Compact implicit integration factor methods for some complex-valued nonlinear equations

The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.

METHOD TO CALCULATE BENDING CENTER AND STRESS INTENSITY FACTORS OF CRACKED CYLINDER UNDER SAINT_VENANT BENDING

Using the single crack solution and the regular solution of plane harmonic function, the problem of Saint_Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross_section is not thin_walled, but of small torsion rigidity is proposed. Some numerical examples are given.

Evaluation of mixed-mode stress intensity factors by extended finite element method

Extended finite element method （XFEM） implementation of the interaction integral methodology for evaluating the stress intensity factors （SIF） of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationallv efficient.

Benefit allocation model of distributed photovoltaic power generation vehicle shed and energy storage charging pile based on integrated weighting-Shapley method

In this study,to develop a benefit-allocation model,in-depth analysis of a distributed photovoltaic-powergeneration carport and energy-storage charging-pile project was performed;the model was developed using Shapley integrated-empowerment benefit-distribution method.First,through literature survey and expert interview to identify the risk factors at various stages of the project,a dynamic risk-factor indicator system is developed.Second,to obtain a more meaningful risk-calculation result,the subjective and objective weights are combined,the weights of the risk factors at each stage are determined by the expert scoring method and entropy weight method,and the interest distribution model based on multi-dimensional risk factors is established.Finally,an example is used to verify the rationality of the method for the benefit distribution of the charging-pile project.The results of the example indicate that the limitations of the Shapley method can be reasonably avoided,and the applicability of the model for the benefit distribution of the charging-pile project is verified.

Analysis of multiple interfacial cracks in three-dimensional bimaterials using hypersingular integro-differential equation method

By using the concept of finite-part integral, a set of hypersingular integro-differential equations for multiple interracial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads is derived. In the numerical analysis, unknown displacement discontinuities are approximated with the products of the fundamental density functions and power series. The fundamental functions are chosen to express a two-dimensional interface crack rigorously. As illustrative examples, the stress intensity factors for two rectangular interface cracks are calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the crack spacing.

A method to calculate displacement factors using SVM

In order to improve the precision of mining subsidence prediction, a mathematical model using Support Vector Machine （SVM） was established to calculate the displacement factor. The study is based on a comprehensive analysis of factors affecting the displacement factor, such as mechanical properties of the cover rock, the ratio of mining depth to seam thickness, dip angle of the coal seam and the thickness of loose layer. Data of 63 typical observation stations were used as a training and testing sample set. A SVM regression model of the displacement factor and the factors affecting it was established with a kernel function, an insensitive loss factor and a properly selected penalty factor. Given an accurate calculation algorithm for testing and analysis, the results show that an SVM regression model can calcu- late displacement factor precisely and reliable precision can be obtained which meets engineering requirements. The experimental results show that the method to calculation of the displacement factor, based on the SVM method, is feasible. The many factors affecting the displacement factor can be consid- ered with this method. The research provides an efficient and accurate approach for the calculation of displacement in mining subsidence orediction.

METHOD TO CALCULATE BENDING CENTER AND STRESS INTENSITY FACTORS OF CRACKED CYLINDER UNDER SAINT-VENANT BENDING

Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.

SINGULAR INTEGRAL EQUATIONS AND BOUNDARY ELEMENT METHOD OF CRACKS IN THERMALLY STRESSED PLANAR SOLIDS

Using the method of the boundary integral equation, a set of singular integral equations of the hear transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived, and then,its numerical method is proposed by the numerical method of the singular integral equations combined with boundary element method. Moreover, the singular nature of temperature gradient field near the crack front is proved by the main-part analysis method of the singular integral equation, and the singular temperature gradients are exactly obtained. Finally, several typical examples calculated.

A Straightforward Direct Traction Boundary Integral Method for Two-Dimensional Crack Problems Simulation of Linear Elastic Materials

This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces.The displacements and tractions were used as unknowns on the external boundary,while the relative crack opening displacement(RCOD)was chosen as unknowns on either side of crack surfaces to keep the single-domain merit.Only one side of the crack surfaces was concerned and needed to be discretized,thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method(DBEM).A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly,and the SIFs were evaluated by the extrapolation of the RCOD.Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.

