Search Results (773)

The shallow water equations (SWEs) model fluid flow in rivers, coasts, and tsunamis. Their nonlinearity challenges analytical solutions. We present a numerical algorithm combining the finite integration method with Chebyshev polynomial expansion (FIM-CPE) to solve one- and two-dimensional SWEs. The method transforms partial differential equations into integral equations, approximates spatial terms via Chebyshev polynomials, and uses forward differences for time discretization. Validated on stationary lakes, dam breaks, and Gaussian pulses, the scheme achieved errors below ${10}^{-12}$ for water height and velocity, while conserving mass with volume deviations under ${10}^{-5}$. Comparisons showed superior shock-capturing versus finite difference methods. For two-dimensional cases, it accurately resolved wave interactions over complex topographies. Though limited to wet beds and small-scale two-dimensional problems, the method provides a robust simulation tool. Full article

Under conservation tillage in the Huang-Huai-Hai wheat–maize rotation area, the ridge-clearing no-till seeder for strip tillage mitigates the adverse impacts of surface residues on seeding quality by clearing stubble specifically within the seed rows, demonstrating significant potential for application and promotion. However, the inadequate understanding of the seeder’s operational performance and governing mechanisms under varying field conditions hinders its high-quality and efficient implementation. To address this issue, this study selected the stubble height, forward speed, and stubble knife rotational speed (PTO speed) as experimental factors. Employing a three-factor quasi-level orthogonal experimental design, coupled with response surface regression analysis, this research systematically elucidated the interaction mechanisms among these factors concerning the seeding depth consistency and seed spacing uniformity of the seeder. An optimized parameter-matching model was subsequently derived through equation system solving. Field trials demonstrated that a lower forward speed improved the seed spacing uniformity and seeding depth consistency, whereas high speeds increased the missing rates and spacing deviations. An appropriate stubble height enhanced the seed spacing accuracy, but an excessive height compromised depth precision. Higher PTO speeds reduced multiple indices but impaired depth accuracy. Response surface analysis based on the regression models demonstrated that the peak value of the seed spacing qualification index occurred within the forward speed range of 8–9 km/h and the stubble height range of 280–330 mm, with the stubble height being the dominant factor. Similarly, the peak value of the seeding depth qualification index occurred within the stubble height range of 300–350 mm and the forward speed range of 7.5–9 km/h, with the forward speed as the primary factor. Validation confirmed that combining stubble heights of 300−330 mm, forward speeds of 8−9 km/h, and PTO speeds of 540 r/min optimized both metrics. This research reveals nonlinear coupling relationships between operational parameters and seeding quality metrics, establishes a stubble–speed dynamic matching model, and provides a theoretical foundation for the intelligent control of seeders in conservation tillage systems. Full article

A rotating imperfect ring resonator of the gyroscope is modeled by a rotating thin ring with evenly distributed point masses. The free response of the rotating ring structure at constant speed is investigated, including the steady elastic deformation and wave response. The dynamic equations are formulated by using Hamilton’s principle in the ground-fixed coordinates. The coordinate transformation is applied to facilitate the solution of the steady deformation, and the displacements and tangential tension for the deformation are calculated by the perturbation method. Employing Galerkin’s method, the governing equation of the free vibration is casted in matrix differential operator form after the separation of the real and imaginary parts with the inextensional assumption. The natural frequencies are calculated through the eigenvalue analysis, and the numerical results are obtained. The effects of the point masses on the natural frequencies of the forward and backward traveling wave curves of different orders are discussed, especially on the measurement accuracy of gyroscopes for different cases. In the ground-fixed coordinates, the frequency splitting results in a crosspoint of the natural frequencies of the forward and backward traveling waves. The finite element method is applied to demonstrate the validity and accuracy of the model. Full article

