表面分形球、柱的光散射

分形和分维是近些年才兴起的一门处理复杂事物的新方法￣［１］。本文主要研究具有表面分形的球、柱的光散射特征。我们首先利用几何光学近似研究了一种表面满足自仿射原理的分形均匀球的散射，其散射特性与分维存在一定的关系。我们还利用微扰法讨论了表面具有沟槽的分形柱的光散射的分形特征。     

角分辩的光散射轮廓及自仿射分形表面的粗糙指数的实验研究

建立了反射式随机表面的光散射特件实验测量系统,利用多幅平均及叠加连接的方法,得出入射角在45°～85°之间不同值时的光散射轮廓.结果表明,随着表面入射角的增加,光散射轮廓的半峰全宽逐渐减小.并且当入射角的增加到一定值时,光散射轮廓出现中央亮斑.由数学上的对称F降函数,推导出光散射轮廓的半峰全宽随散射光波矢的变化关系,从实验测得角分辩的的光散射轮廓中提取了自仿射分形随机表面的粗糙指数.与原子力显微镜测量得到的粗糙指数进行比较,两者符合得很好.     

弱散射屏的像面散斑自相关函数特性的实验研究

在对随机弱散射屏进行表面参数的原子力显微镜测量和建立了门积分取样平均的随机光强自相关函数测量系统的基础上,对弱散射屏在严格像面和离焦像面上产生的散斑自相关函数进行了测量。发现在严格像面上,散斑平均颗粒的大小随表面粗糙度增加而减小,且光强自相关函数次极大的相关间隔宽度随粗糙度增加而减小;而次极大的超伏随粗糙度的增大而增大;在离焦像面上,离焦量的增加使光强的自相关函数下降变得平滑,并使极小值点和次极大点变得不明显或者消失。     

具有分形结构的SiC/SiO2界面的粗糙散射

用结构函数的方法建立了SiC粗糙表面的分形模型,用rms粗糙度Δ,分形维数D,以及相关长度L三个参量来刻画表面高度的自协方差函数,并提出了参数的计算方法.在此分形模型的基础上,能计算出SiC/SiO₂界面对沟道电子的粗糙散射.     

表面特征与软X射线掠入射光学散射

介绍了短波段掠入射表面散射线性模型,并且根据这个理论,分析计算了不同的表面特征对软X射线掠入射光学散射特性的影响。实验发现:随着粗糙度的增加、自相关长度的减小,软X射线掠入射光学散射越来越严重。     

电子束蒸发氧化锆薄膜的粗糙度和光散射特性

利用电子束蒸发工艺，以Ag层为衬底，沉积了中心波长为632.8nm的氧化锆(ZrO₂)薄膜，膜层厚度在80—480nm范围内变化.研究了不同厚度样品的粗糙度变化规律和表面散射特性.结果发现，随着膜层厚度的逐渐增加，其表面均方根(RMS)粗糙度和总积分散射(TIS)均呈现出先减小后增大的趋势.利用非相关表面粗糙度的散射模型对样品的TIS特性进行了理论计算，所得结果与测量结果相一致. 关键词： 氧化锆 表面粗糙度 标量散射 电子束蒸发     

多光束在分形粗糙表面散射的仿真

采用矩量法(MOM),分析了多光束在分形粗糙导体表面的散射分布.对在不同入射角、光束宽度控制因子、光束照射区宽度、表面均方根高度和表面分维数情况下的散射进行了数值仿真.仿真结果表明了各参量的变化对散射分布的影响.根据仿真计算结果给出了最佳的散射测量区域,为减少多光束测量的误差提供了一定的参考.     