Exponential Time Differencing Method for a Reaction-Diffusion System with Free Boundary

For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.

AN INVESTIGATION ON TWO CRACKS PERPEN DICULAR TO THE INTERFACES IN A PIEZOE LECTRIC LAYER BONDED TO TWO HALF SPACES BY THE SCHMIDT METHOD

The behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces is investigated by the Schmidt method. The cracks are vertically to the interfaces of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved using the Schmidt method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of the interacting cracks and the piezoelectric constants of the material upon the stress intensity factor of the cracks.

Numerical solutions of singular integral equations for planar rectangular interfacial crack in three dimensional bimaterials

Stress intensity factors for a three dimensional rectangular interfacial crack were considered using the body force method. In the numerical calculations, unknown body force densities were approximated by the products of the fundamental densities and power series; here the fundamental densities are chosen to express singular stress fields due to an interface crack exactly. The calculation shows that the numerical results are satisfied. The stress intensity factors for a rectangular interface crack were indicated accurately with the varying aspect ratio, and bimaterial parameter.

Implicit integration factor method for the nonlinear Dirac equation

A high-order accuracy time discretization method is developed in this paper to solve the one-dimensional nonlinear Dirac(NLD)equation.Based on the implicit integration factor(IIF)method,two schemes are proposed.Central differences are applied to the spatial discretization.The semi-discrete scheme keeps the conservation of the charge and energy.For the temporal discretization,second-order IIF method and fourth-order IIF method are applied respectively to the nonlinear system arising from the spatial discretization.Numerical experiments are given to validate the accuracy of these schemes and to discuss the interaction dynamics of the NLD solitary waves.

A Dynamical Model to Analyze the Influence of Sliding Friction on Motion on a Curve—An Analytical Method

To demonstrate the influence of sliding friction of motion on a curve, a circular path is considered for simplicity on which a person slides from the highest point to the lowest point. A slide which represents a quadrant of radius 5 m and a person of mass 60 kg are considered for comparison in this paper. A Differential equation for motion considering the fact that the normal force depends both on the sin component of weight and also on the tangential velocity, is established and is solved using integrating factor method, and the motion is analysed for different surface roughness of the slide and is compared using superimposed graphs, also the limiting value of friction coefficient at which the person just exits the slide is determined. The correction factor for exit velocity with friction as compared with the exit velocity for zero friction is determined. The fraction of energy lost to friction at the exit is evaluated. The Variation of normal force with the position of the person on the slide is plotted for different surface roughness of the slide, and the position on the slide where the normal force or the force experienced by the person is maximum, is determined and hence its maximum value is evaluated for different surface roughness. For simplicity, a point contact between the body and the slide is considered.

Dynamic Stress Intensity Factors for Three Parallel Cracks in an Infinite Plate Subject to Harmonic Stress Waves

Dynamic stresses around three parallel cracks in an infinite elastic plate that is subjected to incident time-harmonic stress waves normal to the cracks have been solved. Using the Fourier transform technique, the boundary conditions are reduced to six simultaneous integral equations. To solve these equations, the differences of displacements inside the cracks are expanded in a series. The unknown coefficients in those series are solved using the Schmidt method such that the conditions inside the cracks are satisfied. Numerical calculations are carried out for some crack configurations.

覆岩导水裂隙带发育高度动态演化规律研究

为了研究覆岩导水裂隙带发育高度动态演化规律,以小保当矿区2^(-2)煤层为研究对象,通过理论分析、相似模拟实验及实例验证的方法,对导水裂隙带动态发育高度进行研究;借助概率积分法预计其上部岩层移动变形的理论公式,给出了1种基于覆岩曲率变形的导水裂隙带动态发育高度预计方法。研究表明:导水裂隙带上部岩层下沉系数是1个与挠度及下部自由空间高度相关的分段函数,上部岩层曲率变形大小是决定导水裂隙带发育高度的关键因素;导水裂隙带发育高度与工作面推进长度相关;理论预计小保当矿区2^(-2)煤层导水裂隙带发育高度为160.8 m,相似模拟实验发育高度为155 m,现场实测发育高度为152.01~175.57 m。

