Numerical experiment of anharmonic oscillators by using the symplectic scheme-shooting method

Symplectic scheme-shooting method (SSSM) is applied to solve the energy eigenvalues of anharmonic oscillators characterized by the potentials V(x)=λx 4 and V(x)=(1/2)x 2+λx 2α with α=2,3,4 and doubly anharmonic oscillators characterized by the potentials V(x)=(1/2)x 2+λ 1x 4 +λ 2x 6, and a high order symplectic scheme tailored to the "time"-dependent Hamiltonian function is presented. The numerical results illustrate that the energy eigenvalues of anharmonic oscillators with the symplectic scheme-shooting method are in good agreement with the numerical accurate ones obtained from the non-perturbative method by using an appropriately scaled basis for the expansion of each eigenfunction; and the energy eigenvalues of doubly anharmonic oscillators with the sympolectic scheme-shooting method are in good agreement with the exact ones and are better than the results obtained from the four-term asymptotic series. Therefore, the symplectic scheme-shooting method, which is very simple and is easy to grasp, is a good numerical algorithm.

The Lie-group Shooting Method for Radial Symmetric Solutions of the Yamabe Equation

We transform the Yamabe equation on a ball of arbitrary dimension greater than two into a nonlinear singularly boundary value problem on the unit interval[0;1].Then we apply Lie-group shooting method(LGSM)to search a missing initial condition of slope through a weighting factor r 2(0;1).The best r is determined by matching the right-end boundary condition.When the initial slope is available we can apply the group preserving scheme(GPS)to calculate the solution,which is highly accurate.By LGSM we obtain precise radial symmetric solutions of the Yamabe equation.These results are useful in demonstrating the utility of Lie-group based numerical approaches to solving nonlinear differential equations.

A two-parameter multiple shooting method and its application to the natural vibrations of non-prismatic multi-segment beams

This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.

Geomaterial Constitutive Models in Toe-Shooting Method

For toe-shooting method, geomaterial constitutive models concerned are studied. Analysis shows that, although extensively applied in soil mechanics, due to its angular singularity of yielding surface, the Mohr-Coulomb model is not suitable for numerical simulations in large deformation; in this case the rock-fills may be regarded as the Drucker-Prager model and the seaooze as the Prandtl-Reuss model. By comparing experimental data with numerical results, the constitutive model of the seaooze is numerically verified. It shows that, in high strain rate stage forming the blasting crater, the seaooze behaves as ideal non-compressible fluid, while in low strain rate stage during which the reck-fills flow to the blasting crater, the viscosity of the seaooze is negligible.

Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.

Comparison between Sulfuric Acid-phenol and Sulfuric Acid-anthrone Methods Used for Determination of Polysaccharides in Shoots of Aralia elata (Miq.) Seem.

Sulfuric acid-phenol and sulfuric acid-anthrone methods were used to detect polysaccharide content in shoots of Aralia elata（ Miq.） Seem.,and the conversion factor to glucose was measured with refined polysaccharides. Comprehensive evaluation was carried out by linear relationship,precision,reproducibility,stability and recovery rate. The results showed that the linear relationship between glucose concentration and absorbance was good when glucose concentration was0-40 μg/ml,and the average recovery rate was equal to or higher than 97. 00% with good reproducibility（ RSD 〈 1. 60%,n = 5）. It revealed that the two methods were accurate and reliable,and suitable for the determination of polysaccharide content in the shoots of A. elata. Polysaccharide content detected by sulfuric acid-phenol and sulfuric acid-anthrone methods was 19. 31% and 20. 40% respectively.

Trouble Shooting and Debugging Skills of Rectification and Capacitance Components of Doppler Weather Radar

Based on the CINRAD/SA user manual and the American WSR-88D technical guide,the working principle,parameters,debugging preparation,debugging process and debugging methods of rectification and capacitance components of Doppler radar were analyzed in detail,and the main trouble reasons were also introduced.

A numerical method for solving the boundary layer equations of laminar natural convention about a vertical plate

An improved shooting method was presented for solving the natural convention boundary layer equations, with a coupling of the velocity field to the temperature field. The numerical results are consistent with the approximate solution obtained by former researchers.

