基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

声学超表面的非对称声分束特性研究

非对称声分束超表面是由人工微单元结构按照特定序列构建的二维平面结构,可将垂直入射的声波分成两束传播方向和分束比自由调控的透射波,在声功能器件设计及声通信领域具有广泛的应用前景。本文系统研究了一种实现非对称声分束的设计理论和实现方法,基于局域声功率守恒条件研究了声分束器的设计理论、阻抗矩阵分布、法向声强分布、声压场分布等。利用遗传算法对四串联共振腔结构进行参数优化实现了声分束器所需的阻抗矩阵分布,声压场分布表明声波入射到声分束器后在入射侧激发出两列传播方向相反且幅值和衰减系数均相同的表面波,实现了入射侧与透射侧的局域声功率相互匹配。声波经过声分束器后被分为两束透射波,两束透射波的折射角和透射系数与理论值十分吻合,证明了设计理论及实现方法的正确性和可行性。本文的研究工作可以为新型非对称声分束结构设计提供理论参考、设计方法和技术支持,并促进其在工程领域的实际应用。     

驻波声场中单分散细颗粒的相互作用特性

利用外加声场促进悬浮在气相中的细颗粒发生相互作用,进而引起颗粒的碰撞和凝并,使得颗粒平均粒径增大、数目浓度降低,是控制细颗粒排放的重要技术途径.为探究驻波声场中单分散细颗粒的相互作用,建立包含曳力、重力、声尾流效应的颗粒相互作用模型,采用四阶经典龙格-库塔算法和二阶隐式亚当斯插值算法对模型进行求解.将数值模拟得到的颗粒声波夹带速度和相互作用过程与相应的解析解和实验结果进行对比,验证模型的准确性.进而研究颗粒初始条件和直径对相互作用特性的影响.结果表明,初始时刻颗粒中心连线越接近声波波动方向、颗粒位置越接近波腹点,颗粒间的声尾流效应就越强,颗粒发生碰撞所需要的时间就越短.研究还发现,颗粒直径对颗粒相互作用的影响取决于初始时刻颗粒中心连线偏离声波波动方向的程度.当偏离较小时,颗粒直径越大,颗粒发生碰撞所需要的时间越短;当偏离很大时,直径较小的颗粒能够发生碰撞,而直径较大的颗粒则无法发生碰撞.     

Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation

The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as k = 10 000.     

Analogue Models of and for Gravity

Condensed matter systems, such as acoustics in flowing fluids, light in moving dielectrics, or quasiparticles in a moving superfluid, can be used to mimic aspects of general relativity. More precisely these systems (and others) provide experimentally accessible models of curved-space quantum field theory. As such they mimic kinematic aspects of general relativity, though typically they do not mimic the dynamics. Although these analogue models are thereby limited in their ability to duplicate all the effects of Einstein gravity they nevertheless are extremely important—they provide black hole analogues (some of which have already been seen experimentally) and lead to tests of basic principles of curved-space quantum field theory. Currently these tests are still in the realm of gedanken-experiments, but there are plausible candidate models that should lead to laboratory experiments in the not too distant future.     

固体间界面的物理模型和界面对声波的反射

简要描述了模拟两固体间界面特性的弹簧模型，该模型最早是根据静力学方法提出的，后来用固体间界面薄层的声波反射方法加以改进，从界面弹簧模型可以方便地得到界面外近似边界条件，其中包含界面“弹簧”振子的劲度常数和质量，文章还给出了两相间固体中界面声反射系数的表达式，介绍了测量界面劲度常数的超声反射谱方法。最后讨论了仍关声波与界面相互作用研究领域中最近的一些研究进展。     

声波在一维声子晶体中共振隧穿的研究

通过从实验和理论方面对声波在一维声子晶体单晶体和被小的共振腔分开的双晶体中传播时发生的隧穿和共振隧穿现象的研究，观察到了声子晶体单晶体在带隙频率范围内发生的隧穿现象，而对于双晶体样品，在带隙频率范围内出现了很强的共振透射峰.共振发生时，实验测得的群时间很大，但是没有共振时，群速度却很快. 关键词： 声波 声子晶体 隧穿 共振     

Acoustic reflection from a baffled elastic/piezoelectric plate

A finite difference/boundary integral procedure to determine the acoustic reflected pressure from a fluid-loaded bi-laminated plate is described. The bi-laminate is composed of a piezoelectric layer and an elastic layer in contact with the fluid, and is held by an acoustically hard baffle. In the numerical model, the fluid pressure at fluid/solid interface is replaced by a continuum of point sources weighted by the normal acceleration of the elastic plate, and the governing equation system is solved in the solid domain. With the normal acceleration found, the reflected pressure in the fluid is determined by an integral expression involving the Green's function. It is demonstrated that an appropriate applied voltage potential across the piezoelectric layer has the effect of cancelling either the reflected or scattered pressure of the plate at any chosen field points in the fluid. Project supported by the National Natural Science Foundation of China (No. 10172039).     

Analytical Study of Nonlinear Dust Acoustic Waves in Two-Dimensional Dust Plasma with Dust Charge Variation

The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.