规则表面形貌的分形和多重分形描述

以6种具有典型特征的生成元构造了6个具有相同rms粗糙度的规则表面,用变分法计算了这些表面的分形维数,结果表明,分形维数可以将具有相同rms粗糙度的表面区分开来,它定量表征了表面的总体形貌。进一步将多重分形的方法应用到对这些表面的分析中,发现多重分形谱可以全面反映表面概率的分布特征。多重分形谱的宽度可以定量表征表面的起伏程度,多重分形谱最大、最小概率子集维数的差别可以统计表面最大、最小概率处的数目比例。 关键词： 粗糙度 分形维数 多重分形谱     

基于多个无标度区的多重分形分析方法

用计算机模拟生成了多重分形结构,通过对比分析结构的解析多重分形谱和配分函数法计算得到的多重分形谱,总结出多重分形谱可以描述结构在某一无标度区内生长规律的特性,发现结构的各个无标度区都具有研究价值,针对传统方法不能充分利用数据的缺陷,提出了基于多个无标度区的多重分形谱计算方法.     

400GeV/c pp碰撞自仿射多重分形分析

利用分形来研究高能碰撞多粒子产生机制是新兴的交叉科学,而获取多粒子产生的多重分形谱对了解高能碰撞机制很重要.本文将改进的连续阶数阶乘矩方法应用于40 0GeV/cpp碰撞多重产生的自仿射分析中,首次得到了自仿射多重分形谱.     

薄膜生长的多重分形谱的计算

规则分形具有理想的标度不变性,而随机分形(如薄膜生长)概率分布曲线及标度不变性的范围与计算方法有关:以偏离平均高度的方差值求概率,标度不变性不好,多重分形谱也不光滑;而以薄膜平均底面为基准面求概率得到的标度不变性可延伸到3个数量级,多重分形谱光滑.采用外延的方法修正灰度设置的偏移可以对多重分形谱有所改善.另外,讨论了权重因子q取值范围的影响,确定了q的取值范围.     

基于多重分形谱的高光谱数据特征提取

针对单一分形维数在高光谱数据处理中的不足,提出了一种基于多重分形谱的光谱信号奇异性特征提取方法,引入多重分形谱表征光谱曲线的奇异性特征.该方法根据分形测度将光谱曲线进行划分,用光谱概率测度计算配分函数,通过尺度指数的Legendre变换实现光谱曲线多重分形谱的提取,根据各类地物间的类别可分性准则Bhattacharyya距离选择有效特征,最后利用地物分类实验来验证该方法的有效性.实验结果表明,多重分形谱用于分类时分类精度达95.2%,当其维数为原数据波段数的10%时,总体分类精度仍可达82.2 %.多重分形谱表征了具有相同奇异性的波段子集的分形维数,准确的描述了光谱曲线的奇异性和分布特点,该方法能够有效地实现高光谱数据的特征提取.     

非晶Ni-Cu-P合金化学沉积过程的多重分形谱研究

用原子力显微镜测定了SiTiNPd基体,经不同沉积时间得到的非晶Ni13.1wt%Cu9.3wt%P薄膜的表面形貌,得到了AFM图像的多重分形谱.结果表明:随着沉积时间的增加,多重分形谱的宽度增加,Δf(Δf=f(αmin)-f(αmax))增大.说明沉积表面高度分布随着沉积时间的增加,不均匀性显著增加,镀层在水平和垂直方向生长并逐渐形成连续致密的镀层.这与对AFM图的观察是一致的 关键词： 多重分形谱 Ni-Cu-P合金 化学沉积 AFM图像     

多重分形降趋波动分析法和移动平均法的分形谱算法对比分析

多重分形降趋波动分析法(MFDFA)和多重分形降趋移动平均法(MFDMA)是用来估算一维随机分形信号多重分形谱的两种算法, 已被拓展应用于二维和高维分形信号的分析. 本文简要介绍了MFDFA和MFDMA算法及其在一维时间序列中的应用. 首次系统地从算法模型、计算统计精度、样本量的敏感性、无标度区选取的敏感性、矩选择的敏感性和计算量这六个方面对两种算法进行了对比分析, 以典型多重分形信号BMC信号为例, 分析两种算法的适用性和优劣性. 为实际应用中, 针对具体信号如何选用MFDFA或MFDMA算法, 以及两种算法的参数设置提供了有价值的参考.     

基于小波的雷暴强放电前地面电场的多重分形分析

根据远离平衡的复杂系统演化的雪崩性和自相似倍增串级性，强调了多重分形工具的重要；利用青藏高原中部地区雷暴放电的地面电场仪资料，基于多重分形谱的小波估计方法，对强放电前雷电活动的多重分形特征进行了分析，发现多重分形谱可用推广的多重分形二项倍增串级模式描述，强放电前放电过程具有强烈的奇异性和明显的多重分形性，谱宽度Δα＞1.6，最小标度指数α_min＜-0.3；随着放电的活跃，Δα表现出明显的增加，而强的放电则发生在随后Δα的高值区或下降区，并对相关的原因进行了讨论. 关键词： 多重分形 雪崩 倍增串级 小波 闪电放电     

多重分形分析图象边缘提取算法

提出了一种基于多重分形分析的图象边缘提取算法,通过计算每个象素点的奇异值和多重分形谱,并根据多重分形谱的各种测度修正,提取出图象的边缘信息.在分析图象的各种象素点的多重分形谱特性的基础上,着重分析了多重分形谱常用的若干测度以及选取标准.该算法利用奇异性Hölder指数和多重分形谱以及它们组成的判据来进行图象边缘提取的思路不同于传统的基于梯度的局部极值点来进行图象边缘提取的方法.实验结果表明:该算法可以在保留重要边缘信息的情况下去除不重要细节,更能符合人的视觉心理.     