Numerical analysis on the shoot resistance of heat treated light weight B-grade bulletproof steel plates

Bulletproof steel plates are widely used for the safety of special vehicles.This paper mainly researches on the shoot resistance of heat treated light weight B-grade bulletproof steel plates through numerical analysis.Based on the flow behavior of bulletproof steel plates and bullet at various high strain rates,finite element(FE) model has been set up using ANSYS/LS-DYNA software.The simulation results are compared with the shooting results,which show a good consistency and a high reliability.Therefore,the simulation results are efficient approaches and strategies to decide and select the mechanical property and thickness of bulletproof steel plates,saving a lot of work and the cost of experiments.

Upshot of ohmically dissipated Darcy-Forchheimer slip flow of magnetohydrodynamic Sutterby fluid over radiating linearly stretched surface in view of Cash and Carp method

The present work concerns the momentum and heat transmission of the electro-magnetohydrodynamic (E-MHD) boundary layer Darcy-Forchheimer flow of a Sutterby fluid over a linear stretching sheet with slip. The nonlinear equations for the proposed model are analyzed numerically. Suitable techniques are used to transform the coupled nonlinear partial differential equations (PDEs) conforming to the forced balance law, energy, and concentration equations into a nonlinear coupled system of ordinary differential equations (ODEs). Numerical solutions of the transformed nonlinear system are obtained using a shooting method, improved by the Cash and Carp coefficients. The influence of important physical variables on the velocity, the temperature, the heat flux coefficient, and the skin-friction coefficient is verified and analyzed through graphs and tables. From the comprehensive analysis of the present work, it is concluded that by intensifying the magnitude of the Hartmann number, the momentum distribution decays, whereas the thermal profile of fluid increases. Furthermore, it is also shown that by aug- menting the values of the momentum slip parameter, the velocity profile diminishes. It is found that the Sutterby fluid model shows shear thickening and shear thinning behaviors. The momentum profile shows that the magnitude of velocity for the shear thickening case is dominant as compared with the shear thinning case. It is also demonstrated that the Sutterby fluid model reduces to a Newtonian model by fixing the fluid parameter to zero. In view of the limiting case, it is established that the surface drag in the case of the Sutterby model shows a trifling pattern as compared with the classical case.

Launch Vehicle Reconfigurable Guidance Method Based on Online Trajectory Optimization

In order to improve the safety and reliability of a launch vehicle, we present a reconfigurable guidance method based on online trajectory optimization for thrust decrease at the ascending stage of the launch vehicle in this paper. We used a multiple shooting method to convert the optimal control problem into a nonlinear programming(NLP) problem. Finally, we used the interior point method to solve the NLP problem. The simulation results show that the method can effectively adapt to thrust decreases by 5% and 10%. This reconfigurable guidance method based on online planning is proposed to realize launch missions under the condition of power descent, thus verifying the feasibility of the method.

Three-dimensional suboptimal guidance law for fly-over and shoot-down smart ammunition via virtual target

An optimal burst height is required for the fly-over and shoot-down smart ammunition with an EFP warhead at the instant of explosion which brings a special requirement to the miss distance of the terminal guidance law. In this paper, a guidance law based on the virtual target scheme is proposed. First, the practical pursuit-evasion issue between the ammunition and the target with specific miss distance is transformed into a virtuai pursuit-evasion problem with zero miss distance. Secondly, a complete three-dimensional pursuit-evasion kinematics model is established without any simplifications. And then, a suboptimal guidance law is designed based on the θ-D method which has constraints of the elevation and azimuth angular velocity of the virtual line of sight （LOS）. Finally, in order to verify the performance of the proposed guidance law, three test cases are conducted. Numericai results show that under the proposed terminal guidance law, the smart ammunition not only can fly above the target with an optimal burst height but also have a smaller normal acceleration on the terminal trajectory.

