Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation

This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.

A symplectic finite element method based on Galerkin discretization for solving linear systems

We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.

Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.

Unconditionally Explicit Stable Difference Schemes for Solving Some Linear and Non-Linear Parabolic Differential Equation

We present the numerical method for solution of some linear and non-linear parabolic equation. Using idea [1], we will present the explicit unconditional stable scheme which has no restriction on the step size ratio k/h2 where k and h are step sizes for space and time respectively. We will also present numerical results to justify the present scheme.

A streamline diffusion nonconforming finite element method for the time-dependent linearized Navier-Stokes equations

A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.

A Revised Piecewise Linear Recursive Convolution FDTD Method for Magnetized Plasmas

The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method improves accuracy over the original recursive convolution （RC） FDTD approach and current density convolution （JEC） but retains their advantages in speed and efficiency. This paper describes a revised piecewise linear recursive convolution PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations of the reflection and transmission coefficients through a magnetized plasma layer. The results show that the revised PLRC-FDTD method has improved the accuracy over the original RC FDTD method and JEC FDTD method.

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.

Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations

This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems.The contributions of this paper consist of the following aspects:(1)The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method.(2)A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed.Meanwhile,the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations(FBPDEs).(3)The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented.It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case,but also support the existing operator results and give a more convenient form of computation.

基于位置敏感器件的杨氏模量测量

利用位置敏感器件将经典的拉伸法测杨氏模量中金属丝的微小伸长量转换成电压信号变化,再由放大电路放大后,经过数据采集卡接入计算机进行实时数据采集,实现了杨氏模量的数字化测量。实验运用了现代科技测量的新器件、新技术,将硬件和软件在传统物理实验上进行了融合,实验数据处理设计了代表性的最小二乘法线性拟合和逐差法进行处理,测量结果可靠,可作为一个典型的综合性物理实验进行教学推广和使用。

加工误差对静压气浮主轴静动态性能的影响

为了改善静压气浮主轴静动态性能,研究了非均匀分布变节流孔直径静压气浮主轴结构。基于有限差分和线性小扰动法分析节流孔直径和分布不均匀性对主轴承载能力的影响,研究了轴套存在周向或轴向加工误差(正弦波纹、矩形波纹和三角波纹)对主轴静动态性能的影响。结果表明:节流孔直径系数为0.9~0.95时,承载能力提升最明显;周向或轴向加工误差有助于提高主轴承载能力;矩形和三角形波纹提高新型主轴承载能力更显著;轴向矩形波纹、三角波纹更有助于提高主轴稳定性;随着加工误差幅值增大,主轴稳定性降低。

一类求解非线性对流扩散方程的线性多步法

研究一类非线性对流扩散方程,利用中心差商和线性多步法构造了一种新的在空间和时间上都具有二阶精度的差分格式,并利用Fourier分析和冻结系数方法分析了差分格式的稳定性,最后通过5种不同类型的数值算例验证了新方法求解非线性对流扩散方程的有效性.

多级线性加载下软土一维非线性固结分析

多级加载是一种常见的加载形式,目前软土一维非线性固结方面的研究鲜有考虑多级加载。为研究多级加载下软土一维非线性固结规律,构建考虑多级线性加载和土体非线性的固结模型。利用有限差分法获得固结方程的解答,并通过与现有解答对比验证了所得解答的正确性。进而分析荷载形式和土体非线性对固结特性的影响,结果表明:与瞬时加载或单级加载相比,采用多级线性加载可以充分让土体超静孔隙水压力消散并且可以降低超静孔隙水压力峰值。第一级荷载对土体固结影响最大,工程中采用多级荷载时,应控制第一级荷载的加载量及加载速率,以避免土体发生破坏。

可移动民宿的语义分析与设计策略

可移动民宿是可移动建筑的衍生产品,其更符合现代人惬意随性、四处为家的旅行态度,并能促使民宿行业健康发展。文章首先梳理了可移动民宿这一概念,继而基于语义差分法,建立语义体系,结合意象尺度图寻求产品特定的语义偏好,分析语义呈现与设计趋势,再后为进一步助推实践活动,以线性回归分析的方式挖掘语义项目对居住意愿的影响情况,明晰设计侧重,并以此输出案例。最终设计案例通过了语义评估,证明了设计策略的可行性。文章为可移动民宿正名,并为其设计发展提供了思路。

EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.

Linear Track Estimation Using Double Pulse Sources for Near-Field Underwater Moving Target

双脉搏来源(DPS ) 方法在这个工作为线性轨道评价被介绍。在在水下的移动的噪音鉴定的领域里指向， Doppler 将弄歪散发的噪音的频率和振幅。消除这，轨道评价是必要的。在 DPS 方法，我们首先估计通过放方法的基线在动人的目标安装的二正弦曲线脉搏来源的轴承。同时，每脉搏的射出并且记录的时间也被获得。然后，线性磁道参数将在两倍来源间距的帮助下基于几何学模式被完成。模仿的结果证实 DPS 改进以前的双来源间距方法的表演。模仿的实验用一辆动人的电池汽车被执行进一步评估它的表演。当目标离开是 4060m 时，实验结果证明那轨道方位角并且垂直偏导 DPS 的距离分别地在 0.6o 和 3.4m 下面。并且估计的速度的平均偏差在 0.25m/s 附近。

RANDOM RESPONSES OF A TWO-DEGREE-OF-FREEDOM STRUCTURE WITH STRONGLY NONLINEAR COUPLING AND PARAMETRIC INTERACTION

This paper investigates the random responses of a TDOF structure with strongly nonlinear coupling and parametric vibration. With the nonlinear cou- pling of inertia in the equations of motion of the system being removed by successive elimination, the non-Gaussian moment equation method (NGM) is applied and 69 moment equations are integrated with central cumulative truncation technique. The stochastic central difference-cum-statistical linearization method(SCD-SL) and the digital simulation method(DSM) are also used. A comparison of results by different methods are given and the SCD-SL method is the most efficient method.

