不可压缩球体空穴的动态生成和分叉

利用Gao Y C给出的一类应变能函数,在有限变形动力学的框架内分析了不可压缩均匀球体突受拉伸恒载作用时空穴的动态生成和分叉问题.给出了存在动态分叉解的条件,确定了外载荷与空穴半径的解析关系,得到了临界载荷的表达式、空穴动态生成后应力分布的解析解、空穴半径振动的相图以及近似振动周期.讨论了本构参数对临界载荷、外载荷与最大振幅的关系的影响.结果表明:动态模型可以方便地退化为静态模型;当外加载荷大于临界载荷时,球体中心处存在一个突然生成并能迅速增大的空穴,且空穴半径随着时间的演化是周期性的非线性振动.     

不可压缩橡胶圆柱的空穴和分叉

利用Y.C.Gao给出的一类应变能函数,分析了不可压缩橡胶圆柱受静载荷作用时在等温条件下及有温度场分布时空穴产生的问题,给出了存在分叉解的条件,确定了外载荷与空穴半径的函数关系,研究了空穴形成时应力的分布,讨论了本构参数和温度对极限载荷和应力分布的影响.结果表明:当本构参数满足O＜n＜1时,橡胶圆柱体存在分叉解;由Neo-Hooken材料构成的圆柱体将会很稳定而不存在分叉解;本构参数n越大,材料越不容易发生孔洞化不稳定现象;温度越高,材料越不稳定.     

近于不可压缩非线性橡胶材料的有限元分析

橡胶材料的应变能密度函数,通常按不可压缩,可压缩分为两类,本文应用Ｇａｏ的建议的应变能密度函数,把它们统一起来分析橡胶材料的变形特征,适当选择本构常数,可以满足近于不可压缩橡胶材料的变形特征,对平面应力橡胶薄片进行分析,计算结果与实验符合得很好,表明该本构关系在模拟橡胶材料的中,小变形时是合理的,并讨论了本构常数的变化对变形的影响。     

不可压缩核废料污染问题的修正迎风差分法

对无弥散项的不可压缩核废料污染问题模型建立修正迎风差分格式，由于压力函数比浓度和温度函数变化慢的多，采用两种不同的时间步长从而提高计算效率：对压力函数采用大步长△tp，对浓度和温度函数采用较小步长△tc，并进行了收敛性分析，最后得到O(△tc (△tp^o)^3/2 △tp^2 h^2)阶的l^2误差估计。     

不可压缩核废料污染问题的修正迎风差分法

对无弥散项的不可压缩核废料污染问题模型建立修正迎风差分格式 ,由于压力函数比浓度和温度函数变化慢的多 ,采用两种不同的时间步长从而提高计算效率 :对压力函数采用大步长Δtp,对浓度和温度函数采用较小步长Δtc.并进行了收敛性分析 ,最后得到O(Δtc+(Δt0 p) 3 / 2 +Δt2 p+h2 )阶的l2 误差估计 .     

不可压缩橡胶类材料缺口顶端的奇异应力场

借助于新的应变能函数和变形模式，推出了缺口顶端场各区的渐近方程，得到了顶端的完整描述。     

轴对称不可压缩超弹性体的渐近有限元方法

本文采用渐近法与有限元结合的方法,有效地解决了轴对称不可压缩超弹性体在名义应变为中等程度大小情况的计算问题。这种方法具有计算量小,计算稳定的优点。     

贴近墙面移动圆柱体周围的不可压缩流体的数值仿真

采用边界压力单向条件的流函数-旋度方程,对在不可压缩流体中贴近墙面平行移动的圆柱体周围的流场进行了二维数值仿真.计算结果与实验结果有较高的一致性,证明了在边界压力单向条件下流函数-旋度方程的有效性.     

求解不可压缩粘性流的GLS单元之比较

比较了用于求解不可压缩粘性流的四边形双线性、双二次单元及三角形二次单元的性能,这些单元采用GLS稳定化有限元格式,而压力和速度采用等阶数插值。对得出的非线性有限元方程,使用Newton-Raphson迭代来求解,推导了计算切线矩阵的所需公式。完成了对雷诺数分别为1000、5000、10000和20000的方腔上板流的数值模拟,并对不同单元的结果的精度和收敛率进行了比较。数值算例显示,较之于另两种单元,三角形的二次单元在精度和收敛性上达到最好的匹配。     

一类可压缩燃烧方程的渐近极限

采用能量估计和Helmholtz分解的方法,证明了在二维或三维空间上当马赫数趋于零时,一类可压缩燃烧方程的解收敛到相应的不可压缩燃烧方程的解.文中对外力、速度和时间没有限制,只是要求方程的初值足够光滑.     

