分数阶p-Laplace方程解的单调性公式

研究了分数阶p-Laplace方程解的单调性公式.基于Caffarelli-Silverstre的延拓技术,将分数阶p-Laplace方程相应的扩展问题表述为半空间中一个退化或奇异局部方程.通过建立与扩展问题相关的Almgren型频率函数,结合散度定理和积分估计获得了延拓函数的单调性公式.     

对RC桥式振荡器工程计算方法的探讨

探讨集成运放的开环电压增益和电路各电阻对RC桥式振荡电路表达式的影响.基于集成运放低频简化模型,提出采用拉氏变换与电阻比值相结合的方法,推导振荡器在不同工况下的数学表达式.研究结果对现有工程表达式提出了修正,对振荡参数的现场计算有指导意义,计算机软件仿真验证了结论的正确性.     

考虑运动受限的履带式移动机器人轨迹跟踪控制

针对履带式移动机器人的轨迹跟踪控制问题进行研究,首先,建立了履带式移动机器人的运动学模型和跟踪误差模型；其次,设计了转速有限时间控制和线速度滑模控制的轨迹跟踪控制律,并给出了考虑运动受限作用下的控制律修正表达式；最后,基于MATLAB对所提控制律进行仿真,对比分析了不考虑运动受限情况下跟踪控制效果;结果表明,设计的跟踪控制律能够实现履带式移动机器人对圆轨迹的有效跟踪,且考虑运动受限作用的控制律更加符合实际;文章研究分析了运动受限作用对于移动机器人轨迹跟踪控制的影响,分析结果对其他移动机器人的运动控制研究具有参考价值。     

数字全息视频成像技术及其在肝吸虫尾蚴观测中的应用

由于传统的显微镜成像需要精确的光学聚焦过程,很难检测到在水体中运动的肝吸虫尾蚴,更难以对其进行连续的动态观测.针对此问题,提出了利用单光束同轴数字全息视频技术对在水体中运动的肝吸虫尾蚴进行连续动态观测的方法,研究了其中的动态跟踪聚焦算法和视频处理算法.利用上一帧再现像中尾蚴的中心位置作为下一帧全息再现中聚焦窗口的中心位置,使聚焦窗口始终跟随观测的尾蚴移动,从而保证处理全息视频时每一帧再现像都能准确自动聚焦,使再现视频中肝吸虫尾蚴始终处于清晰状态.进行了肝吸虫尾蚴观测实验,得到肝吸虫尾蚴在水体中运动的全息再现视频,并对其运动轨迹进行了跟踪,总结了肝吸虫尾蚴在水体中的运动规律.实验结果表明,利用数字全息技术拍摄一张数字全息图即可观察到水体中不同位置的肝吸虫尾蚴,检测更加方便高效;本文提出的数字全息视频成像技术能实现对水体中的肝吸虫尾蚴或其它浮游生物进行连续动态观测.     

耳蜗结构对低频信号频散特性的影响

耳蜗是人体最为精密的力学元器件,能处理频率从几十到几万赫兹的声信号.实验研究表明,声波进入耳蜗后,沿着基底膜传播,基底膜能够将不同频率的声信号分散到不同的位置,并为位于基底膜上的毛细胞所感知,就像一个天然的Fourier(傅里叶)滤波器.在von Békésy行波理论框架体系下,基于Manoussaki等的三维螺旋基底膜流固耦合耳蜗模型,考虑耳蜗导管高度和基底膜刚度均为纵向梯度变化,推导出基底膜声波传播的频散方程,分别分析了基底膜刚度和耳蜗导管高度对频散特性的影响.发现耳蜗内淋巴液的存在大大提高了耳蜗对低频信号的处理能力,且捕获频率随基底膜刚度和耳蜗导管高度的减小而降低,两者梯度变化在声信号调制中起协同作用.最后,以人、沙鼠和豚鼠的具体耳蜗参数为例,得到3种生物耳蜗频率-点位图,并验证了低频段模型预测的正确性,比较分析了耳蜗频散功能与生物适应性之间的关系.     

Fabrication of large-scale ripples on fluorine-doped tin oxide films by femtosecond laser irradiation

The large-scale uniform self-organized ripples are fabricated on fluorine-doped tin oxide （FTO） coated glass by femtosecond laser. They can be smoothly linked in a horizontal line with the moving of XYZ stage by setting its velocity and the repetition rate of the laser. The ripple-to-ripple linking can also be realized through line-by-line scanning on a vertical level. The mechanism analysis shows that the seeding effect plays a key role in the linking of ripples.     

一种模拟动边界绕流的锐利界面浸入边界法

When the structural wall moves over a fixed grid, the structure coverage will change, resulting in many dead and emerging elements. To avoid the influence of malformation and reconstruction of body-fitted grids on the calculation efficiency and accuracy of the fluid-structure interaction problems with coupled boundary movement on the fixed grid, an improved numerical method for describing the interaction between an immersed rigid body and fluid based on a sharp-interface is proposed. In this method, both the fluid and solid are regarded as pure fluid domains in the whole computational domain, and the solid boundary is divided into several Lagrangian grid points. The flow parameter or velocity is reconstructed by interpolation at the interface element, which is then directly used as the boundary condition of the flow field, thus reflecting the influence of the wall boundary conditions. The method constructs the calculation structure of “virtual point, force point and vertical foot point”, and the velocity of the virtual point is obtained by bilinear interpolation. Then, the velocity of the force point is calculated by forcing the solid boundary to meet the no-slip condition, and the equations of the coupling system based on the immersion boundary method are finally solved to realize the numerical simulation of the flow with a complex moving boundary. The numerical program for this immersed boundary method is established using C++, then the accuracy and reliability of the proposed method are validated by comparison with the literature and experimental results of the basic numerical example of flow around a cylinder. Furthermore, the effects of the structural shape and the angle of attack on the trailing vortex structure, the vortex shedding frequency, and the lift/ coefficient characteristics of the flow around the elliptical cylinder have been analyzed. The anti-symmetric S-type, “P+S” Ⅰ-type and “P+S” Ⅱ-type trailing vortex shedding modes, as well as the variation laws of the vortex structure size, vortex shedding frequency and lift-drag coefficients ratio with axis ratio and angle of attack, are captured. The critical angle of attack (25°) corresponding to the maximum lift-drag ratio is determined as 25°.     

用功的互等定理求解矩形薄板的自然频率

从虚功原理出发，证明了薄板小挠度弯曲问题的功的互等定理，并由此推出了求解矩形薄板自然频率的公式．算例表明，该公式计算简便，精度较高．     

识别求解路径上奇异点的一个计算方法

提出一个在路径跟踪计算中识别分支点和极值点的实用方法，给出了算例。     

电磁探测技术在冰层厚度检测中的应用探究

根据海冰、内陆湖泊、河流、冰川等冰资源与环境中的自然科学问题及冬季结冰地区水工结构物安全运行管理中对冰层厚度时空变化资料的需求,基于电磁场的特有性质,讨论了可用于冰层厚度检测的两种电磁探测方法-时间域电磁法和频率域电磁法,较详细讨论了它们的工作原理、研究进展、适用范围和在冰层厚度检测中获得的初步应用结果,并通过对实际测量结果的分析比较,提出了频率域电磁法,相对于时间域电磁法,在冰层厚度检测中具有更多的优势.