时间尺度上具阻尼项的二阶半线性时滞动力方程振动性的新结果

本文讨论一类具阻尼项的二阶半线性时滞动力方程解的振动性质, 利用广义Riccati 变换和不等式技巧, 在一定条件下, 建立了4 个新的振动准则, 其结果改进和推广了已知的一些结果.     

具有振动系数的二阶非线性中立型时滞动力方程的有界振动性

研究时标T上具有振动系数的二阶非线性中立型时滞动力方程(r(t)(y(t)+p(t)y(r(t))]△)α)△+f(t,y(δ(t)))=0的有界振动性,其中p是一个定义于T上的振动函数,α＞0是两个正奇数之比.利用一种Riccati变换技术,获得了该方程所有有界解振动的几个充分条件,推广和补充了文献中要求p(t)≥ 0的一些结果,并举例说明了该文主要结果的应用.     

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研究了电漂移对通行高能离子与新经典撕裂模(NTM)共振相互作用的影响。利用漂移动力论方法,在求解共振相互作用产生的作用在磁岛上的环向力矩的过程中重新考虑了电漂移的作用。结果表明,在与磁岛运动相关的环向动量平衡中v>0的通行高能离子与v<0的通行高能离子作用恰好相反,当磁岛沿电子抗磁漂移方向传播时,前者趋向于使磁岛传播频率减小,后者趋向于使磁岛传播频率增大,通行高能离子产生的总的环向力矩几乎为零。仅将v>0的通行高能离子所产生的环向力矩带入由环向动量平衡方程和修正的卢瑟福方程所组成的方程组中,数值计算结果表明,描述磁岛旋转频率与宽度随时间做非线性振荡的稳定极限环并不存在。     

基于摩擦-动力应力模型模拟喷动床气固流动

建立同时考虑颗粒和颗粒之间瞬间碰撞作用(瞬间接触)和非流化下颗粒滑动和滚动运动产生的颗粒半接触作用的颗粒碰撞-摩擦应力模型。推导具有普适性的固相动量守恒方程,建立高颗粒浓度气固两相流动模型,对喷动床内气体颗粒流动过程进行了数值模拟。模拟计算预测喷动床内喷射区、环隙区和喷泉区颗粒流动特性。预测喷动床内颗粒浓度和速度分布与他人实验结果相吻合。     

Flutter of Finite-Span Flexible Plates in Uniform Flow

The flutter instability and response of finite-span flexible plates in uniform flow are investigated experimentally. The effects of the plate aspect ratio on its dynamic responses are mainly analyzed. A hysteretic phenomenon is observed and can be described such that the plate flutters spontaneously as the flow velocity is greater than a critical value UC and the plate returns to its stable state as the flow velocity is slowly decreased to another critical one UD. We find that the aspect ratio has a greater effect on UC than on UD. The flutter frequency decreases and the amplitude increases with the increase in the flow velocity. When the flutter instability of the plate occurs, three typical flutter modes are identified and are associated with the aspect ratio and the flow velocity.     

具有分布时滞的二阶非线性中立型时标动力方程的振动定理

利用广义Riccati变换技术, 研究时标上具有分布时滞的二阶非线性中立型动力方程 \[\big(r(t)\big(\big(y(t)+p(t)y(\tau(t))\big)^{\it \Delta}\big)^\beta\big)^{\it \Delta}+\int_c^dF(t,\xi,y(\delta(t,\xi))){\it \Delta}\xi=0 \]的振动性, 其中$\beta>0$是两个正奇数之比, 获得了方程所有解振动的几个充分条件,推广和改进了一些已知的结果, 并给出了几个应用实例.     

数学教学课前导语的两个案例

素质教育新课程，要求培养学生主动学习、探究学习、勤于动手、善于思考的习惯，而这个习惯的养成需要以兴趣为基础，没有兴趣就难以形成持久的学习动力．新课程主张适当设置教学情景，以激发学生的学习兴趣．课前导语就是教学情景的一种形式．本文就高中数学教学中如何设计课前导语，谈点儿想法．     

Vibration induced flow in hoppers: DEM 2D polygon model

A two-dimensional discrete element model （DEM） simulation of cohesive polygonal particles has been developed to assess the benefit of point source vibration to induce flow in wedge-shaped hoppers. The particle-particle interaction model used is based on a multi-contact principle. The first part of the study investigated particle discharge under gravity without vibration to determine the critical orifice size （Bc） to just sustain flow as a function of particle shape. It is shown that polygonal-shaped particles need a larger orifice than circular particles. It is also shown that Bc decreases as the number of particle vertices increases. Addition of circular particles promotes flow of polygons in a linear manner. The second part of the study showed that vibration could enhance flow, effectively reducing Bc. The model demonstrated the importance of vibrator location （height）, consistent with previous continuum model results, and vibration amplitude in enhancing flow.