三分球投篮技术及其训练方法的研究

研究旨在探讨三分球投篮技术及训练方法,以提高球员的投篮命中率。基础训练包括站位、姿势校正和出手动作练习,瞄准训练通过目标设定提高准确性,力量训练增强上肢和核心稳定性,节奏训练则通过反复练习提高投篮的连贯性和效率。此外,提高命中率的技巧包括控制情绪、增强自信心、模拟比赛场景、利用录像回放分析和持续练习。通过这些方法,球员可以在比赛中更有效地执行三分球投篮。

苦竹鲜笋废弃物中总黄酮提取工艺优化研究

采用超声波辅助溶剂浸取法提取苦竹笋废弃物中总黄酮,研究不同工艺条件对苦竹笋废弃物中总黄酮提取的影响,确定苦竹笋废弃物中总黄酮提取最佳工艺条件。以总黄酮含量为评价指标,选取乙醇体积分数、液固比、浸提温度、浸提时间为影响因素,运用Minitab软件进行试验设计,建立响应曲面回归模型,进行响应曲面分析,优化苦竹笋废弃物中总黄酮提取工艺条件。试验结果显示,超声波辅助溶剂浸取法提取苦竹笋废弃物中总黄酮的最佳工艺条件为:乙醇体积分数95%,液固比40 mL/g,浸提温度60℃,浸提时间40 min。在此条件下,苦竹笋废弃物中总黄酮的提取量可达9.68 mg/g,与《植物源性食品中总黄酮的测定》(DB43T 476—2009)《食品中总黄酮的测定分光光度法》(SZDB/Z 349—2019)等标准相比,总黄酮的提取量显著提高,增长率可达22.69%~31.34%。

响应面法优化方竹笋超微粉制作曲奇饼干的关键配方及品质评价

【目的】探明方竹笋超微制作曲奇饼干的最优配方,为方竹笋深加工提供新思路。【方法】以方竹笋超微粉为主要原料,辅以糖粉、黄油、蛋液等制作方竹笋曲奇饼干,分析感官及外观色泽,确定4个单因素(方竹笋超微粉、糖粉、黄油和蛋液)添加量的优化范围。在单因素试验基础上,采用Design-Expert试验设计进行响应面优化设计,考察方竹笋超微粉、糖粉、黄油和蛋液添加量对方竹笋曲奇饼干感官品质的影响,确定方竹笋曲奇饼干最优配方,并对优化配方的方竹笋曲奇饼干进行理化指标分析。【结果】方竹笋曲奇饼干最佳配方以低筋面粉质量为100%,方竹笋超微粉、黄油、糖粉和蛋液添加量分别为6.00%、55.00%、40.00%和20.00%,烘焙上下火温度150℃,时间20 min。在此条件下制得的方竹笋曲奇饼干,感官审评得分91.50分,具有特殊方竹笋香、口感松脆、甜度适宜、色泽均匀、组织形态良好,饼干中膳食纤维含量达19.16g/100g,蛋白质和脂肪含量分别为4.99 g/100g和27.6 g/100g,过氧化值和酸价分别为0.04 g/100g和0.56 mg/g,符合国家标准《饼干质量通则》(GB/T 20980—2021)要求。【结论】方竹笋曲奇饼干最佳配方应用于方竹笋的精深加工,可使烘焙食品(饼干类)中保留方竹笋的风味和减轻焦化,属于特色产品,各项理化指标均符合国标要求。

