Adaptation of the law of the wall boundary treatment to include volumetric heating effects

Computational Fluid Dynamics (CFD) simulations of liquid–metal spallation targets, such as MEGAPIE and ESS, which utilize the High Reynolds number k–ε turbulence model, invariably incorporate an implicit law of the wall treatment in which a linear or logarithmic fit to the velocity and temperature profiles is made next to heated, non-slip surfaces. The law is well-established, but has been derived from the assumptions that the wall shear stress and the normal heat flux are constant through the viscous sub-layer and buffer zone, which lie beneath the turbulent boundary layer. However, in the case of the heat flux, this condition will be violated for applications in which there is intense volumetric heating in the near-wall layers. This is just the case for the spallation reactions taking place in liquid–metal targets as a result of proton bombardment. In this article, a modified law of the wall is derived to be used under such conditions. Use of the law is illustrated by means of flow in a flat channel and one application to a spallation target. From the applications considered, it is found that the effect of the modification is small, provided the local mesh resolution is chosen appropriately. Specific recommendations regarding optimum mesh size for liquid–metal heat transfer problems are given, which will be of general interest, with or without volumetric heating.     

The Upper Envelope of Positive Self-Similar Markov Processes

We establish integral tests in connection with laws of the iterated logarithm at 0 and at +∞, for the upper envelope of positive self-similar Markov processes. Our arguments are based on the Lamperti representation and on the study of the upper envelope of the future infimum due to the author (see Pardo in Stoch. Stoch. Rep. 78:123–155, [2006]). These results extend laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdős (Proceedings of the Second Berkeley Symposium, [1951]) and stable Lévy processes with no positive jumps conditioned to stay positive due to Bertoin (Stoch. Process. Appl. 55:91–100, [1995]). Research supported by a grant from CONACYT (Mexico).     

Exact rates in log law for positively associated random variables

Let be a strictly stationary sequence of positively associated random variables with mean zero and finite variance. Set , Mn=maxk?n|Sk|, n?1. Suppose . In this paper, we study the exact convergence rates of a kind of weighted infinite series of , and as ε↘0, respectively.     

U-统计量对数律的精确渐近性

设{X_n, n ≥1}是独立同分布随机变量序列, U_n 是以对称函数(x, y) 为核函数的U -统计量. 记U_n =2/n(n-1)∑_{1≤i h(Xi, Xj), h1(x) =Eh(x, X2). 在一定条件下, 建立了∑n=2^∞(logn)^δ-1EUn²I {I U n |≥n ^1/2√lognε}及∑n=3^∞(loglognε)^δ-1/logn EUn² I {|U n|≥n^1/2√log lognε} 的精确收敛速度.}     

Fresnel absorption of 1 μm- and 10 μm-laser beams at the keyhole wall during laser beam welding: Comparison between smooth and wavy surfaces

The angle-dependent absorption of laser beams at metal surfaces is described by the Fresnel-equations. During keyhole laser welding the essential interaction takes place at very striping angles of incidence of the order of 1-8 degrees at the front of the vapour capillary, called the keyhole. For a smooth vapour capillary, laser beams with a wavelength of about 1 μm operate in a Fresnel-regime where the absorptance increases with the angle of incidence at the wall, towards the weak Brewster-angle maximum. In contrast, for 10 μm-lasers high absorptance around the more pronounced Brewster-angle peak takes place. From high speed imaging keyhole surface waves were observed. Mathematical modelling of the laser-keyhole interaction demonstrates that already relatively little waviness of the melt surface at the keyhole strongly modulates the angles of incidence and in turn the Fresnel-absorption due to varying angles of incidence, soon also leading to shadow zones. Due to this local variation of the angle of incidence the absorptance tends towards the angle-averaged value, with the consequence that for 1 μm-lasers the direct absorptance and in turn the penetration depth increases, particularly at low welding speed, while for 10 μm-lasers it generally decreases.     

基于均分配焦椭流线法的LED匀光管菲涅尔反射器设计

基于边光原理和椭流线理论提出了均分配焦椭流线的非成像光学设计方法,通过对LED光源的能量均分、椭流线虚实焦点的配对和光学仿真优化三个规范步骤实现了应用于LED匀光管均匀配光的菲涅尔反射器的光学设计.分析了光源、反射器和投射目标面三者之间的复杂关系,为LED照明设计的优化提供了方便.仿真结果表明,LED匀光管管壁照度的均匀度超过0.93,有效降低了LED光源的眩光性.     

风云四号辐射计的高精度动态测角系统

为了测试风云四号气象卫星扫描成像辐射计的扫描镜的动态运动精度,设计了一种高精度动态测角仪。该测角仪利用了扫描成像辐射计的可见光通道,采用622 nm的LED可见光,经过菲涅耳透镜投射到目标板上,然后充满投影光学系统的入瞳,利用光学成像分析像点位置及相互关系的方法来评价扫描镜的运动精度。介绍了该测角仪的投影光学系统、照明系统和系统总体的设计。     

An Optical Image Encryption Method Using Hopfield Neural Network

In this paper, aiming to solve the problem of vital information security as well as neural network application in optical encryption system, we propose an optical image encryption method by using the Hopfield neural network. The algorithm uses a fuzzy single neuronal dynamic system and a chaotic Hopfield neural network for chaotic sequence generation and then obtains chaotic random phase masks. Initially, the original images are decomposed into sub-signals through wavelet packet transform, and the sub-signals are divided into two layers by adaptive classification after scrambling. The double random-phase encoding in 4f system and Fresnel domain is implemented on two layers, respectively. The sub-signals are performed with different conversions according to their standard deviation to assure that the local information’s security is guaranteed. Meanwhile, the parameters such as wavelength and diffraction distance are considered as additional keys, which can enhance the overall security. Then, inverse wavelet packet transform is applied to reconstruct the image, and a second scrambling is implemented. In order to handle and manage the parameters used in the scheme, the public key cryptosystem is applied. Finally, experiments and security analysis are presented to demonstrate the feasibility and robustness of the proposed scheme.     

微焦点源X射线相衬成像技术

 相衬成像方法利用硬X射线对低密度弱吸收物质成像,可获得高衬度图像。用菲涅尔衍射理论分析了X射线图像的形成机理。在频域中根据光学传递函数,对物像距离、样品空间频率等对图像相位衬度的影响进行了分析。分辨率和衬度是决定图像可见度的两个依据,分辨率主要依赖于光源的空间相干性,空间相干性又决定于源点尺寸,而时间相干性（单色性）是一个不重要的影响因子。利用多色微焦点源实现了X射线相衬成像技术,获得了有价值的相衬图像,如低原子序数低密度泡沫材料的硬X射线相衬图像,与吸收衬度成像相比,其图像质量得到了很大提高,能观察到泡沫材料的细微结构,分辨率可达μm量级。     

三维物体菲涅耳计算全息图的研究

介绍一种用计算全息显示三维物体的方法.记录三维物体在非相干白光照明条件下两个正交方向上不同视角的一系列连续二维像,根据计算机断层成像原理,由这些二维像计算出物体的三维傅立叶频谱,从中提取出一特征傅立叶频谱,用卷积算法计算出在一定传播距离处的菲涅耳衍射分布,用计算全息编码方法制出一张菲涅耳计算全息图,并进行模拟再现,给出了不同再现距离处的再现像.