Search Results (8,643)

Atmospheric state estimation is an important part of weather forecasting, and its accuracy determines the accuracy of the forecasting results. Traditional methods for atmospheric state estimation mainly rely on assimilation systems, using physical models and dynamic equations to predict the atmospheric state. However, these methods have certain limitations when dealing with large-scale meteorological data and complex meteorological phenomena. In order to solve the above problems, this study first integrates and processes data from multiple datasets including ground, upper-air, satellite, and atmospheric state, representing these data as graph structures. Secondly, a graph neural network-based network model is constructed, which is pre-trained using self-supervised methods and fine-tuned for specific tasks. Finally, gradient-based interpretability analysis is used to evaluate the importance of observed nodes. The experimental results show that both the atmospheric state estimation model and the interpretable analysis method proposed in this paper are superior to some existing representative models and methods. Full article

Currently, there are three fundamental theoretical issues that need to be addressed in the research field of the Archimedes Spiral Wind Blade (ASWB): (1) the existing description of the generation principle of the ASWB’s surface is qualitative, which needs to be formally described using mathematical tools; (2) in the published literature, no studies were found that attempt to fully describe the surface of the ASWB using mathematical tools; (3) in the published literature, no clear definition of the ASWB can be found. The first and second of the above three problems are relatively easy to solve, whereas the ultimate solution to the third problem requires long-term communication and discussion among researchers from various countries. Therefore, this paper focuses primarily on the first of the above problems, namely, to describe the intermediate process of transforming an irregular planar figure into the 3D surface of an ASWB in a standardized manner using mathematical tools including a polar coordinate system, planar and spatial Cartesian coordinate systems, the curve equation of an Archimedes spiral, differential equations, and so on. For the second problem, this paper proposes an alternative approach: namely, conjecturing that the ASWB surface can be approximated by an infinite number of 3D Archimedes spirals, and an example with a finite number of such spirals is provided. For the third problem, this paper can currently only suggest that the precise definition of the ASWB should be based on a standardized description of the generation principle of the ASWB surface, or, alternatively, on an accurate geometric description of the shape of the ASWB surface. The scientific contribution of this paper lies in proposing, for the first time from a purely geometric perspective (independent of aerodynamics), three fundamental theoretical problems concerning ASWB, along with preliminary alternative ideas toward their solution. Full article

An analysis is presented for the steady thermophoresis and photophoresis of a homogeneous dispersion of identical aerosol spheres of typical physical properties and surface characteristics. The analysis assumes a moderately small Knudsen number (less than about 0.1), such that the gas motion lies within the slip-flow regime, including thermal creep, temperature jump, thermal stress slip, and frictional slip at the particle surfaces. Under conditions of low Peclet and Reynolds numbers, the coupled momentum and energy equations are analytically solved using a unit cell approach that explicitly incorporates interparticle interactions. Closed-form expressions are derived for the mean particle migration velocities in both thermophoresis driven by a uniform temperature gradient and photophoresis induced by an incident radiation field. The results reveal that the normalized particle velocities, referenced to those of an isolated particle, generally decrease with increasing particle volume fraction, though exceptions occur for thermophoresis. While thermal stress slip and thermal creep exert no influence on the normalized thermophoretic velocity, they markedly affect the normalized photophoretic velocity, which rises with the thermal stress slip to the thermal creep coefficient ratio. For both phenomena, the normalized migration velocities increase monotonically with the particle-to-fluid thermal conductivity ratio. Full article

Discontinuous phase flooding (such as polymer microspheres) is an important method for enhancing oil recovery. With the hydration swelling and elastic properties, a unique “migration–entrapment–remigration” discontinuous flow behavior is identified during flooding. And a more pronounced conformance control effect is observed in high-permeability flow channels and deeper reservoir regions compared to continuous phase flooding. These complex seepage mechanisms pose significant challenges to reservoir numerical simulation. Based upon a chemical reaction framework, a multi-component mathematical model comprising oil, gas, water, pre-discontinuous phase, and discontinuous phase components is developed in this study. The discontinuous phase is generated through chemical reactions involving the pre-discontinuous phase. A minimum reaction porosity is first introduced in the chemical reaction process to enhance the discontinuous phase generation in high-permeability regions. A threshold pressure is incorporated into the discontinuous phase equation for the “migration–entrapment–remigration” discontinuous flow characteristics. The model is subsequently solved using a fully implicit finite volume method. A new numerical simulator implementing this approach is developed in C++. Validation through physical experiments confirms the method’s accuracy. The discontinuous migration process of “migration–entrapment–remigration” is clearly reflected through the injection pressure fluctuations during simulation. Mechanistic models and field-scale simulations both confirm that discontinuous phase flooding significantly enhances oil recovery efficiency, outperforming both water flooding and continuous phase flooding. The novel reaction specification enhances conformance control in high-permeability channels, as demonstrated by the simulation results. The proposed model accurately captures the migration characteristics of the discontinuous phase and holds important practical value for reservoirs with discontinuous phase flooding. Full article