Aiming at the multifunctional requirements of the limited space in high-end vehicle side-door latches, a double single-loop RRUPRR mechanism driven by a single motor for both electric releasing and cinching is proposed based on the POC set. The kinematical equations of the RRURR mechanism possess 2 × 2 analytical solutions. In order to apply the current motion/force transmission performance index of the parallel mechanisms to the transmission performance analysis of the serial mechanisms, matching methods for chain-driving transference and the moving/fixed platform inversion are proposed. The solution of the performance index of a single-degree-of-freedom single-loop mechanism is equivalent to the solution of the input motion/force transmission performance index of a parallel mechanism. The overall motion/force transmission performance index of a single-loop mechanism is constructed, and the corresponding calculation procedure is defined. Chain-driving transference can be obtained through forward and inverse solutions of the RRURR mechanism. In response to the extremely high requirements for motion/force transmission performance of electric release mechanisms, the proposed overall motion/force transmission performance index is used to calculate for the input motion screw and corresponding transmission-force screw of the single-loop RRURR mechanism and obtain the overall motion/force transmission performance of the mechanism. The performance atlas of the mechanism shows that it has excellent motion/force transmission characteristics within the workspace. Using ADAMS simulation software, the driving torque required for electric releasing and cinching of a vehicle side-door latch mechanism with a single motor is analyzed. The overall motion/force transmission performance index of a single-loop mechanism can be applied to single-loop overconstrained mechanisms and non-overconstrained mechanisms. Full article

The time-domain electromagnetic method has been widely applied in mineral exploration, oil, and gas fields in recent years. However, its response characteristics remain unclear, and there is an urgent need to study the response characteristics of the borehole-surface transient electromagnetic(BSTEM) field. This study starts from the time-domain electric field diffusion equation and discretizes the calculation area in space using tetrahedral meshes. The Galerkin method is used to derive the finite element equation of the electric field, and the vector interpolation basis function is used to approximate the electric field in any arbitrary tetrahedral mesh in the free space, thus achieving the three-dimensional forward simulation of the BSTEM field based on the finite element method. Following validation of the numerical simulation method, we further analyze the electromagnetic field response excited by vertical line sources.. Through comparison, it is concluded that measuring the radial electric field is the most intuitive and effective layout method for BSTEM, with a focus on the propagation characteristics of the electromagnetic field in both low-resistance and high-resistance anomalies at different positions. Numerical simulations reveal that BSTEM demonstrates superior resolution capability for low-resistivity anomalies, while showing limited detectability for high-resistivity anomalies Numerical simulation results of BSTEM with realistic orebody models, the correctness of this rule is further verified. This has important implications for our understanding of the propagation laws of BSTEM as well as for subsequent data processing and interpretation. Full article

The chiral nonlinear Schrödinger equation (CNLSE) serves as a simplified model for characterizing edge states in the fractional quantum Hall effect. In this paper, we leverage the generalization and parameter inversion capabilities of physics-informed neural networks (PINNs) to investigate both forward and inverse problems of 1D and 2D CNLSEs. Specifically, a hybrid optimization strategy incorporating exponential learning rate decay is proposed to reconstruct data-driven solutions, including bright soliton for the 1D case and bright, dark soliton as well as periodic solutions for the 2D case. Moreover, we conduct a comprehensive discussion on varying parameter configurations derived from the equations and their corresponding solutions to evaluate the adaptability of the PINNs framework. The effects of residual points, network architectures, and weight settings are additionally examined. For the inverse problems, the coefficients of 1D and 2D CNLSEs are successfully identified using soliton solution data, and several factors that can impact the robustness of the proposed model, such as noise interference, time range, and observation moment are explored as well. Numerical experiments highlight the remarkable efficacy of PINNs in solution reconstruction and coefficient identification while revealing that observational noise exerts a more pronounced influence on accuracy compared to boundary perturbations. Our research offers new insights into simulating dynamics and discovering parameters of nonlinear chiral systems with deep learning. Full article

In this paper, we present the concept of “sequencing economics”, consisting of (A) segmentation, (B) construction sequencing, and (C) functions. An agglomeration is organized into segments, and sequencing economics examines the sequential process of efficiently building such segments. The functions (C) of the segments act as a master switch, an accelerator, a brake, etc. in the implementation of agglomeration policy. In this paper, we identify a master switch and an accelerator in scientific city agglomeration policy and draw two conclusions. First, in agglomeration policy, the construction of the master switch lowers “transport costs”, as derived from the monocentric city model of spatial economics by Fujita and Krugman. Second, the accelerator segment represents the activities of the service sector that have the highest forward-linkage effect in an input–output relationship. Regarding science city agglomeration policy, it can be concluded that the master switch is high-speed rail and the accelerator is research and education activities. In this paper, the new scientific urban agglomeration that emerges from monocentric cities is referred to as railroad-driven agglomeration (RDA), which is a type of transit-oriented development (TOD). This paper demonstrates that the Tsukuba Express, as a case study of RDA, caused the agglomeration of Tsukuba Science City. This paper establishes the concept of sequencing economics, a policy implementation rule that differs from Tinbergen’s rule. The latter is based on the concept of simultaneous equations, whereas the rule of sequencing economics is based on sequential equations. RDA enables middle-income countries to surpass their middle-income status. Full article