台阵和噪声源分布对微动成像的影响及其在盐矿溶腔探测中的应用

随着节点地震仪的发展,被动源地震成像方法在不同尺度的地下结构成像中得到了越来越广泛的应用.对于小尺度浅地表成像,因高频噪声源时空分布不均,一般采用基于台阵平均的方法,即所谓的微动成像方法提取高频被动源面波频散数据,但是不同类型的台阵一定程度上也会受到噪声源分布不均匀的影响.本文以水溶型盐矿溶腔探测为例,通过实测数据较为系统地分析了不同台阵的响应函数及其对噪声源方向不均匀性的适应能力.研究发现,当噪声源分布不均时,三角形台阵可以获得更可靠的频散数据,但对应的数据采集效率较低,而其他类型的台阵虽然布设相对简便,但是提取的相速度与真实速度存在较大的误差.当线性台阵和噪声源方位一致时,可以提取与三角形台阵一致甚至更好的频散数据.在这个基础上,我们分别采用三角形台阵和考虑噪声源的线性台阵在湘衡盐矿开展了两条剖面的数据采集,并利用适应性更好的扩展空间自相关方法(ESPAC)计算面波频散数据.最后,利用蒙特卡洛方法生成的随机初始模型进行了频散数据反演,获得研究区600 m以浅的横波速度结构,并刻画了盐溶腔的发育位置和空间分布形态.

滚动直线导轨温度场建模与分析

滚动直线导轨作为数控机床进给系统重要的功能部件,其热特性对数控机床的性能有重要影响。提出了一种导轨截面瞬态温度场理论模型建立、求解的方法,实现了对滚动直线导轨热特性的分析。首先,确定了滚动直线导轨的导热模型,基于有限差分法建立了导轨截面各节点离散方程组,建立了导轨截面瞬态热特性理论模型,求解获得了导轨截面瞬态温度场;其次,建立了导轨热特性仿真分析模型,获得导轨的稳态温度场;最后,进行了热特性实验,验证了所建立的理论和仿真分析模型。结果表明:稳态温度场理论模型和实验结果最大误差为7.25%,且瞬态温度场的变化趋势与实验结果一致,验证了温度场理论分析模型的正确性。有限元分析结果与实验测量的结果最大误差为6.22%,验证了热特性仿真分析的可靠性。

不同消毒方式对口腔印模消毒效果、线性尺寸变化及细节再现性的影响

目的研究不同消毒方式对口腔印模材料消毒效果、线性尺寸变化及细节再现性的影响。方法根据印模材料(藻酸盐、聚醚和硅橡胶),消毒剂(次氯酸钠、戊二醛),消毒方法(喷洒、浸泡),以及不同消毒浓度和消毒时间等进行实验分组,并设未消毒处理组作为空白对照,共计15组,通过涂布平板法进行菌落计数以实施印模消毒效果试验,并利用细节再现性试验块及配套环形模具实施线性尺寸变化和细节再现试验。结果藻酸盐印模样品需经0.5%次氯酸钠喷洒消毒10 min后方可达到印模消毒要求;硅橡胶(重体+轻体)印模样品需在0.5%次氯酸钠或2%戊二醛浸泡消毒10 min后才可达到印模消毒要求;而聚醚和硅橡胶(重体)印模样品在用0.5%次氯酸钠浸泡消毒5~10 min或2%戊二醛浸泡消毒10 min后均符合印模消毒要求。所有组印模材料样品消毒前后的线性尺寸变化和细节再现性试验结果均符合要求。结论不同消毒方式对印模材料消毒后的线性尺寸变化及细节再现性均符合要求,但从消毒的有效性考虑,藻酸盐印模材料可选用0.5%次氯酸钠喷洒消毒10 min,聚醚印模材料可选用0.5%次氯酸钠浸泡消毒5~10 min或2%戊二醛浸泡消毒10 min,硅橡胶印模材料可选用0.5%次氯酸钠或2%戊二醛浸泡消毒10 min。

基于统计学法分析雅安地区降水差异性特征

文章利用统计学法观察雅安地区国家气象观测站1991—2020年期间年季降水量、年平均暴雨日数、年平均夜雨率,分析雅安地区近30年来降水的差异性特征。结果表明:近30年雅安地区年降水量变化波动较大、南北差异较大,中部年季降水量偏大,属湿润气候,年暴雨日数雨城和天全略有减少,名山、芦山、荥经略有增加,年平均夜雨日数最多,最高值为天全193.9d;北部年季降水量偏少,年暴雨日数略有增加,年平均夜雨日居中为149.3d;南部年季降水量最少,属干暖气候,年暴雨日数汉源略有减少,石棉略有增加,年平均夜雨日最少,最少值为汉源39.7d。