We develop a novel Steffensen-type iterative solver to solve nonlinear scalar equations without requiring derivatives. A two-parameter one-step scheme without memory is first introduced and analyzed. Its optimal quadratic convergence is then established. To enhance the convergence rate without additional functional evaluations, we extend the scheme by incorporating memory through adaptively updated accelerator parameters. These parameters are approximated by Newton interpolation polynomials constructed from previously computed values, yielding a derivative-free method with R-rate of convergence of approximately 3.56155. A dynamical system analysis based on attraction basins demonstrates enlarged convergence regions compared to Steffensen-type methods without memory. Numerical experiments further confirm the accuracy of the proposed scheme for solving nonlinear equations. Full article

In this study, an improved particle swarm optimization (PSO) algorithm is designed to construct a weighting model for line-of-sight (LOS) and non-line-of-sight (NLOS) channels in an ultra-wideband (UWB) indoor positioning system. In the proposed algorithm, the particle position represents candidate weight vectors, and the fitness function is defined by the 3D positioning error over multiple test points. An optimized weight modeling framework is proposed for a multi-anchor, three-dimensional UWB indoor positioning system under LOS and NLOS channels. First, the three-dimensional positioning problem is formulated as a multilateration model, and the tag coordinates are estimated via a linearized matrix equation solved by the least-squares method, which explicitly links anchor geometry and ranging errors to the positioning accuracy. To evaluate the proposed method, extensive ranging and positioning experiments are conducted in a realistic indoor environment using up to eight anchors with different LOS/NLOS configurations, including dynamic scenarios with varying numbers of NLOS anchors. The results show that, compared with the conventional unweighted multi-anchor scheme, the PSO-based weighting model can reduce the average 3D positioning error by more than 30% in typical LOS-dominant settings and significantly suppress error bursts in severe NLOS conditions. These findings demonstrate that the combination of mathematical modeling, least-squares estimation, and swarm intelligence optimization provides an effective tool for designing intelligent engineering positioning systems in complex indoor environments, which aligns with the development of smart factories and industrial Internet-of-Things (IIoT) applications. Full article

This study introduces a multidimensional mathematical model and a robust numerical algorithm with second-order accuracy for modeling the complex coupled processes of heat and moisture transfer with gas-pressure-driven flow, based on time-fractional differential equations (with Caputo derivatives of order 0 < α ≤ 1), which capture the memory effects and anomalous diffusion inherent in heterogeneous porous media. The proposed model integrates conductive and convective heat transfer; moisture diffusion and phase change; and pressure dynamics within the pore space and their bidirectional couplings. It also incorporates environmental interactions through boundary conditions for heat and moisture exchange with the ambient air; internal heat and moisture release; transient influx of solar radiation; and material heterogeneity, where all transport coefficients are spatially variable functions. To solve this nonlinear and coupled system, we developed a high-order, stable finite-difference scheme. The numerical algorithm employs an alternating direction-implicit approach, which ensures computational efficiency while maintaining numerical stability. We demonstrate the algorithm’s capability through numerical simulations that monitor and predict the spatiotemporal evolution of coupled transport temperature, moisture content, and pressure fields. The results reveal how heterogeneity, diurnal solar radiation, and internal sources create localized hot spots, moisture accumulation zones, and pressure gradients that significantly influence the overall dynamics of storage and drying processes. Full article