多重分形谱研究溶胶-凝胶SiO2疏水减反膜的激光预处理作用

采用溶胶-凝胶提拉技术制备了SiO₂疏水减反膜.使用Nd：YAG激光（波长为1064nm,脉宽为7.5ns）采用“R on 1”方式对所得膜层进行了激光预处理.在预处理前后采用“1 on 1”方式考察了薄膜的激光损伤阈值的变化,使用原子力显微镜（AFM）观察了薄膜的表面形貌的变化,并使用多重分形谱（MFS）方法分析了薄膜分形结构的变化.结果表明经过激光预处理后薄膜的抗激光损伤阈值有了明显提高,均方根表面粗糙度（R_q）稍有减小,膜面变平整,多重分形谱宽度收缩,分形区间的分布均匀性改善.这说明经过激光预处理后薄膜表面微结构趋向规整,使之能够承受更强的激光的辐照.同时也说明借助多重分形谱可以获得更多薄膜表面结构变化的信息,多重分形谱是探索强激光对光学薄膜辐照作用机理的一个十分有用的方法. 关键词： 2疏水减反膜')" href="#">SiO₂疏水减反膜 激光预处理 多重分形谱 激光损伤阈值     

Intermittency and fractals in nuclear collisions at 1.52 A GeV

The techniques of scaled factorial moments and multifractals have been employed to study the dynamical fluctuations of the produced singly charged particles in collisions of⁸⁴Kr ions at 1.52 A GeV in nuclear emulsion. The power law behaviors are observed in the data. The generalized dimensions are determined by using the methods of intermittency and multifractals.     

Numerical investigations of discrete scale invariance in fractals and multifractal measures

Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with observable log-periodicity. We perform detailed numerical analyses of lattice multifractals and explain the origin of three different scaling regions found in the moments. A novel numerical approach is proposed to extract the log-frequencies. In the non-lattice case, there is no visible log-periodicity, i.e., no preferred scaling ratio since the set of complex exponents spreads irregularly within the complex plane. A non-lattice multifractal can be approximated by a sequence of lattice multifractals so that the sets of complex exponents of the lattice sequence converge to the set of complex exponents of the non-lattice one. An algorithm for the construction of the lattice sequence is proposed explicitly.     

Singularity spectra of strongly inhomogeneous multifractals

Generalized multifractal formalism is used to study singularity spectra of strongly inhomogeneous multifractals characterized by coarse-grained probability measures with zero minimal and/or infinite maximal H?lder exponents. Due to involving two additional types of scaling indices, the generalized formalism is shown to be able to describe complex multifractal objects by families of bivariate spectra rather than familiar single spectra of singularity strengths of one type, providing a more complete and adequate characteristics of such objects. It is proved that the families of extended singularity spectra can reveal unusual forms with many maxima, reflecting complex scaling structures of strongly inhomogeneous multifractals. Received 25 April 2001 and Received in final form 26 February 2002     

On the Estimation of the Large Deviations Spectrum

We propose an estimation algorithm for large deviations spectra of measures and functions. The algorithm converges for natural examples of multifractals.     

Incomplete normalization of probability on multifractals

This work is an extension of the incomplete probability theory from the simple case of monofractals previously studied to the more general case of multifractals that can occur in the phase space without equiprobable partition.     

Superpositions of multifractals: Generators of phase transitions in the generalized thermodynamic formalism

We investigate the superposition of multifractals in the generalized thermodynamic formalism. It is shown analytically that phase transitions of first and second order are obtained and that the topology of the corresponding critical lines endows bicritical behavior. We demonstrate that these phase transitions can be observed in the spectrum of fractal dimensions and in the spectra of related quantities. Therefore, the obtained results are of importance for the interpretation of experimental systems.     

Negative binomial distributions in different pseudorapidity windows in 800 GeV proton-nucleon interactions

Experimental results on multiplicity distributions for full phase space and in different pesudorapidity windows of charged secondary particles produced in proton-nucleon collisions at 800 GeV are presented and discussed. It is found that all these multiplicity distributions are well described by negative binomial distributions. We interpret our results on the basis of clan model. The bin size dependence of multiplicity distribution of charged secondary particles in proton-nucleon interactions is analysed in terms of multifractals. The values of generalised dimensions obtained from fitted distributions show a good agreement with those obtained from the data.     

Universal multifractal approach to intermittency in high energy physics

A new stochastic approach to intermittency in high energy physics is proposed. It yields to intermittency exponents defined independently of phase-space dimensions; their role in the calculation of generalized moments is discussed. A straightforward application of universal multifractals is suggested and a new parametric technique for phase-space analysis is provided.     

Intermittency Growth in Fluid Turbulence

Measurement and phenomenological analyses of intermittency growth in an experimental turbulent pipe flow and numerical turbulence are performed, for which working definitions such as degree, increment, and growth rate of intermittency are introduced with the help of quasiscaling theory. The logarithmic-normal inertial scaling model is extended to quasiscaling as the second-order truncation of the Taylor expansion and is used for studying the intermittency growth problem. The extended self-similarity properties are shown to be not consistent with the monotonicity of the third order local quasiscaling exponent and the nonmonotonic behaviour of the intermittency growth rate as a result of bottleneck. Digestions of the results with scale-dependent multifractals are provided.