Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.     

Electrophoresis simulations using Chebyshev pseudo-spectral method on a moving mesh

We present the implementation and demonstration of the Chebyshev pseudo-spectral method coupled with an adaptive mesh method for performing fast and highly accurate electrophoresis simulations. The Chebyshev pseudo-spectral method offers higher numerical accuracy than all other finite difference methods and is applicable for simulating all electrophoresis techniques in channels with open or closed boundaries. To improve the computational efficiency, we use a novel moving mesh scheme that clusters the grid points in the regions with poor numerical resolution. We demonstrate the application of the Chebyshev pseudo-spectral method on a moving mesh for simulating nonlinear electrophoretic processes through examples of isotachophoresis (ITP), isoelectric focusing (IEF), and electromigration-dispersion in capillary zone electrophoresis (CZE) at current densities as high as 1000 A/m. We also show the efficacy of our moving mesh method over existing methods that cluster the grid points in the regions with large concentration gradients. We have integrated the adaptive Chebyshev pseudo-spectral method in the open-source SPYCE simulator and verified its implementation with other electrophoresis simulators.     

平面波超声成像中的波束合成方法研究进展

平面波成像通过单次全孔径发射-接收即可获取整幅图像,将成像帧频显著地提升至1000帧/秒以上.然而,平面波成像过程中发射的非聚焦波束将导致回波信号信噪比降低,进而使图像的分辨率和对比度变差.通过多角度相干复合成像技术可以改善平面波成像的图像质量,但是会以牺牲帧频为代价.因此研究人员们开始将新型波束合成技术引入平面波成像...     

基于LMS自适应时延估计和FPGA的超声波测风系统研究

利用超声波传感器进行风速测量时,温度对超声波传播有很大影响,时延估计对超声波测风系统的精度起到很大的作用。本超声波测风系统为避免温度对风速测量中的影响,采用了基于时差法的测量原理,为了提高时延估计值的精度,提出了基于最小均方(LMS)自适应时延估计的测量方法,研制了以单片机Atmega128和现场可编程门阵列(FPGA)为核心的硬件系统。仿真和实际测试的结果表明,该超声波测风系统的时延估计值精确度较高,具有很高的应用价值。     

共孔径偏振耦合分光的旋转四分之一波片相位补偿技术

 在地平式折轴望远镜中开展自适应光学激光导星实验,研究了共孔径发射接收信标激光束偏振耦合分光效率随望远镜方位角和天顶角变化的补偿技术。提出了一种由四分之一波片和法拉第旋光器构成的相位补偿器,通过旋转四分之一波片以实时补偿由于望远镜旋转导致的光路相位延迟量的变化。数值计算表明,望远镜处于任意方位角和天顶角位置时,通过1°步长旋转四分之一波片,可使补偿后的偏振分光效率理论上达到99.90％以上。实验从原理上定性地验证了该方法的有效性。只要测量出镜面的相位延迟,便可计算得到望远镜处于不同方位角和天顶角情况下有效补偿所需的四分之一波片旋转角度,据此可建立实用的旋转波片偏振补偿装置。     

共孔径偏振耦合分光系统中反射镜造成的相位延迟差的测量

 激光信标共孔径发射接收偏振分光系统的动态相位补偿需要测量望远镜各反射镜对s光和p光的相位延迟差。利用Stokes矢量和Mueller矩阵建立了物理模型,并推导出用测得的回光功率计算相位延迟差的解析式。提出一种通过实验测量回光功率计算反射镜相位延迟差的方法,解决了在0～2p范围内唯一确定反射镜相位延迟差的问题。实际测量了两块反射镜的相位延迟差,并将测量结果用于动态相位补偿偏振分光实验,验证了该方法的正确性。分析了偏振分光棱镜、法拉第旋光器以及近似计算这3个主要的测量误差源,并估计总测量误差约为1°。     

微加工薄膜变形镜特性分析

 借助测量微加工薄膜变形镜驱动器的面形影响函数,分析了驱动器的电压-位移函数和驱动器之间的线性叠加性;通过对连续面形变形镜拟合像差的理论分析和实验研究,建立了微加工薄膜变形镜电压解耦模型。分析了对前36阶Zernike模式的拟合残差和拟合能力,指出微加工薄膜变形镜仅可用来拟合低级像差并且有较大的拟合能力和较小的拟合残差,而不能拟合高级像差。     

Adaptive optics for airborne platforms—Part 1: modeling

Adaptive optics systems mitigate the atmospheric turbulence-induced distortion of a propagating light wavefront. The use of adaptive optics entails the design of a feedback controller, which requires the development of a model of the plant to be controlled. In adaptive optics, the plant consists of the atmosphere through which light is traveling. Moreover, a distinct feature of the adaptive optics control application is the presence of random signals in the plant. In optics, Zernike orthonormal polynomials are commonly used as a basis set for the expansion of wavefront phase distortions. Due to the atmospheric turbulence-induced random nature of the underlying physical process, the spatial-temporal correlation functions of the Zernike polynomial phase distortion expansion coefficients must be evaluated if a proper stochastic model of the plant is to be developed and adaptive optics is to be employed. In Part 1 of this paper, these correlation functions are developed using a layered atmospheric model and calculations for the first few low-order Zernike modes are performed. Using these correlation functions, an underlying stochastic linear dynamical system, which is adequate for control design, is synthesized. This system models the plant and, in turn, provides the basis for the employment of advanced model-based control and estimation concepts in an adaptive optics system for an airborne platform application.     

圆弧形面阵自适应波束形成快速计算方法

针对圆弧形面阵估计水下目标二维波达方向的问题,提出一种降维处理的自适应波束形成方法。利用圆弧形面阵模型简化阵列内插矩阵的计算,通过垂直和水平两阶段波束加权,降低自适应波束形成维数,从而实现快速估计声源二维波达方向的目的。仿真结果表明,所提改进方法的计算量较传统二维最小方差无失真波束形成方法降低约一个数量级,且在低快拍条件下具有更明显的噪声抑制优势。湖上实验数据处理结果验证,在复杂水声环境下,所提方法具有较好的目标分辨性能。