高散射媒质中的光程可分割动态光散射研究

为研究散射光强度随光子在散射媒质中散射光程的变化,基于单散射理论与扩散波光谱理论,采用了低相干动态光散射装置对不同粒径大小的聚苯乙烯悬浮液进行研究。将测量得到的背散射光光场强度谱的线宽与相应的理论计算结果相比较发现,在短光程区域,考虑容器壁附近拖曳效应的影响后,对于不同粒径的颗粒,光程为约5倍粒子平均自由程的区域可看成为单散射区域;对于光程大于225 m的区域可看成为扩散光波区域。实验结果表明低相干动态光散射法可实现高散射媒质从单散射区域到低次散射再到扩散区域的全光程的可分割的光场强度谱测量。     

光学表面光散射特性分析

通过对光学表面光散射特性的研究,结果表明:光散射强度随入射光波长的增加而减小,随表面粗糙度增加而增加.     

大尺度分层介质粗糙面电磁散射的特性研究

首先建立大尺度分层介质粗糙面散射的物理模型, 基于Stratton-Chu积分方程和Kirchhoff近似导出了粗糙面散射场的计算公式. 采用高斯随机粗糙面来模拟实际的分层介质粗糙面, 通过数值计算得到了正下视单站雷达接收到的后向散射回波. 理论推导了散射场强度与表面粗糙度之间的定量关系, 并从数值仿真的角度分析了表面和次表面的粗糙度对散射回波的影响, 给出了散射场随粗糙度变化的曲线. 最后考察了分层介质的电特性参数(介电常数和电导率)对分层粗糙面散射场的影响, 并对计算结果做出了分析.     

粗糙表面形貌对湿润性的影响

采用自仿射分形对粗糙表面形貌进行了定量描述。基于分形粗糙表面形貌,建立了粗糙表面润湿性的理论模型并进行了数值计算,分析讨论了均方根粗糙度和表面分形维数对接触角的影响。研究结果表明,均方根粗糙度对接触角的影响较大,而粗糙表面的分形维数对润湿性的影响则并不明显。     

随机表面散射光场的格林函数法与基尔霍夫近似的比较

从简谐光波满足的亥姆霍兹方程出发，将由格林定理得到的介质分界面上的积分方程转化为以表面上的光波及其导数为未知量的线性方程组，并对其进行数值求解，实现了光场的数值计算. 同时，由透射光场的格林函数积分得出了基尔霍夫近似下光场的表达式. 通过类比推导夫琅和费面上散斑场自相关函数的方法，提出了产生随机表面及其导数的傅里叶变换方法. 在此基础上，对采用基尔霍夫近似进行自仿射分形随机表面的散射光场数值计算的精确程度进行了研究. 发现在随机表面粗糙度比较小时，基尔霍夫近似的精度比较高；在粗糙度相同的情况下，表面的分形 关键词： 格林函数积分 基尔霍夫近似 自仿射分形随机表面     

Study on Properties of Intensity Profiles Scattered from the Self-Affine Fractal Random Surfaces: an Approximate Theory and Simulations

We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces. Weuse the mathematical decay function to approximate the duple negative exponent function in the rigorous theory ofscattering, by letting them have the same maximum value and half-width, and the expression for the half-widths of theintensity profiles in the whole range of the perpendicular wave vector component is obtained. The previous results in thetwo extreme cases are included in the results of this paper. In the simulational verification, we propose a method for thegeneration of self-affine fractal random surfaces, using the square-root of Fourier transform of the correlation function ofthe surface height. The simulated results conform well with the theory.     

Non-contact adhesion to self-affine surfaces: A theoretical model

Strength of adhesion between materials is known to be strongly influenced by interface irregularities. In this work, I devise a perturbative approach to describe the effect of self-affine roughness on non-contact adhesive interactions. The hierarchy of the obtained analytical solutions is the following. First, analytical formulae are deduced to describe roughness corrections to the van der Waals interaction energies between a hemi-space adherend, bounded by a self-affine surface, and a point-like adherent. Second, the problem of two hemi-spaces, one of which has a planar surface, and the other is bounded by a self-affine surface, is solved analytically. In the latter case, a numerical analysis is performed to delineate the behavior of the roughness corrections as a function of the parameters, characterizing self-affine fractal surface roughness. The problem of two hemi-spaces, both bounded by self-affine fractal surfaces, is also addressed in this work. The model?s predictions are compared with previously reported theoretical results and available experimental data.     

