On Characterizations of Rigid Graphs in the Plane Using Spanning Trees

We study characterizations of generic rigid graphs and generic circuits in the plane using only few decompositions into spanning trees. Generic rigid graphs in the plane can be characterized by spanning tree decompositions [5,6]. A graph G with n vertices and 2n − 3 edges is generic rigid in the plane if and only if doubling any edge results in a graph which is the union of two spanning trees. This requires 2n − 3 decompositions into spanning trees. We show that n − 2 decompositions suffice: only edges of G − T can be doubled where T is a spanning tree of G. A recent result on tensegrity frameworks by Recski [7] implies a characterization of generic circuits in the plane. A graph G with n vertices and 2n − 2 edges is a generic circuit in the plane if and only if replacing any edge of G by any (possibly new) edge results in a graph which is the union of two spanning trees. This requires decompositions into spanning trees. We show that 2n − 2 decompositions suffice. Let be any circular order of edges of G (i.e. ). The graph G is a generic circuit in the plane if and only if is the union of two spanning trees for any . Furthermore, we show that only n decompositions into spanning trees suffice.     

利用散射波远场模第P个傅立叶系数重建声波阻尼系数

阐述了利用声波散射远场模Fourier展开的第P个傅立叶系数（声散射远场模的不完全信息）,重建声阻抗系数的一种非线性最优化方法．并给出了该方法收敛性的证明,其数值例子说明这种方法的有效性和可行性．     

改性可膨胀石墨的制备及在硬质聚氨酯泡沫中的阻燃性能

采用表面接枝硅烷偶联剂法将硼酸负载在可膨胀石墨(EG)表面制得了改性EG(MEG), 并考察了MEG在硬质聚氨酯泡沫(RPUF)中的阻燃性能. 利用扫描电子显微镜、 X射线光电子能谱、 傅里叶变换红外光谱、 膨胀试验及热失重分析对MEG进行了形貌、 元素组成及结构性能表征, 通过热失重分析、 极限氧指数(LOI)及锥形量热仪考察了RPUF/MEG的热稳定性及燃烧性能. 结果表明, 硼硅化合物作为硅硼陶瓷前驱体已负载在EG表面; MEG及RPUF/MEG体系膨胀炭层更为致密, 800 ℃时的残余量分别较EG和RPUF/EG提高了8.7%和3.7%; RPUF/MEG体系的LOI较RPUF/EG有所提高, 热释放速率峰值降低了10%, 产烟速率及CO生成速率均显著降低. RPUF/MEG阻燃性能的提高与MEG负载的硅硼陶瓷前驱体促进了阻燃RPUF各组分间的相互作用及增强了炭层的阻隔性有关.     

Analytical solutions for dynamics of dual-spin spacecraft and gyrostat-satellites under magnetic attitude control in omega-regimes

The attitude dynamics of a dual-spin spacecraft (a gyrostat with one rotor) with magnetic actuators attitude control is considered in the constant external magnetic field at the presence of the spacecraft’s own magnetic dipole moment, which is created proportionally to the angular velocity components (this motion regime can be called as “the omega-regime” or “the omega-maneuver”). The research of the dual-spin spacecraft angular motion under the action of the magnetic restoring torque is fulfilled in the generalized formulation close to the classical mechanics’ task of the heavy body/gyrostat motion in the Lagrange top. Analytical exact solutions of differential equations of the motion are obtained for all parameters in terms of elliptic integrals and the Jacobi functions. New obtained analytical solutions can be classified as results developing the classical fundamental problem of the rigid body and gyrostat motion around the fixed point. The technical application of the omega-regime to the angular reorientation of the spacecraft longitudinal axis along the angular momentum vector is considered.     

方孔障碍物对瓦斯火焰传播影响的实验与大涡模拟

为揭示置障管道内甲烷/空气预混火焰传播特性,运用高速摄影技术对甲烷/空气预混火焰的形状变化和火焰前锋的速度特性进行实验,并利用大涡模拟对管道内的流场结构进行数值分析。结果表明:置障管道内依次出现了球形火焰、指尖形火焰及“蘑菇”状火焰,且“蘑菇”状火焰出现之后,火焰开始反向传播;“蘑菇”状火焰是双涡旋结构与火焰前锋面相互作用的结果,而火焰的反向传播是由流场中出现逆流结构引起的;障碍物对火焰前锋有明显的加速作用;大涡模拟成功再现了实验中观察到的火焰形状、火焰前锋速度及流场结构,说明大涡模拟适用于置障管道内预混火焰传播特性的研究。     

三维溃坝流的光滑粒子动力学方法模拟

采用光滑粒子动力学SPH(Smoothed Particle Hydrodynamics)方法对三维溃坝流问题进行了数值模拟。为了逼真地模拟出坝内水体与壁面间相互作用而产生的水花飞溅、融合以及近壁面流动等现象,加入了混合长度形式的湍流模型。为了有效地防止粒子穿透固壁,提出了一种新型的适合三维数值模拟的固壁边界处理方法。应用SPH方法对三维溃坝流进行了数值模拟,并分别考虑了未添加障碍物和添加圆柱障碍物两种情形。计算结果表明,改进SPH方法能够精细地捕捉溃坝流在不同时刻的自由液面,并获得稳定而精确的数值结果。     

New solvable problems in the dynamics of a rigid body about a fixed point in a potential field

We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the problem of motion is reduced to inversion of a single integral. A several-parameter generalization of the classical case due to Bobylev and Steklov is found. Special cases solvable in elliptic and ultraelliptic functions of time are discussed.     

利用光学显微镜研究溶剂诱导的梯形苯基聚倍半硅氧烷结晶

通过溶剂诱导结晶的方法研究了梯形苯基聚倍半硅氧烷(PPSQ)的球晶结构. 采用光学显微镜研究了溶液的浓度、溶剂的挥发时间以及温度等影响因素对梯形苯基聚倍半硅氧烷的球晶结构形貌的影响. 实验结果表明:稀释溶液浓度与提高结晶温度在改变球晶的形态方面具有相同的效果. 球晶的尺寸会随着溶液浓度的降低或者结晶温度的升高而增加. 这都归因于梯形苯基聚倍半硅氧烷在二甲苯中的溶解度的增加. 在不改变其它结晶条件的情况下,延长溶剂的挥发时间也会形成更大的球晶. 当在光学显微镜下旋转样品时球晶的结构不会发生改变,这表明球晶具有均一的晶体学取向结构. 负性球晶的特征也表明梯形苯基聚倍半硅氧烷的分子链是沿着球晶的切线方向排列. 考虑到梯形苯基聚倍半硅氧烷具有刚性的分子链,还提出了梯形苯基聚倍半硅氧烷可能的球晶结构模型.     

Numerical solution of an optimal investment problem with proportional transaction costs

This paper mainly concerns the numerical solution of a nonlinear parabolic double obstacle problem arising in a finite-horizon optimal investment problem with proportional transaction costs. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints and the properties of the utility function allow to obtain the optimal investment solution from a nonlinear problem posed in one spatial variable. The proposed numerical methods mainly consist of a localization procedure to pose the problem on a bounded domain, a characteristics method for time discretization to deal with the large gradients of the solution, a Newton algorithm to solve the nonlinear term in the governing equation and a projected relaxation scheme to cope with the double obstacle (free boundary) feature. Moreover, piecewise linear Lagrange finite elements for spatial discretization are considered. Numerical results illustrate the performance of the set of numerical techniques by recovering all qualitative properties proved in Dai and Yi (2009) [6].