsf{\mu }\mathrm{m}$) enables precise resolution of multi-scale interface dynamics while maintaining mass conservation errors below 0.1‱. High-fidelity simulations reveal distinct atomization cascades originating from the jet tip, characterized by liquid sheet roll-up, interface expanding, interface tearing, and ligament/droplet formation. Through extraction and surface characterization of representative shed liquid ligaments, we quantify temporal and spatial variations between ligaments propagating toward and away from the jet core region. Key findings demonstrate that ligament impingement on the liquid core serves as the dominant mechanism for surface wave destabilization, surpassing the influence of initial gas–liquid shear at the nozzle exit. Spectral analysis of upstream surface waves reveals a pronounced correlation between high-wavenumber disturbances and the mean diameter of shed ligaments. These results challenge assumptions in classical atomization models (e.g., LISA) by highlighting self-destabilization mechanisms driven by droplet–ligament interactions. This work provides critical insights for refining engineering atomization models through physics-based ligament diameter prediction criteria. Full article

We conducted a comprehensive comparative study of numerical solvers for the generalized Korteweg–de Vries (gKdV) equation, focusing on classical Fourier-based Crank–Nicolson methods and physics-informed neural networks (PINNs). Our work benchmarks these approaches across nonlinear regimes—including the cubic case ($\nu =3$)—and diverse initial conditions such as solitons, smooth pulses, discontinuities, and noisy profiles. In addition to pure PINN and spectral models, we propose a novel hybrid PINN–spectral method incorporating a regularization term based on Fourier reference solutions, leading to improved accuracy and stability. Numerical experiments show that while spectral methods achieve superior efficiency in structured domains, PINNs provide flexible, mesh-free alternatives for data-driven and irregular setups. The hybrid model achieves lower relative $L^2$ error and better captures soliton interactions. Our results demonstrate the complementary strengths of spectral and machine learning methods for nonlinear dispersive PDEs. Full article

Irregular wave generation in numerical simulations is critical for accurately modeling realistic sea conditions, which is essential in coastal and offshore engineering applications, such as for wave energy conversion. Therefore, this study presents theoretical recommendations for generating realistic irregular waves using the WaveMIMO methodology and validates its accuracy against experimental data. For the parameters investigation, spectral data are processed to obtain orbital velocity profiles of wave propagation, which are imposed as boundary conditions (BCs) in a numerical wave channel. The simulations were conducted using the ANSYS-Fluent 2024 R2 software, which employs the multiphase volume of fluid (VOF) model to treat the interface between phases. Seeking theoretical recommendations for the application of this methodology, the present study investigated the discretization of the region where the prescribed velocity BC is imposed, the mesh sensitivity in the free surface region, the time step used, and the location of the velocity vector in each segment of the prescribed velocity BC imposition region. The results obtained were compared with realistic sea state data obtained from the TOMAWAC spectral model, referring to the municipalities of Rio Grande and Tramandaí, in the state of Rio Grande do Sul, Brazil. The results indicated that, compared to recommendations from the previous literature, the recommended configuration improved wave generation accuracy by 7–8% for Rio Grande and 2–3% for Tramandaí. Finally, the WaveMIMO methodology and its theorical recommendations were validated against experimental data found in the literature, reaching an excellent agreement. Full article

Extreme ultraviolet (EUV) imagers are key tools to monitor the space environment and forecast space weather. EUV filters are important components to block radiation in the ultraviolet (UV), visible, and near-infrared (IR) regions. In this study, various characterization methods were proposed for the nickel mesh-supported indium (In) filter, and their spectral characteristics were comprehensively studied. The material and thickness of the filter were chosen based on atomic scattering principles, determined through theoretical calculation and software simulation. The metal film was deposited using the vacuum-resistive thermal evaporation method. The measured transmission of the filter was 10.06% at 83.4 nm. The surface elements of the sample were analyzed using X-ray photoelectron spectroscopy (XPS). The surface and cross-sectional morphologies of the filter were observed using a scanning electron microscope (SEM). The impact of the oxide layer and carbon contamination on the filter’s transmittance was investigated using an ellipsometer. A multilayer “In-In₂O₃-C” model was established to determine the thickness of both the oxide layer and carbon contamination layer on the filter. This model introduces the filling factor based on the original model and considers the diffusion of the contamination layer, resulting in more accurate fitting results. The transmittance of the filter in the visible light range was measured using a UV-VIS spectrophotometer, and the measurement error was analyzed. This article provides preparation methods and test methods for the 83.4 nm EUV filter and conducts a detailed analysis of the spectral characteristics of the prepared optical filters, which hold significant value for space exploration applications. Full article

This paper, taking as reference channel data previously obtained by using a rigorous and well-tested ray-tracing method for a concentrated massive multiple-input multiple-output (mMIMO) system, focuses on the optimization of the set of potential antennas required in a distributed mMIMO system to achieve the same channel spectral efficiency as the concentrated system. Concerning the optimizer, a binary particle swarm optimization algorithm was considered to decide whether to activate or deactivate any of the antennas within the original mesh, taking into account, in order to direct the search, the total spectral efficiency, the equality between the spectral efficiency of users, and the number of receiver antennas at the distributed base station. The analysis was carried out in a large indoor environment at the 5G n258 frequency band (26 GHz), concentrating on the up-link and considering a set of 20 uniformly distributed active users. The results obtained show that, in the distributed mMIMO system, an arrangement with fewer than half the number of receiver antennas of the initial mesh is required to achieve a similar performance to that of the concentrated one taken as a reference. Full article

