含摩擦与碰撞平面多刚体系统动力学线性互补算法

基于接触力学理论和线性互补问题的算法, 给出了一种含接触、碰撞以及库伦干摩擦, 同时具有理想定常约束(铰链约束) 和非定常约束(驱动约束) 的平面多刚体系统动力学的建模与数值计算方法. 将系统中的每个物体视为刚体, 但考虑物体接触点的局部变形, 将物体间的法向接触力表示成嵌入量与嵌入速度的非线性函数,其切向摩擦力采用库伦干摩擦模型. 利用摩擦余量和接触点的切向加速度等概念, 给出了摩擦定律的互补关系式; 并利用事件驱动法, 将接触点的黏滞-滑移状态切换的判断及黏滞状态下摩擦力的计算问题转化成线性互补问题的求解. 利用第一类拉格朗日方程和鲍姆加藤约束稳定化方法建立了系统的动力学方程, 由此可降低约束的漂移, 并可求解该系统的运动、法向接触力和切向摩擦力, 还可以求解理想铰链约束力和驱动约束力. 最后以一个类似夯机的平面多刚体系统为例, 分析了其动力学特性, 并说明了相关算法的有效性.      

On Preconditioning of Incompressible Non-Newtonian Flow Problems

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the finite element method and utilize the two-by-two block structure of the matrices in the arising algebraic systems of equations. The Krylov subspace iterative methods are chosen to solve the linearized discrete systems and the development of computationally and numerically efficient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian flows, the viscosity is not constant and its variation is an important factor that affects the performance of some already known preconditioning techniques. In this paper we examine the performance of several preconditioners for variable viscosity applications, and improve them further to be robust with respect to variations in viscosity.     

An Existence Result for a Class of Chemically Reacting Systems with Sign-Changing Weights

We prove the existence of positive solutions for the system$$\begin{align*}\begin{cases}-\Delta_{p} u =\lambda a(x){f(v)}{u^{-\alpha}},\qquad x\in \Omega,\\-\Delta_{q} v = \lambda b(x){g(u)}{v^{-\beta}},\qquad x\in \Omega,\\u = v =0, \qquad x\in\partial \Omega,\end{cases}\end{align*}$$where $\Delta_{r}z={\rm div}(|\nabla z|^{r-2}\nabla z)$, for $r>1$ denotes the r-Laplacian operator and $\lambda$ is a positive parameter, $\Omega$ is a bounded domain in $\mathbb{R}^{n}$, $n\geq1$ with sufficiently smooth boundary and $\alpha, \beta \in (0,1).$ Here $ a(x)$ and $ b(x)$ are $C^{1}$ sign-changingfunctions that maybe negative near the boundary and $f,g $ are $C^{1}$ nondecreasing functions, such that $f, g :\ [0,\infty)\to [0,\infty);$ $f(s)>0,$ $g(s)>0$ for $s> 0$, $\lim_{s\to\infty}g(s)=\infty$ and$$\lim_{s\to\infty}\frac{f(Mg(s)^{\frac{1}{q-1}})}{s^{p-1+\alpha}}=0,\qquad \forall M>0.$$We discuss the existence of positive weak solutions when $f$, $g$, $a(x)$ and $b(x)$ satisfy certain additional conditions. We employ the method of sub-supersolution to obtain our results.     

Modulus-Based GSTS Iteration Method for Linear Complementarity Problems

In this paper, a modulus-based generalized skew-Hermitian triangular splitting (MGSTS) iteration method is present for solving a class of linear complementarity problems with the system matrix either being an $H_+$-matrix with non-positive off-diagonal entries or a symmetric positive definite matrix. The convergence of the MGSTS iteration method is studied in detail. By choosing different parameters, a series of existing and new iterative methods are derived, including the modulus-based Jacobi (MJ) and the modulus-based Gauss-Seidel (MGS) iteration methods and so on. Experimental results are given to show the effectiveness and feasibility of the new method when it is employed for solving this class of linear complementarity problems.     

An Alternative Method for Solving Lagrange's First-Order Partial Differential Equation with Linear Function Coefficients

An alternative method of solving Lagrange's first-order partial differential equation of the form $$(a_1x+b_1y+c_1z)p+(a_2x+b_2y+c_2z)q=a_3x+b_3y+c_3z,$$ where p=∂z/∂x, q=∂z/∂y and a_i, b_i, c_i (i=1,2,3) are all real numbers has been presented here.     

Complex Classical Mechanics of a QES Potential

We study a combined parity (P) and time reversal (T) invariant non-Hermitian quasi-exactly solvable (QES) potential, which exhibits PT phase transition, in the complex plane classically to demonstrate different quantum effects. The particle with real energy makes closed orbits around one of the periodic wells of the complex potential depending on the initial condition. However interestingly the particle escapes to an open orbits even with real energy if it is placed beyond a certain distance from the center of the well. On the other hand when the particle energy is complex the trajectory is open and the particle tunnels back and forth between two wells which are separated by a classically forbidden path. The tunneling time is calculated for different pair of wells and is shown to vary inversely with the imaginary component of energy. Our study reveals that spontaneous PT symmetry breaking does not affect the qualitative features of the particle trajectories in the analogous complex classical model.     