For ground with trapezoidal distributed subgrade reaction coefficients caused by natural sedimentation, a calculation model for pile(wall) deflection deformation under lateral loads was established. Based on the theory of power series solution of differential equations, a power series solution for pile(wall) deflection deformation that considers the trapezoidal distribution of lateral loads and subgrade reaction coefficients was proposed. The power series solution can be degraded into the traditional K-method and m-method formulas for calculating pile(wall) deflection deformation. The results show that when the number of calculation terms of the power series solution is taken as 20, the maximum relative truncation error of the horizontal displacement is 0.19%, and the calculation accuracy can meet the requirements of theoretical analysis and engineering calculation. For long pile(wall) with a converted depth $\overline{h}$ greater than 5 m, it is suggested to calculate at 5 m. The analysis of engineering examples demonstrates the validity. The proposed power series calculation method solves the problem of pile(wall) deflection deformation with trapezoidal distributed subgrade reaction coefficients under lateral loads, which the traditional K-method and m-method cannot solve. Compared with the finite element method, the computational efficiency of the deterministic method is improved. Therefore, the proposed method can support the establishment of calculation methods for complex problems such as pile(wall) deflection deformation in multi-layered ground and anti-slide piles under local lateral loads. Full article

Far-field narrow-band Direction-of-Arrival (DOA) estimation is a practical challenge in passive and active sonar applications. While the Conventional Beamformer (CBF) is a robust Maximum Likelihood Estimator (MLE), its precision is inherently constrained by the discrete scanning interval. To overcome this limitation, this paper proposes a novel Model Solution Algorithm (MSA estimator that leverages the exact theoretical beam pattern of the array to resolve the DOA. Unlike the classical Parabolic Interpolation Algorithm (PIA) estimator, which exhibits significant estimation bias due to polynomial approximation errors, the proposed MSA estimator numerically solves the deterministic beam pattern equation to eliminate such model mismatch. Quantitative simulation results demonstrate that the MSA estimator approaches the Cramér-Rao Lower Bound (CRLB) with a stable RMSE of approximately 0.12° under sensor position errors and a frequency-invariant precision of ~0.23°, significantly outperforming the PIA estimator, which suffers from systematic errors reaching 1.1° and 0.75°, respectively. Furthermore, the proposed method exhibits superior noise resilience by extending the operational range to −24 dB, surpassing the −15 dB breakdown threshold of Multiple Signal Classification (MUSIC). Additionally, complexity analysis and geometric evaluations confirm that the method retains a low computational burden suitable for real-time deployment and can be effectively generalized to arbitrary array geometries without accuracy loss. Full article

In new distribution systems with high penetration of renewable energy, inverter-based sources exhibit significant differences in fault characteristics compared to traditional power sources due to the absence of a constant electromotive force and their operation under nonlinear control links, rendering conventional fault current calculation methods inadequate. To address these challenges, a full-time-domain analysis-based method for modelling and calculating fault transient characteristics is proposed. First, a dynamic model of inverter-based sources accounting for current loop saturation effects is established, and phase plane analysis is employed to resolve nonlinear control regions. On this basis, a full-time-domain fault current calculation method is proposed, wherein the steady-state operating point after a fault is determined by iteratively solving the network node voltage equations. By integrating control strategies and derived transient differential equations, the fault current expression across the full-time-domain scope is formulated. Furthermore, a multi-objective optimization control strategy is proposed to achieve effective fault current suppression, and an improved Simulated Annealing-Particle Swarm Optimization (SA-IPSO) hybrid algorithm is adopted for efficient solution. Finally, SIMULINK-based simulation experiments validate the accuracy and effectiveness of the proposed method in transient characteristic analysis and current suppression. Full article

This study investigates the two-dimensional (2D) steady-state frictional contact behavior of functionally graded piezoelectric material (FGPM) coatings under a high-speed rigid cylindrical punch. An electromechanical coupled contact model considering inertial effects is established, while a layered model is employed to simulate arbitrarily varying material parameters. Based on piezoelectric elasticity theory, the steady-state governing equations for the coupled system are derived. By utilizing the transfer matrix method and the Fourier integral transform, the boundary value problem is converted into a system of coupled Cauchy singular integral equations of the first and second kinds in the frequency domain. These equations are solved semi-analytically, using the least squares method combined with an iterative algorithm. Taking a power-law gradient distribution as a case study, the effects of the gradient index, relative sliding speed, and friction coefficient on the contact pressure, in-plane stress, and electric displacement are systematically analyzed. Furthermore, the contact responses of FGPM coatings with power-law, exponential, and sinusoidal gradient profiles are compared. The findings provide a theoretical foundation for the optimal design of FGPM coatings and for enhancing their operational reliability under high-speed service conditions. Full article