Uncertain singular non-causal systems represent a class of singular systems distinguished by the presence of regularity constraints and the involvement of uncertain variables. This paper considers optimal control problems for such systems under the Hurwicz criterion. By integrating dynamic programming with uncertainty theory, a recurrence equation is developed to address these problems. This equation has been shown to be effective in handling the optimal control problems of both linear and nonlinear uncertain singular non-causal systems, thereby enabling the derivation of analytical expressions for their corresponding optimal solutions. Moreover, the transformation of the original system into forward and backward subsystems reveals a fundamental temporal and structural symmetry, which significantly contributes to problem simplification. A detailed example is presented to illustrate the proposed results. Full article

Accurate and reliable pedestrian positioning service is essential for providing Indoor Location-Based Services (ILBSs). Zero-Velocity Update (ZUPT)-aided Strapdown Inertial Navigation System (SINS) based on foot-mounted wearable Inertial Measurement Units (IMUs) has shown great performance in pedestrian navigation systems. Though the velocity errors will be corrected once zero-velocity measurement is available, the navigation system errors accumulated during measurement outages are yet to be further optimized by utilizing historical data during both stance and swing phases of pedestrian gait. Thus, in this paper, a novel Forward–Backward navigation and Rauch–Tung–Striebel smoothing (FB-RTS) navigation scheme is proposed. First, to efficiently re-estimate past system state and reduce accumulated navigation error once zero-velocity measurement is available, both the forward and backward integration method and the corresponding error equations are constructed. Second, to further improve navigation accuracy and reliability by exploiting historical observation information, both backward and forward RTS algorithms are established, where the system model and observation model are built under the output correction mode. Finally, both navigation results are combined to achieve the final estimation of attitude and velocity, where the position is recalculated by the optimized data. Through simulation experiments and two sets of field tests, the FB-RTS algorithm demonstrated superior performance in reducing navigation errors and smoothing pedestrian trajectories compared to traditional ZUPT method and both the FB and the RTS method, whose advantage becomes more pronounced over longer navigation periods than the traditional methods, offering a robust solution for positioning applications in smart buildings, indoor wayfinding, and emergency response operations. Full article

In this paper, we develop an HIV/AIDS epidemic model that incorporates a saturated incidence rate to reflect the limited transmission capacity and the impact of behavioral saturation in contact patterns. The model is formulated as a system of seven non-linear ordinary differential equations representing key population compartments. In addition to model formulation, we introduce an optimal control problem involving three control measures: educational campaigns, screening of unaware infected individuals, and antiretroviral treatment for aware infected individuals. We begin by establishing the positivity and boundedness of the model solutions under constant control inputs. The existence and local and global stability of both the disease-free and endemic equilibrium points are analyzed, depending on the effective reproduction number (${\mathcal{R}}_e$). Bifurcation analysis reveals that the model undergoes a forward bifurcation at ${\mathcal{R}}_e=1$. A local sensitivity analysis of ${\mathcal{R}}_e$ identifies the disease transmission rate as the most sensitive parameter. The optimal control problem is then formulated by incorporating the dynamics of infected subpopulations, control costs, and time-dependent controls. The existence of optimal control solutions is proven, and the necessary conditions for optimality are derived using Pontryagin’s Maximum Principle. Numerical simulations support the theoretical analysis and confirm the stability of the equilibrium points. The optimal control strategies, evaluated using the Incremental Cost-Effectiveness Ratio (ICER), indicate that implementing both screening and treatment (Strategy D) is the most cost-effective intervention. These results provide important insights for designing effective and economically sustainable HIV/AIDS intervention policies. Full article