Evaluation of Oil Yield of Oil Shale by Infrared Spectrometry Coupled with Ultrasound-assisted Extraction

The oil yield of oil shale was evaluated by Fourier transform infrared(FTIR) spectrometry coupled with ultrasound-assisted extraction. The extraction conditions, including the amount of sample, extraction time and extraction temperature, were examined and optimized. Twenty-four oil shale samples were collected and divided into calibration set and prediction set randomly with a ratio of 2:1. The oil yields of all the samples were determined by the routine method(low-temperature retorting) for reference. The linear regression(LR) equations of oil yield vs. the total area of the spectrum peaks in a wavenumber range of 3100-2800 cm^-1 as well as the sum of absorbance of three absorption peaks(2855, 2927 and 2955 cm^-1), and the multiple linear regression(MLR) model of oil yield vs. the absorbances of the three absorption peaks were constructed with the samples in calibration set and applied to the evaluation of the oil yields of the samples in prediction set, respectively. The results show that the MLR model provides more accurate predictions than the other LR two equations. The determination coefficient(R_p²), the root-mean-square error of prediction(RMSEP) and the residual prediction deviation(RPD) of the MLR model are 0.9616, 0.6458 and 3.6, respectively. The present method is a rapid and effective alternative to the routine low-temperature retorting method.     

Electric Field-driven Acid-base Transformation: Proton Transfer from Acid(HBr/HF) to Base(NH3/H2O)

The proton-transfer between ammonia/water and HF/HBr without and with the stimulus of external electric fields(E_ext) was investigated with the ab initio calculations. When external electric field is applied, the proton transfer occurs, resulting in ion-paired H₄N⁺X^- and H₃O⁺X^-(X=Br and F) from hydrogen-bonded complexes in view of the great changes of geometrical structures, dipole moments, frontier molecular orbitals and potential energy surfaces in the critical external electric fields(E_c) of 1.131×107 V/cm for H₃N-HBr, 1.378×108 V/cm for H₃N-HF, 9.358×107 V/cm for H₂O-HBr and 2.304×108 V/cm for H₂O-HF, respectively. Furthermore, one or three excess electrons can trigger the proton transfer from H₃N-HBr and H₃N-HF to H₄N⁺Br^- and H₄N⁺F^-, while two and four excess electrons can induce the proton transfer from H₂O-HBr and H₂O-HF to H₃O⁺Br^- and H₃O⁺F^-, respectively. Compared with that of the analogous NH₃/H₂O-HCl systems, the strength of E_c of proton transfer increases from HBr to HCl and HF for either H₃N-HX or H₂O-HX series, which is understandable by the fact that the acidity sequence is HBr>HCl>HF. And the larger of acidity of conjugated acid, the smaller of needed E_c. On the other hand, the E_c for the systems of NH₃ with a stronger basicity is generally smaller than that of H₂O systems for the same conjugated acid.     

基于LIBS技术的钢铁合金中元素多变量定量分析方法研究

针对钢铁合金样品元素组成相对复杂,基体效应较严重的问题,利用激光诱导击穿(LIBS)光谱技术对钢铁合金中的元素进行了定量分析。以Nd∶YAG脉冲激光器基频1 064 nm波长激光作为激发光源,采用中阶梯光栅光谱仪和ICCD分光探测钢铁合金样品的LIBS光谱。通过优化实验确定最佳探测延时为1.5 μs,最佳探测门宽为2 μs,激光聚焦点位置在实验样品靶面以下1.5 mm。采用单变量定量分析、多变量线性回归和偏最小二乘(PLS)三种方法分析钢铁合金中Cr元素和Ni元素的含量。结果表明,采用单变量定标方法定标曲线相关系数不高,对待测样的预测误差相对较大,难以有效地定量分析基体元素复杂的钢铁合金中金属元素的含量;采用多变量线性回归分析方法能有效提高定量分析的精度;采用PLS方法得到的Cr和Ni元素的拟合曲线相关系数r分别为0.981和0.995,对两个待测样品中Cr元素和Ni元素的预测相对误差在6.4%和7.1%以内,分析结果优于多变量线性回归方法。可见,采用多变量校正的PLS方法能更有效地校正基体效应对定量分析的影响,提高定量分析的精度。     

服务系统中位相型分布的随机比较

本文运用应用概率中的随机占优研究位相型(PH)分布的随机比较问题,具体给出在一阶、二阶随机占优下比较两个离散PH分布或两个连续PH分布的充分条件及充分必要条件。研究表明,比较两个离散PH分布可变性的条件与比较两个连续PH分布可变性的条件不同,在二阶随机占优意义下比较两个连续PH分布的条件与均值无关,而比较两个离散PH分布的条件与均值有关。本文的结果可用于研究PH分布的最小变异系数问题和可变性问题,也可用于研究带有PH到达间隔或PH服务的排队系统中到达过程或服务时间可变性对系统队长或等待时间的影响。