直升机整体式惯性粒子分离器研究现状

整体式惯性粒子分离器是一种直升机进气防护装置,其性能优异、应用广泛,对于保护直升机发动机、延长其使用寿命具有重要意义。本文从4个方面对整体式惯性粒子分离器的研究现状进行归纳总结,包括:总结了现有直升机进气防护装置的类型及相关气动参数,梳理了整体式惯性粒子分离器现有的研究方法及取得的相关成果,分析了影响整体式惯性粒子分离器工作性能的因素,并展望了整体式惯性粒子分离器未来的发展方向。研究成果可为今后开展整体式惯性粒子分离器研究及优化设计提供一定参考。

基于模糊PID汽车变速箱自动控制方法

为改善汽车变速箱的目标速度跟踪水平,提升汽车的动力性,基于模糊PID汽车变速箱自动控制方法,确定汽车行驶的目标车速,计算目标车速与实际车速之间的偏差,以及速度偏差的变化率,将上述结果作为PID控制器的输入,利用参数整定后的PID控制器,确定汽车变速箱的控制变量,控制汽车传动机构输出理想车速。实验结果表明,汽车以阶跃信号、斜坡信号和正弦信号状态行驶时,该方法均可以精准跟踪汽车变速箱的速比,控制效果与动态跟踪性能优异,为保持汽车的最佳动力性能提供了良好的控制策略。

连续化肥减量配施有机肥提升植烟土壤肥力质量的综合评价

为准确评价连续多年化肥减量配施有机肥料对烤烟产量及植烟土壤综合肥力质量的影响,探究植烟土壤质量提升与烤烟绿色优质协同的化肥减量有机替代技术。以长期定位试验的第7年数据为基础,运用因子分析法、相关系数法、内梅罗指数法,对不施肥(CK)、当地推荐常规施肥(100%化肥,CF)、化肥减量20%配施有机肥(OF)和配施生物有机肥(BIO)4个处理的土壤肥力质量进行综合评价,并采用随机森林回归分析,探讨各土壤单项肥力指标对烤烟产量的解释度。结果表明,在连续7年化肥减量20%条件下,配施有机肥和生物有机肥均能降低烤烟青枯病和黑胫病的发病率和病情指数,提高烤烟经济性状、产量可持续性与稳定性,提高植烟土壤养分含量和土壤肥力综合质量。随机森林分析表明,植烟土壤有效磷、碱解氮、全氮是影响烤烟产量的决定因素,其解释率分别为19.66%、15.38%、12.07%。在3种评价方法下,植烟土壤综合肥力指数IFI值均表现为BIO>OF>CF>CK,BIO和OF处理较CF处理分别提高23.03%~31.75%和4.92%~7.94%。3种评价方法的IFI值与烤烟相对产量均呈显著或极显著正相关关系,相关系数大小依次为内梅罗指数法(0.884)>因子分析法(0.867)>相关系数法(0.747)。因此,连续多年化肥减量配施不同有机肥具有提高植烟土壤综合肥力质量和烤烟产量及质量的持续效应,且以化肥减量20%配施生物有机肥的效果最优。

农村“三块地”改革对县域城乡融合发展的影响研究——基于准自然实验的证据

文章基于2007—2020年1256个县(市、区)的面板数据,结合理论分析法和双重差分法,从准自然实验角度出发,探究以农村土地征收、集体经营性建设用地入市和宅基地制度改革为内容的“三块地”改革试点政策对县域城乡融合发展的影响效应及影响机理,为深化新一轮土地制度改革、推动县域城乡融合发展提供参考。基准回归分析表明,“三块地”改革对县域城乡融合发展具有显著且稳健的促进作用;机制研究发现,“三块地”改革通过促进土地、劳动力、资金要素在城乡之间自由流动推动了县域城乡融合发展;异质性分析发现,“三块地”改革在低城乡融合度县域、较低发展水平县域、中部县域的影响效应更加明显。据此,应进一步深化“三块地”改革,不断总结试点县域的政策实施经验,在差异化城乡融合基础、经济发展水平、自然地理条件下,因地制宜、审慎推进农村土地制度改革,强化城乡地域系统的连接纽带,促进城乡要素自由流动和平等交换,推动县域城乡经济、社会、人口、空间和生态全面融合发展,实现政策的长期效应。