不同干燥方式对毛竹笋全粉中氨基酸含量和蛋白质结构的影响

为探究不同干燥方式对竹笋全粉氨基酸含量及蛋白质结构的影响,该实验采用喷雾干燥(spray drying,SD)、热风干燥(hot air drying,HAD)、微波干燥(microwave drying,MD)、低温真空干燥(low-temperature vacuum drying,LVD)4种方式制备毛竹笋全粉(Phyllostachys pubescens shoot powder,PPSP),分析了4种干燥方式的PPSP氨基酸组成及含量,并基于拉曼光谱酰胺Ⅰ带比较了4组样品蛋白质二级结构变化。结果表明,LVD制备的PPSP总氨基酸含量最高,为29.19 g/100 g,其次为SD,HAD制备的PPSP总氨基酸含量最低。LVD组的PPSP中必需氨基酸含量最高,为10.43 g/100 g,占总氨基酸含量的35.73%。LVD和SD制备的PPSP中呈味氨基酸含量分别为17.58 g/100 g、15.81 g/100 g,显著高于HAD和MD组的呈味氨基酸含量。LVD样品中氨基酸组成最接近于标准模式谱。通过主成分分析提取出2个主成分,累计方差贡献率达89.45%,综合评分结果为:LVD>SD>MD>HAD,聚类热图将4种干燥方式分为3类。干燥后的PPSP蛋白质中β-折叠结构最高,占总二级结构的74.66%~83.35%,HAD样中β-折叠、α-螺旋结构含量明显高于其他样品。该研究可为毛竹笋干燥及竹笋全粉的开发利用提供理论参考。

连续小推力轨迹优化间接法研究进展综述

针对空间探测中连续小推力轨迹优化,总结了间接法在最优控制理论、初值估计和同伦延拓方法等方面的研究进展。首先介绍了连续小推力轨迹优化问题的建模及其相应的最优控制问题的状态方程、约束方程和性能指标,对比了两类主要优化方法,即直接法和间接法的求解思路与优缺点。随后总结了轨迹优化初步设计、间接法初值估计以及同伦延拓方面的研究进展,探讨了智能优化和深度学习在轨迹优化间接法中的应用,进一步结合当前大规模任务规划、实时最优控制等需求讨论了间接法的应用。最后,对连续小推力轨迹优化间接法的发展展望进行了总结。

一种应用于冬笋探测的高隔离度和高灵敏度天线设计

为满足微波法冬笋探测的高灵敏度与低成本需求,设计一种加载扼流槽的背腔收发天线,该天线采用蝶形偶极子天线作为辐射单元,通过使用四面折叠的金属屏蔽盒围绕辐射单元与馈电结构耦合实现天线的定向辐射并提高增益,同时在双天线单元之间加载扼流槽,改善收发天线之间的隔离度。借助电磁仿真软件对天线进行了设计,并进行实物加工与测试。仿真结果表明,当输入回波损耗S_(11)<-10 dB时,天线的工作频率为0.94~1.49 GHz,绝对带宽达到0.55 GHz,相对带宽为45%,工作频段内增益为6.40~10.80 dBi,收发隔离度最高达到-51.6 dB。实测结果与仿真结果较贴合,天线在各方面性能良好。在土壤中测试该天线对冬笋的探测效果,测试结果表明,本研究设计的天线可以较好地分辨出有无冬笋的信号特征。

复合地基极限承载力的变分极限平衡法分析——竖向增强

基于变分极限平衡法,对设置竖向增强体的复合地基极限承载力开展了理论研究。首先,以竖向增强体复合地基中滑动土体的静力学平衡方程为基本方程,结合变分原理建立了地基极限承载力泛函极值的等周约束模型。在此基础上,利用欧拉方程得到了以潜在滑动面、滑面上法向正应力以及拉格朗日乘子等为基本未知量的控制方程,并通过引入辅助变量将可动边界转化为固定边界。最后,利用打靶法对该耦合的两点边值问题进行了数值求解,得到了问题的精确解答,并与复合地基设计中简化的等效强度指标法进行了比较,且分析了置换率、增强体黏聚力和内摩擦角对地基极限承载力的影响。数值分析结果表明,简化的等效强度指标法可以有效分析竖向增强复合地基极限承载力。

分段光滑机械振动系统亚谐振动的复杂分岔

以一类单自由度分段光滑机械振动系统为研究对象.数值计算两参数平面上亚谐振动的模式及分布区域,利用延拓打靶法对亚谐包含域内亚谐振动的分岔特征、稳定性及转迁规律进行了详细研究.结果表明:弹性碰撞振动系统中擦边分岔是连续可逆的.在亚谐包含域内,倍化型擦边分岔普遍存在,鞍结型擦边分岔和亚临界周期倍化分岔使系统响应发生跳跃和迟滞.高频亚谐包含域内多吸引子共存,混沌吸引子发生边界激变而突然消失.