Two-dimensional Riemann problem of the Euler equations to the Van der Waals gas around a sharp corner

In this paper, we study the Riemann problem of the two-dimensional (2D) pseudo-steady supersonic flow with Van der Waals gas around a sharp corner expanding into vacuum. The essence of this problem is the interaction of the centered simple wave with the planar rarefaction wave, which can be solved by a Goursat problem or a mixed characteristic boundary value and slip boundary value problem for the 2D self-similar Euler equations. We establish the hyperbolicity and a priori C¹ estimates of the solution through the methods of characteristic decompositions and invariant regions. Moreover, we construct the pentagon invariant region in order to obtain the global solution. In addition, based on the generality of the Van der Waals gas, we construct the subinvariant regions and get the hyperbolicity of the solution according to the continuity of the subinvariant region. At last, the global existence of solution to the gas expansion problem is obtained constructively.     

Practical alternating least squares for tensor ring decomposition

Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low-rank patterns in multidimensional and higher-order data. A well-known method for TR decomposition is the alternating least squares (ALS). However, solving the ALS subproblems often suffers from high cost issue, especially for large-scale tensors. In this paper, we provide two strategies to tackle this issue and design three ALS-based algorithms. Specifically, the first strategy is used to simplify the calculation of the coefficient matrices of the normal equations for the ALS subproblems, which takes full advantage of the structure of the coefficient matrices of the subproblems and hence makes the corresponding algorithm perform much better than the regular ALS method in terms of computing time. The second strategy is to stabilize the ALS subproblems by QR factorizations on TR-cores, and hence the corresponding algorithms are more numerically stable compared with our first algorithm. Extensive numerical experiments on synthetic and real data are given to illustrate and confirm the above results. In addition, we also present the complexity analyses of the proposed algorithms.     

Finite difference method for 2-D and 3-D nonlinear free surface wave problems

A finite difference method is developed for the numerical modelling of the 2-D and 3-D unsteady potential flow generated by transient disturbances on the free surface, on which the nonlinear boundary conditions are fully satisfied. The unknown function is computed with an iteration scheme processing in a transformed time-invariant space. After the velocity is calculated, the location of the free surface is renewed and so is the value of velocity on it. The boundary-value problem of the governing equation is then solved at the next time step. The present method incorporates the FFT. Consequently, a tri-diagonal equation system is obtained which could be readily solved. The feasibility of this method has been demonstrated by 2-D and 3-D examples corresponding to different initial disturbances. This work is supported by the science foundation of Academia Sinica. The paper had been accepted by the XVIth International Congress of IUTAM, Lyngby, Denmark, August, 1984.     

磁过滤器电流对非晶碳薄膜摩擦学特性影响的研究

研究了过滤阴极真空电弧技术中,不同的磁过滤器电流下(5—13 A),制备的四面体非晶碳(ta-C)薄膜对摩擦学特性的影响.通过对薄膜厚度,薄膜结构以及薄膜表面粗糙度随磁过滤电流的变化结果进行了测试,结果表明,随着磁过滤器电流的增大,薄膜的sp³键含量逐渐减少,表面粗糙度从0.13增大到0.38.磁过滤器电流在5 A时,薄膜的摩擦系数最小约为0.08,当电流增大到7 A时,摩擦系数显著增大,磁过滤器电流从7 A增大到13 A时,薄膜的摩擦系数再次减小约为0.1. 关键词： 四面体非晶碳 过滤阴极真空电弧 磁过滤器电流 摩擦系数     

The A 1Σ+ → X 1Σ+ bands of the isotopic lithium hydrides

In order to obtain a better understanding of the X¹Σ⁺ ground state and the A¹Σ⁺ state potential energy curves of lithium hydride and to examine in detail the concept of “mass-reduced quantum numbers” for both an ordinary (X¹Σ⁺) and an anomalous (A¹Σ⁺) electronic state, the emission spectra of the A¹Σ⁺ → X¹Σ⁺ bands of the isotopic lithium hydrides and deuterides were photographed in the 3000–5000-Å region with a 3.4-m Ebert Spectrograph. The bands found involved v″ = 0 to 7 to various v′ = 0 to 17 for ⁶LiH, and v″ = 0 to 7 to various v′ = 1 to 16 for ⁶LiD. Additional bands involving v″ = 4 and 5 were also found for ⁷LiH. The vibrational-rotational spectroscopic analysis of ⁷LiH, ⁶LiH, and ⁶LiD are reported here, as are the reanalyses of the ⁷LiH and ⁷LiD data reported by Crawford and Jorgensen. New Rydberg-Klein-Rees (RKR) A¹Σ⁺ and X¹Σ⁺ potential curves have been constructed for each individual molecule and are reported, but detailed isotopic comparisons will be reported in subsequent publications.     

Forbidden domains of a toroidal magnetic shield

Russian Physics Journal -     

基于层次简化的三维场景快速绘制方法

实时三维场景快速绘制是实现漫游和仿真的基础,提出了一种基于分层简化和碰撞检测的快速渲染算法．该算法先采用八叉树的分层简化三维场景模型,然后用包围盒实现视景的实时碰撞检测,最后采用基于场景剔除的图像缓存技术．从实验结果分析,此方法在效率和显示效果上是可行的．     

大鼠脑缺血再灌注后运动皮质细胞凋亡的体视学观察

用体视学方法分析大鼠脑缺血再灌注后大脑运动皮质细胞的凋亡情况。随机将24只SD大鼠分为缺血再灌注后6、12、24 h和对照组。采用结扎大鼠左侧颈总动脉和夹闭右侧颈总动脉15m in后放开的方法制备大鼠脑缺血再灌注模型。应用Hoechst33258荧光染色及免疫组化Bax蛋白表达来检测细     

环形光纤激光器自混合散斑数值模拟及频谱性能分析

在环形激光器的理论基础上,结合环形掺铒光纤激光器自混合散斑速度传感实验系统,数值模拟了激光器自混合散斑信号的功率输出.分析了自混合散斑信号的平均散斑频率,频谱能量密度性能.研究结果表明,频谱平均频率与物体速度成近似的线性关系,频谱能量密度与探测距离成近似线性关系.     

不同种植方式对陆生植物去除富营养化水体中磷的影响

以陆生植物美人蕉（Canna generalis）、紫背万年青（Rhoeo discolor）为对象,研究了其不同的种植方式对净化富营养化水体中磷的影响．结果表明,美人蕉、紫背万年青的双倍生物量组对水体中TP、DTP和DIP的去除率与它们的单倍生物量组呈显著性差异,植物对水体中P的去除效果随着植物生物量的适度增加而提高．两种陆生植物的复合种植体系对TP、DTP和DTP的去除率和单一种植体系差别不明显,说明美人蕉、紫背万年青的不同种植体系对水体中TP、DTP和DIP去除率的影响不大．从美人蕉、紫背万年青去除水体中TP、DTP和DIP的动态过程拟合模型可以看出各植物处理组对水体中不同形态P有良好的去除效应．