A comprehensive numerical analysis has been conducted to investigate unsteady natural convection (UNC), bifurcation behavior, and heat transfer (HT) in a rectangular enclosure containing thermally stratified air. The enclosure comprises a uniformly heated bottom wall, thermally stratified vertical sidewalls, and a cooled top wall. To assess thermal performance, square and rectangular cavities with identical boundary conditions and working fluid are considered. The finite volume method (FVM) is used to solve the governing equations over a wide range of Rayleigh numbers (Ra = 10¹ to 10⁹) for air with a Prandtl number (Pr) of 0.71. Flow dynamics and thermal performance are analyzed using temperature time series (TTS), limit point–limit cycle behavior, average Nusselt number (Nu_avg), average entropy generation (S_avg), average Bejan number (Be_avg), and the ecological coefficient of performance (ECOP). In the rectangular cavity, the transition from steady to chaotic flow exhibits three bifurcations: a pitchfork bifurcation at Ra = 3 × 10⁴–4 × 10⁴, a Hopf bifurcation at Ra = 3 × 10⁶–4 × 10⁶, and the onset of chaotic flow at Ra = 9 × 10⁷–2 × 10⁸. The comparative analysis indicates that Nu_avg remains nearly identical for both cavities within Ra = 10⁵ to 10⁷. However, at Ra = 10⁸, the HT rate in the rectangular cavity is 29.84% higher than that of the square cavity, while S_avg and Be_avg differ by 39.32% and 37.50%, respectively. Despite higher HT and S_avg in the rectangular enclosure, the square cavity demonstrates superior overall thermal performance by 13.52% at Ra = 10⁸. These results offer significant insights for optimizing cavity geometries in thermal system design based on energy efficiency and entropy considerations. Full article

Thermo-hydrodynamic (THD) lubrication is a key mechanism in injection pumps, where frictional heating and heat transfer strongly influence lubrication performance. Accurate numerical modeling remains challenging due to the nonlinear coupling of temperature- and pressure-dependent fluid properties and the high computational cost of iterative solvers. The rising relevance of bio-hybrid fuels, however, demands the investigation of a great number of fuel mixtures and conditions, which is currently infeasible with traditional solvers. Physics-informed neural networks (PINNs) have recently been applied to lubrication problems; existing approaches are typically restricted to stationary cases or rely on data to improve training. This work presents a novel, purely physics-based PINN framework for solving coupled, transient THD lubrication problems in injection pumps. By embedding the Reynolds equation, energy conservation laws, and temperature- and pressure-dependent fluid models directly into the loss function, the proposed approach eliminates the need for any simulation or experimental data. The PINN is trained solely on physical laws and validated against an iterative solver for 16 transient test cases across two fuels and eight operating scenarios. The good agreement of PINN and iterative solver demonstrates the strong potential of PINNs as efficient, scalable surrogate models for transient THD lubrication and iterative design applications. Full article

This paper presents a reduced-order Legendre–Galerkin extrapolation (ROLGE) method combined with the scalar auxiliary variable (SAV) approach (ROLGE-SAV) to numerically solve the time-fractional Allen–Cahn equation (tFAC). First, the nonlinear term is linearized via the SAV method, and the linearized system derived from this SAV-based linearization is time-discretized using the shifted fractional trapezoidal rule (SFTR), resulting in a semi-discrete unconditionally stable scheme (SFTR-SAV). The scheme is then fully discretized by incorporating Legendre–Galerkin (LG) spatial discretization. To enhance computational efficiency, a proper orthogonal decomposition (POD) basis is constructed from a small set of snapshots of the fully discrete solutions on an initial short time interval. A reduced-order LG extrapolation SFTR-SAV model (ROLGE-SFTR-SAV) is then implemented over a subsequent extended time interval, thereby avoiding redundant computations. Theoretical analysis establishes the stability of the reduced-order scheme and provides its error estimates. Numerical experiments validate the effectiveness of the proposed method and the correctness of the theoretical results. Full article

An infinite-horizon $H_{\infty }$ linear-quadratic control problem is considered. This problem has the following features: (i) the control cost in the cost functional has a positive small coefficient (small parameter), meaning that the control cost is much smaller than the state cost; (ii) the current cost of the fast state variable in the cost functional is a non-zero positive semi-definite quadratic form. These features require developing a significantly novel approach to asymptotic analysis of the matrix Riccati algebraic equation appearing in the solvability conditions of the considered $H_{\infty }$ problem. Using this solution, an asymptotic analysis of the $H_{\infty }$ problem is carried out. This analysis yields parameter-free solvability conditions for this problem and a simplified controller solving this problem. An example illustrating the theoretical results is presented. Full article