Poincaré Mapping Method for Hydrodynamic Systms. Dynamic Chaos in a Fluid Layer between Eccentrically Rotating Cylinders

Investigation of the plane–parallel motion of particles of an incompressible medium reduces to investigation of a Hamiltonian system. The Hamiltonian function is a stream function. The timeperiodic mixing of an incompressible medium is described by a timeperiodic Hamiltonian function. The mixing of the medium is associated with dynamic chaos. Transition to dynamic chaos is studied by analysis of the positions of Lagrangian particles at times divisible by the period — Poincaré recurrence points. The set of Poincaré recurrence points is studied with the use of Poincaré mapping on the phase flow. A method for constructing Poincaré maps in parametric form is proposed. A map is constructed as a series in a small parameter. It is shown that the parametric method has a number of advantages over the generating function method is shown. The proposed method is used to examine the motion of particles of an incompressible viscous fluid layer between two circular cylinders. The outer cylinder is immovable, and the inner cylinder rotates about a point that does not coincide with the centers of both cylinders. An optimal mode for the motion is established, in which the area of the chaotic region is maximal.     

Instability of a Collision Surface During High-Velocity Impact

The physical mechanisms of development of hydrodynamic instability during high-velocity impact are analyzed analytically and using numerical simulation. A new mechanism of development of instability based on the assumption of the existence of initial perturbations on the surfaces of the colliding plates is proposed. The progressive displacement of the maximum of the specific surface mixed mass from the shortwave to the longwave spectrum range and the self-similarity of the variation of the interface are established.     

The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

非线性增益介质中的小尺度自聚焦特性分析

由光束在吸收 (增益 )介质中传输的非线性近轴波方程 ,推导出了光束在两种介质中传输时 ,由于小尺度调制的非线性增长所引起的小尺度自聚焦所满足的微分方程。进而讨论了光束在增益介质中传输时产生的小尺度自聚焦特性 ,得出了其截止频率、最快增长频率、纹波的积分指数增益等特性随各参量的变化 ,并推出了小尺度自聚焦产生的最小传输距离     

富勒烯衍生物中的自散焦、自聚焦及其相互转化

用Z扫描方法研究了富勒烯有机铬衍生物fac- and mer- [bis (1,2-diphenylphosphino) ethane] (tricarbonyl) (η²-fullerene-C₆₀) chromium的非线性折射特性;用速率方程理论分析了激发态光学非线性材料非线性折射行为,以及大光强下高阶激发态折射度如何引起材料自散焦-自聚焦相互转化.计算出了转变光强.并数值模拟了不同光强下Z扫描实验曲线的变化过程.理论计算与实验符合得较好. 关键词： 自散焦 自聚焦 富勒烯衍生物 Z扫描     

Toward one nanometer X-ray focusing: a complex refractive lens design

We report a design for one nanometer X-ray focusing by a complex refractive lens, which is capable of focusing 20 keV X-rays down to a lateral size of 0.92 nm （full-width at half-maximum （FWHM）） and an axial size of 98 nm （FWHM） with intensity gain of 49050. This complex refractive lens is comprised of a series of kinoform lenses, whose aperture is gradually matched to the converging trace of the X-ray beam so as to increase the numerical aperture （NA）. The theoretical principle of the proposed complex refractive lens is presented. The NAs of these lenses are calculated. The numerical simulation results demonstrate that the proposed design can focus the X-ray beam into sub-nanometer while remaining high gain.     

Flat acoustic lens by acoustic grating with curled slits

We design a flat sub-wavelength lens that can focus acoustic wave. We analytically study the transmission through an acoustic grating with curled slits, which can serve as a material with tunable impedance and refractive index for acoustic waves. The effective parameters rely on the geometry of the slits and are independent of frequency. A flat acoustic focusing lens by such acoustic grating with gradient effective refractive index is designed. The focusing effect is clearly observed in simulations and well predicted by the theory. We demonstrate that despite the large impedance mismatch between the acoustic lens and the matrix, the intensity at the focal point is still high due to Fabry–Perot resonance.     

镜面偏心测量光学系统设计及其杂光分析

为了解决现有镜面偏心测量设备存在的问题,本文研究了一种采用切换镜头和调焦相结合的方法来设计的镜面偏心测量光学系统,使用这个光学系统,既能使被测镜面的曲率半径扩展到-∞~+∞范围,又能保证测量精度。通过Lighttools软件对这个光学系统进行光线追迹,分析其杂光分布,结果表明:准直镜头内部多次反射产生的杂光强度很低,可以忽略。而当被测镜头中存在相邻球心像距的镜面时,产生的杂光强度比较大,在后续的图像处理过程中,必须增强目标图像的对比度。利用研制的镜面偏心测量设备进行测量实验,结果进一步验证了杂光分析的正确性。     

铷蒸气激光器3D理论模型的建立及阈值特性模拟

基于三能级速率方程理论,结合惠更斯-菲涅尔衍射积分公式,利用分步光束传播方法建立了半导体泵浦碱金属蒸气激光器(DPAL)端面泵浦3D理论计算模型,用于模拟研究铷蒸气激光器的泵浦阈值特性。该模型将光束传播、光与物质相互作用独立考虑,利用迭代算法求解。考虑激光器腔内模式与泵浦光模式匹配对阈值特性的影响,模拟了单端泵浦铷蒸气激光器内部的三维动力学过程。在具体算例中研究了模式匹配最佳时,在阈值工作状态下铷蒸气室中的三维粒子数分布,以及沿不同轴线的增益分布。仿真了在最佳模式匹配位置附近,泵浦光模式变化对阈值特性的影响。根据蒸气池中粒子数分布和光场分布具体分析了模式匹配影响阈值特性的机理。同时还模拟了不同长度蒸气池对阈值特性的影响。结果表明,腔参数与泵浦光模式之间存在一定的关系,对于特定的泵浦光模式,存在恰当的腔参数,使得阈值达到最小。