一类捕食-食饵模型平衡解的局部分歧的存在性

利用局部分歧理论,研究了一类捕食-食饵模型在Neumann边界条件下平衡解的局部分歧的存在性,从而得到其正解存在的充分条件。     

一类具有时滞的HIV感染模型的稳定性分析

研究了一类具有时滞的HIV体内感染模型,引入了以受感染T＊细胞释放出病毒的持续时间为时滞参数.通过Routh-Hurwitz准则和构造Lyapunov函数及对系统非负不变性分析,得出边界平衡点具有全局稳定性.并证明了存在临界值τ0,当τ〈τ0时,内部平衡点是局部渐近稳定的;当τ〉τ0时,内部平衡点是不稳定的;当τ=τ0时,系统具有Hopf分支.最后利用Matlab软件进行数值模拟并验证了分析的合理性.     

Nonlinear instability and dynamic bifurcation of a plane interface during solidification

By taking average over the curvature, the temperature and its gradient, the solute concentration and its gradient at the flange of planar interface perturbed by sinusoidal ripple during solidification, the nonlinear dynamic equations of the sinusoidal perturbation wave have been set up. Analysis of the nonlinear instability and the behaviors of dynamic bifurcation of the solutions of these equations shows that (i) the way of dynamic bifurcation of the flat-to-cellular interface transition varies with different thermal gradients. The quasi-subcritical-lag bifurcation occurs in the small interface thermal gradient scope, the supercritical-lag bifurcation in the medium thermal gradient scope and the supercritical bifurcation in the large thermal gradient scope. (ii) The transition of cellular-to-flat interface is realized through supercritical inverse bifurcation in the rapid solidification area.     

Stability switches and Bogdanov-Takens bifurcation in an inertial two-neuron coupling system with multiple delays

In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system has a unique equilibrium as well as three equilibria for different values of coupling weights.The local asymptotic stability of the equilibrium point is studied using the corresponding characteristic equation.We find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic motion.Stability regions with delay-dependence are exhibited in the parameter plane of the time delays employing the Hopf bifurcation curves.To obtain the global perspective of the system dynamics,stability and periodic activity involving multiple equilibria are investigated by analyzing the intersection points of the pitchfork and Hopf bifurcation curves,called the Bogdanov-Takens(BT)bifurcation.The homoclinic bifurcation and the fold bifurcation of limit cycle are obtained using the BT theoretical results of the third-order normal form.Finally,numerical simulations are provided to support the theoretical analyses.     

Catastrophe,hysteresis and bifurcation of mode transition in scramjet engines and its model

This paper describes a class of nonlinear phenomena existing in the hypersonic flow and supersonic combustion process of scramjet engines: catastrophe, hysteresis and bifurcation, and further finds out the general rules (topological invariance) for the stability boundaries of mode transition in scramjet engines. With this topological invariance, a topological approach is put forward to model the stability boundaries, which may contribute to a complexity reduction of high-dimensional modeling when considering more perturbation parameters, and help to explore the physical laws of the nonlinear phenomena. Accordingly, this paper interprets the characteristic of combustion mode transition based on the cusp topological model in singular theories, and observes the bifurcation characteristic in combustion mode transition. Moreover, a modeling approach is proposed to mathematically describe the stability boundaries of combustion mode transition in scramjet engines, and the model has high accuracy comparing to the simulation data, which proves the validation of the basic ideas proposed in this paper. Finally, future research directions are proposed. Supported by the Key Program of the National Natural Science Foundation of China (Grant No. 90816028)     

强电场和磁场中电子运动轨道的混沌现象分析——半经典闭合轨道理论

电场和磁场在原子物理的发展中占有非常重要的地位。当电子在较弱的电场和磁场中运动时，其运动轨迹比较清晰。但是，当电场和磁场很强时，电子的运动轨道开始分岔，运动出现混沌。利用半经典闭合轨道理论，对电子在强电场和磁场中的运动轨道的混沌现象进行了分析，该理论具有物理图象清晰、应用范围广的优点。同时，应用该理论还可以对原子谱的混沌现象进行分析。     

谐和激励下单边碰撞系统的同宿分岔

研究了谐和激励下带平方非线性项的单边碰撞系统的同宿分岔.利用动力系统稳定性理论和Melnikov方法,分析了单边碰撞系统的同宿分岔,得到了系统出现Smale马蹄混沌的阀值.通过稳定与不稳定流形等数值仿真,对解析结果进行了验证和分析.     

Preparation and Characterization of Zinc Aluminosilicate Transparent Glass-Ceramics

Zinc aluminosilicate glasses containing Li2 O, ZnO , Al2O3 and SiO2 were prepared by conventional melting and quenching technique, and subsequently converted to transparent glass-ceramics by controlled nucleation and crystallization. The glass was melted in a platinum crucible at 1 600 ℃ for 2 h and then two-step heat treated for the nucleation and the crystal growth. The nucleation and crystallization temperatures were determined by differential thermal analysis. Specimens heat-treated on different schedules were analyzed by the X-ray diffraction to determine crystalline phases. Scanning electron microscopy was used to study the glass-ceramics morphology, the grain size and distribution in the residual glass matrix. The reorganization of the amorphous solid was confirmed by FT-IR spectroscopy. The transmittance was measured by a UV-Vis-NIR scanning spectrophotometer .