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| 1 | Correcting the initialization of models with fractional derivatives via history-dependent conditions显示文摘Fractional differential equations are more and more used in modeling memory(history-dependent,nonlocal,or hereditary) phenomena.Conventional initial values of fractional differential equations are define at a point,while recent works defin initial conditions over histories.We prove that the conventional initialization of fractional differential equations with a Riemann–Liouville derivative is wrong with a simple counter-example.The initial values were assumed to be arbitrarily given for a typical fractional differential equation,but we fin one of these values can only be zero.We show that fractional differential equations are of infinit dimensions,and the initial conditions,initial histories,are define as functions over intervals.We obtain the equivalent integral equation for Caputo case.With a simple fractional model of materials,we illustrate that the recovery behavior is correct with the initial creep history,but is wrong with initial values at the starting point of the recovery.We demonstrate the application of initial history by solving a forced fractional Lorenz system numerically. | Maolin Du Zaihua Wang | 2016 | Acta Mechanica Sinica2016，32，2： | 1 |
| 2 | 间隙环流作用下的泰勒涡演化及环流速度分布特性研究显示文摘屏蔽电机运转过程中由于粘性旋转流体所受到的离心力作用,间隙内部出现泰勒涡结构,使得间隙环流有着复杂的速度分布特性.这种速度分布特性不仅对屏蔽电机水力损耗及散热特性具有重要影响,而且也是屏蔽电机转子动力学所关注的基础科学问题.本文借助间隙环流流动性能实验平台,采用高速摄像机拍摄观测了湍流核心区泰勒涡的演化过程,面向工程应用阐明了间隙环流湍流核心区流动对边界层速度的影响规律,可为设计屏蔽电机间隙流道的尺度提供理论依据.采用计算流体动力学软件建立间隙环流仿真模型,研究了定间隙条件下泰勒涡的演化过程与环流速度分布特性,初步探讨了变间隙比对间隙环流速度结构的影响规律.研究结果表明,泰勒涡随间隙比及转子转速演化的仿真计算结果与实验测试结果的变化趋势较吻合.泰勒涡在径向与轴向方向上的速度分布具有显着差异,间隙环流涡的流动方向会改变流动边界的速度结构.当转速增大时,间隙环流由层流转变为湍流,速度形状不再沿间隙径向线性分布,而是产生畸变,呈现出壁面周围速度快速减小,中间速度渐趋平稳的轮廓. | 陈明明 薛亚波 | 2023 | 力学季刊2023，44，2： | 1 |
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