A joint distribution of significant wave heights ($H_s$) and peak wave periods ($T_p$) in the northwestern South China Sea is created using a conditional distribution model in this work. An unstructured triangular mesh wave model covering the northwestern South China Sea is established based on the third-generation spectral wave model SWAN. This wave model has been extensively validated against field data and was run from 1979 to 2020 to generate long enough one-hourly $H_s$ and $T_p$. Four probability density functions including Normal, Lognormal, Gamma and 3P Weibull distributions are adopted to construct the marginal independent distribution of $H_s$. The results show that the 3P Weibull distribution is more suitable in fitting the marginal distribution of $H_s$ compared to the other three distributions. Three combinations of dependence functions ($\mu \mathrm{and} \sigma$), namely, power3 and exp3, insquare2 and asymdecrease3, and logistics4 and alpha3, are used to create the Normal and Lognormal distributions for $T_p$. The estimations of dependence functions and corresponding fitted $T_p$ demonstrate that the $\mu \mathrm{and} \sigma$ using power3 and exp3 perform best in producing the conditional distribution of $T_p$. In addition, the environmental contours derived by an IFORM are used to generate the extreme sea states with return periods of 1, 5, 10, 25, 50 and 100 years. Full article

Reducing distortion of spectral simulation signals in infrared detection systems is essential to improve the precision of detecting fine spectra in space-based carbon monitoring satellites. The rigid-flex printed circuit board (PCB), a vital interconnection structure between detectors and signal conditioning circuits, exhibits signal quality variations due to impedance fluctuations and parasitic capacitance changes induced by its meshed return plane geometry. This periodically varying structure necessitates full-wave field solutions to include longitudinal discontinuity. Although full-wave simulations provide accurate characterization, they demand substantial computational resources and time. To address these challenges, we propose an innovative approach to effectively determine optimal meshed return plane designs across various transmission rates. The method integrates a convolutional neural network (CNN) with improved particle swarm optimization (IPSO). First, a CNN model is employed efficiently to predict scattering parameters (S-parameters) for different design configurations, thereby overcoming the inefficiencies associated with iterative full-wave simulation optimization. Then, an IPSO algorithm has been implemented to address the optimization challenge of crosstalk and inter-symbol interference (ISI) in signal transmission. Furthermore, to increase the optimization speed and evaluate the system performance under extreme conditions, we propose a fitness function construction method based on double-edge responses (DER) to rapidly generate a worst-case peak distortion analysis (PDA) eye diagram within the IPSO algorithm. The proposed methodology reduces computational complexity by two orders of magnitude relative to the full-wave simulation. Quantitative analysis conducted at a transmission rate of 5 Gbps demonstrates substantial signal quality improvements compared to empirical PCB design: the eye height increased by 49.7%, and the eye width expanded by 35.7%. The effectiveness of these improvements has been verified through commercial simulation software, proving that the method can provide design support for infrared detection systems. Full article

Background: Prostate cancer management optimally requires non-invasive, objective, quantitative, accurate evaluation of prostate tumors. The current research applies visual inspection and quantitative approaches, such as artificial intelligence (AI) based on deep learning (DL), to evaluate MRI. Recently, a different spectral/statistical approach has been used to successfully evaluate spatially registered biparametric MRIs for prostate cancer. This study aimed to further assess and improve the spectral/statistical approach through benchmarking and combination with AI. Methods: A zonal-aware self-supervised mesh network (Z-SSMNet) was applied to the same 42-patient cohort from previous spectral/statistical studies. Using the probability of clinical significance of prostate cancer (PCsPCa) and a detection map, the affiliated tumor volume, eccentricity was computed for each patient. Linear and logistic regression were applied to the International Society of Urological Pathology (ISUP) grade and PCsPCa, respectively. The R, p-value, and area under the curve (AUROC) from the Z-SSMNet output were computed. The Z-SSMNet output was combined with the spectral/statistical output for multiple-variate regression. Results: The R (p-value)–AUROC [95% confidence interval] from the Z-SSMNet algorithm relating ISUP to PCsPCa is 0.298 (0.06), 0.50 [0.08–1.0]; relating it to the average blob volume, it is 0.51 (0.0005), 0.37 [0.0–0.91]; relating it to total tumor volume, it is 0.36 (0.02), 0.50 [0.0–1.0]. The R (p-value)–AUROC computations showed a much poorer correlation for eccentricity derived from the Z-SSMNet detection map. Overall, DL/AI showed poorer performance relative to the spectral/statistical approaches from previous studies. Multi-variable regression fitted AI average blob size and SCR results at a level of R = 0.70 (0.000003), significantly higher than the results for the univariate regression fits for AI and spectral/statistical approaches alone. Conclusions: The spectral/statistical approaches performed well relative to Z-SSMNet. Combining Z-SSMNet with spectral/statistical approaches significantly enhanced tumor grade prediction, possibly providing an alternative to current prostate tumor assessment. Full article