运用三维离散元技术模拟落锤撞击下奥克托今颗粒的点火燃烧过程

炸药颗粒的点火燃烧过程一直是人们关注的热点问题。近年来，三维离散元技术在中尺度观测颗粒材料的动力学过程中拥有显著优势。炸药燃烧属于颗粒材料的反应动力学，运用三维离散元技术(DM3)可以有效地观测炸药燃烧传播的过程。以奥克托今(HMX)颗粒为例，本文成功模拟并观测到了HMX颗粒的燃烧反应程度，确定了颗粒开始燃烧反应的时间，以及燃烧反应传播的时间。同时，结合落锤冲击颗粒的三维图像以及其表观压强和放热功率，得到了HMX颗粒燃烧反应、燃烧传播的整个反应动力学过程，包括颗粒在冲击加载下碎化塑性变形的过程，颗粒燃烧反应放热的过程，落锤回弹颗粒喷射的过程等。同时，进一步说明了尖顶颗粒更利于颗粒点火，平顶颗粒有抑制颗粒点火的能力。     

A note on Hadwiger’s conjecture for W5-free graphs with independence number two

The Hadwiger number of a graph $G$, denoted $h\left(G\right)$, is the largest integer $t$ such that $G$ contains $K_t$ as a minor. A famous conjecture due to Hadwiger in 1943 states that for every graph $G$, $h\left(G\right)\ge \chi \left(G\right)$, where $\chi \left(G\right)$ denotes the chromatic number of $G$. Let $\alpha \left(G\right)$ denote the independence number of $G$. A graph is $H$-free if it does not contain the graph $H$ as an induced subgraph. In 2003, Plummer, Stiebitz and Toft proved that $h\left(G\right)\ge \chi \left(G\right)$ for all $H$-free graphs $G$ with $\alpha \left(G\right)\le 2$, where $H$ is any graph on four vertices with $\alpha \left(H\right)\le 2$, $H=C_5$, or $H$ is a particular graph on seven vertices. In 2010, Kriesell subsequently generalized the statement to include all forbidden subgraphs $H$ on five vertices with $\alpha \left(H\right)\le 2$. In this note, we prove that $h\left(G\right)\ge \chi \left(G\right)$ for all $W_5$-free graphs $G$ with $\alpha \left(G\right)\le 2$, where $W_5$ denotes the wheel on six vertices.     

基于LS -DYNA公路桥车桥耦合的车辆模型研究

研究公路桥梁在移动车辆荷载作用下的动力响应,建立合理的车辆模型非常重要。为更真实地体现桥梁在车载作用下的动力响应,基于LS-DYNA程序,结合常用重型车辆的结构特性及参数,对车辆的橡胶轮胎、轮胎内气体压力、车轮转动和车辆悬架系统进行模拟,使车辆模型更接近实际车辆。通过车辆轴重和动力特性初步验证车辆有限元模型的有效性;同时,以一座混凝土简支空心板梁桥为算例,验证车轮转动和车桥相互接触力,并将LS-DYNA计算结果与桥梁实测结果进行对比,进一步验证车辆有限元模型的有效性。研究结果表明,基于LS-DYNA建立的三维车辆有限元模型是可行的,可以用于研究车桥相互作用。     

Application of wake oscillators to two-dimensional vortex-induced vibrations of circular cylinders in oscillatory flows

A nonlinear time-domain simulation model for predicting two-dimensional vortex-induced vibration (VIV) of a flexibly mounted circular cylinder in planar and oscillatory flow is presented. This model is based on the utilization of van der Pol wake oscillators, being unconventional since wake oscillators have typically been applied to steady flow VIV predictions. The time-varying relative flow–cylinder velocities and accelerations are accounted for in deriving the coupled hydrodynamic lift, drag and inertia forces leading to the cylinder cross-flow and in-line oscillations. The system fluid–structure interaction equations explicitly contain the time-dependent and hybrid trigonometric terms. Depending on the Keulegan–Carpenter number (KC) incorporating the flow maximum velocity and excitation frequency, the model calibration is performed, entailing a set of empirical coefficients and expressions as a function of KC and mass ratio. Parametric investigations in cases of varying KC, reduced flow velocity, cylinder-to-flow frequency ratio and mass ratio are carried out, capturing some qualitative features of oscillatory flow VIV and exploring the effects of system parameters on response prediction characteristics. The model dependence of hydrodynamic coefficients on the Reynolds number is studied. Discrepancies and limitations versus advantages of the present model with different feasible solution scenarios are illuminated to inform the implementation of wake oscillators as a computationally efficient prediction model for VIV in oscillatory flows.     

Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

Euler Characteristics on virtually free products

We define Euler characteristics on classes of residually finite and virtually torsion free groups and we show that they satisfy certain formulas in the case of amalgamated free products and HNN extensions over finite subgroups. These formulas are obtained from a general result which applies to the rank gradient and the first L²?Betti number of a finitely generated group.