粗糙表面形貌对微尺度流动换热的影响

基于分形几何定量描述了多尺度自仿射的粗糙表面形貌,建立了微通道内层流流动换热的理论模型并对表面形貌的影响进行了数值模拟.研究表明,自仿射分形维数直接反映了表面轮廓的不规则度,对于两个具有相同统计粗糙度的轮廓,可能存在不同的分形维数;与常规尺度通道不同,雷诺数、粗糙高度和粗糙表面分形维数都对微通道内层流流动换热有着重要影...     

Near-field speckles produced by random self-affine surfaces and their contrast transitions

By use of a numerical calculation based on Green's integral equation, we study the near-field speckles produced by the random self-affine fractal surfaces of a dielectric medium. The speckle intensities evolve considerably in the near-field region, and the local fluctuations in them disappear before they have traversed the distance of a wavelength. The transition of the speckle contrast either on the surface or in the near field and in the neighborhood non-near-field regions depends on lateral correlation length xi and roughness exponent alpha of the random surfaces.     

表面粗糙度的分形特征及其对微通道内层流流动的影响

基于分形几何学,研究了表面粗糙度的分形特征.采用Weierstrass- Mandelbrot函数对多尺度自仿射的表面粗糙度进行了描述;建立了微通道内层流流动的三维模型并对表面粗糙度的影响进行了数值模拟,分析了雷诺数、相对粗糙度和分形维数对流动阻力特性的影响.研究结果表明,与常规尺度通道不同,粗糙微通道的Poiseuille数不再是常数,而是随雷诺数近似线性增加;相对粗糙度越大,流动产生的回流和分离所导致的流动压降越明显.在相同的相对粗糙度下,粗糙表面的分形维数越大,表面轮廓变化就越频繁,这也将导致流动阻 关键词： 粗糙度 层流阻力系数 微通道 分形     

A discrete dislocation plasticity analysis of a single-crystal semi-infinite medium indented by a rigid surface exhibiting multi-scale roughness

Discrete dislocation plasticity was used to analyse plane-strain indentation of a single-crystal elastic–plastic semi-infinite medium by a rigid surface exhibiting multi-scale roughness, characterised by self-affine (fractal) behaviour. Constitutive rules of dislocation emission, glide and annihilation were used to model short-range dislocation interactions. Dislocation multiplication and the development of subsurface shear stresses due to asperity microcontacts forming between a single-crystal medium and a rough surface were examined in terms of surface roughness and topography (fractal) parameters, slip-plane direction and spacing, dislocation source density, and contact load (surface interference). The effect of multi-scale interactions between asperity microcontacts on plasticity is elucidated in light of results showing the evolution of dislocation structures. Numerical solutions yield insight into plastic flow of crystalline materials in normal contact with surfaces exhibiting multi-scale roughness.     

A Monte Carlo method for simulating fractal surfaces

A Monte Carlo method is presented for simulating rough surfaces with the fractal behavior. The simulation is based on power-law size distribution of asperity diameter and self-affine property of roughness on surfaces. A probability model based on random number for asperity sizes is developed to generate the surfaces. By iteration, this method can be used to simulate surfaces that exhibit the aforementioned properties. The results indicate that the variation of the surface topography is related to the effects of scaling constant G and the fractal dimension D of the profile of rough surface. The larger value of D or smaller value of G signifies the smoother surface topography. This method may have the potential in prediction of the transport properties (such as friction, wear, lubrication, permeability and thermal or electrical conductivity, etc.) on rough surfaces.     

Influence of surface roughness on superhydrophobicity

Superhydrophobic surfaces, with a liquid contact angle theta greater than 150 degrees , have important practical applications ranging from self-cleaning window glasses, paints, and fabrics to low-friction surfaces. Many biological surfaces, such as the lotus leaf, have a hierarchically structured surface roughness which is optimized for superhydrophobicity through natural selection. Here we present a molecular dynamics study of liquid droplets in contact with self-affine fractal surfaces. Our results indicate that the contact angle for nanodroplets depends strongly on the root-mean-square surface roughness amplitude but is nearly independent of the fractal dimension D(f) of the surface.