Based on the single-crank linkage mechanism and the double-pendulum rod mechanism, herein, a reciprocating swing single-blade cutting device is appropriately designed for the needs of GLVs’ planting and cutting operations. It can effectively solve the existing double-blade cutting device’s in-soil operation issue, where clods of soil and stones adhere to the upper and lower cutting blades, resulting in problems such as excessive wear and blade fracture. Using ADAMS, a virtual model of the cutting device is established, and a kinematic analysis of the cutting process is performed to accurately determine the cutting trajectory curve and the mathematical model of the cutting rate. The single-factor test and quadratic regression orthogonal combination test are designed to investigate the influence of the test factors, including crank length, crank rotation speed, and forward speed on the repeated-cutting rate and the miss-cutting rate. Comprehensively considering the stability and reliability of cutting, power consumption, device design, and processing difficulty, the optimal operating parameters of the cutting device are obtained as crank length 19 mm, crank rotation speed 650 r/min, and forward speed 0.5 km/h. On this basis, the fitted regression equations of the repeated-cutting rate and the miss-cutting rate are established, the miss-cutting rate and the repeated-cutting rate under the optimal parameters are 1.519% and 28.503%, and the corresponding errors with the simulation values are obtained as 11.36% and −0.45%, respectively, which verified the validity of the fitted regression equations. In the present investigation, the motion behavior of the single-blade cutting device is methodically examined for the first time, and the cutting motion rules of the cutter are illustrated. The research results aim to provide a fairly solid theoretical basis and practical reference for the optimization design of the in-soil cutting device of GLVs’ orderly harvester. Full article

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: How can models utilize physics or mathematical principles to enhance predictions when dealing with sparse, noisy, or incomplete data? Physics-Informed Neural Networks (PINNs) put this idea into practice by incorporating a forward model, such as Partial Differential Equations (PDEs), as soft constraints. This guidance helps the networks find solutions that align with established laws. Recently, researchers have expanded this framework to include Bayesian NNs (BNNs) which allow for uncertainty quantification. However, what happens when the governing equations of a system are not completely known? In this work, we introduce methods to automatically select PDEs from historical data in a parametric family. We then integrate these learned equations into three different modeling approaches: PINNs, Bayesian-PINNs (B-PINNs), and Physical-Informed Bayesian Linear Regression (PI-BLR). To assess these frameworks, we evaluate them on a real-world Multivariate Time Series (MTS) dataset related to electrical power energy management. We compare their effectiveness in forecasting future states under different scenarios: with and without PDE constraints and accuracy considerations. This research aims to bridge the gap between data-driven discovery and physics-guided learning, providing valuable insights for practical applications. Full article

In this study, we aim to construct a finite set of orthogonal matrix polynomials for the first time, along with their finite orthogonality, matrix differential equation, Rodrigues’ formula, several recurrence relations including three-term relation, forward and backward shift operators, generating functions, integral representation and their relation with Jacobi matrix polynomials. Thus, the concept of “finite”, which is used to impose parametric constraints for orthogonal polynomials, is transferred to the theory of matrix polynomials for the first time in the literature. Moreover, this family reduces to the finite orthogonal M polynomials in the scalar case when the degree is 1, thereby providing a matrix generalization of finite orthogonal M polynomials in one variable. Full article

The design and analysis of a new wave actuator for boats is presented in this paper. The wave actuator is installed beneath the boat hull and converts the hydrodynamic forces generated by rising waves on the boat into translational thrusting forces. The wave actuator consists of a flexible water tank, revolving springs, and inlet/outlet nozzles to enable passive wave-driven thrust generation without intermediate energy conversion. The compressed water in the tank of the wave actuator is expelled by the wave pressure exerted on the actuator, and the water thrust out of the nozzles propels the boat forward. The dynamics and hydrodynamics of the new wave actuator are newly modelled using second-order differential equations in this paper. The hydrodynamics of the boat with the wave actuator is mathematically analyzed, and the energy conversion capability of the wave actuator is analyzed. The results demonstrate that at a wave frequency of 0.3 Hz, the system achieves a cruising speed of 6.098 m/s and a high energy conversion efficiency of 67.9%. These findings highlight the actuator’s potential for efficient and sustainable marine propulsion in regular sea conditions. Full article

This study proposes the use of Physics-Informed Neural Networks (PINNs) to further advance the curvature interference analysis method. The nonlinear equation system encountered in determining the curvature interference limit line is embedded into the PINN loss function, thereby enabling the solution of high-dimensional, nonlinear equations. Computational results demonstrate that the PINN model achieves a solution accuracy on the order of 10⁻¹³ when solving multidimensional nonlinear systems, which is comparable to the classical Fsolve algorithm. The curvature interference analysis reveals the presence of two curvature interference boundary lines, although they rarely extend to the worm gear tooth surface. A study on the influence of design parameters on the interference boundaries indicates that the axial installation distance has the greatest impact. Inadequate axial spacing causes the interference limit line to shift toward the inner end of the worm gear, significantly increasing the risk of interference in that region. The proposed curvature interference analysis method based on PINNs can be extended to other types of gear drives. It also lays the foundation for future work on establishing both forward and inverse mappings between design parameters and curvature interference using PINNs. Full article