α模型中不固定多重数下的阶乘矩、粒子数关联矩

利用二维相空间自仿射分形的随机级联α模型,采用蒙特卡罗模拟的方法,研究了阶乘矩､粒子数关联矩在不固定多重数下,对应于多重数相对起伏强度n_f的依赖关系,得到:阶乘矩、粒子数关联矩依赖于多重数相对起伏n_f,但间歇指数一般不依赖于n_f,当n_f较小时这种依赖性得以消除.     

400GeV/c pp碰撞连续阶数阶乘矩和多重分形分析

对华家照提出的F_q矩的矩阶数连续化方案进行了检验,发现它不能用于真实数据的分析,对此作了改进,使它能用于真实的实验数据的分析,对400GeV/c pp碰撞产生的带电粒子赝快度分布实验数据的分析结果表明,阶乘矩的矩阶数连续崐化方法是可行的,说明在400GeV/c pp碰撞多重产生过程中可能存在多重分形行为.     

400GeV/cpp碰撞中的多粒子关联、阶乘累积矩和关联积分

利用CERN NA27合作组提供的LEBC泡室照片,测量了400GeV/c pp碰撞产生的带电粒子赝快度分布.计算了标度阶乘累积矩K_q,与具有同样单粒子谱但是没有关联的蒙特卡罗事例得到的结果相比较,表明对于宽的混合多重数分布,K₂的一个显著部分是由于多重数涨落引起单粒子密度涨落造成的.利用星形关联积分法计算得到的阶乘累积矩,显著地降低了高阶阶乘累积矩的统计误差,但基本结论保持不变.     

阶乘累积矩与阶乘矩之比随相空间大小的变化

利用400GeV/cpp碰撞多重产生的实验数据计算了不同赝快度窗口时多重数分布的阶乘累积矩与阶乘矩之比.结果表明,随着阶数q的增加,比值H_q首先迅速下降,然后在零附近振荡.这与PQCD的预言是一致的.不同的是第一极小值的位置在赝快度窗口变小时移向较高的级数.     

3.7A GeV 16O-Em作用中的间歇行为

对3.7A GeV ¹⁶O-Em作用产生的慢粒子标度阶乘矩分布进行研究, 得出间歇指数随矩阶数的增加而增加, 随靶核质量的增加而减小; 反常分形维数 随q的增加而增加; 对于每一个q值, d_q随平均多重数的增加而减小, 表明在3.7A GeV ¹⁶O-Em作用中多粒子产生具有自相似级联的性质.     

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.     

H矩振荡与三火球模型

本文用三火球模型(TFM)研究了pp和pp的实验数据中观察到的H矩振荡行为.发现,和负二项式分布(NBD)相似,完整的TFM分布的H矩是q的单调函数,而当分布在一个不很大的n_cut值被截断时发生振荡.这表明,H矩振荡不是pQCD或NBD的特殊性质,而是许多被截断的多重数分布的共同性质.     

400GeV/c pp碰撞集束参数和集束关联子数据

利用400GeV/c pp碰撞产生的带电粒子赝快度分布和方位角分布计算了集束参数和集束关联子.结果表明集束参数不仅依赖于多重数分布的宽度,还与粒子间的关联有关.在赝快度和方位角空间,集束参数_η 2(M)和η₃ (M)遵循同样的幂律行为,表明在400GeV/c　pp碰撞多重产生中多重分形行为被观测到了.在赝快度空间二级集束关联子依赖于多重数分布的宽度,并随子区间之间的距离的增加而减小.     

矩分析法与ξ(2220)

为减少几何接收度的影响,提高精度,我们引进矩的赝标介子角分布H_J(jm,θ).对于辨别ξ(2220)的自旋为2还是4,要比通常的投影赝标介子角分布W_J(θ)灵敏.我们还给出了矩分析所需的矩,以及直接用矩的关系式表示的螺旋度振幅之比x_J和y_J.     

J/ψ→ωf2(1270)衰变过程极化结构的研究

本文用推广的矩分析法研究了过程J/ψ→ωf₂(1270),f₂(1270)→ππ的极化结构,给出了用矩关系式表示的过程的四个螺旋度振幅之比.     

Fractal Analysis of Pseudorapidity Distribution Fluctuation in 400GeV/c pp Collisions

The fractal behaviour of multiplicity production in 400 GeV/c pp collisions is analyzed using the modified multifractal moments.The generalized dimensions D_q,q=2—5,are calculated.A comparison with the results obtained by the method of scaled factorial moments has been made. The results show that the multifractal character is observed.The fractal analysis method proposed by Fujio Takagi has been tested.     

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.     

Intermittency in 3.7 A GeV ^16O-emulsion interactions

The intermittency effect has been studied for an interaction of 3.7 A GeV ^16O with emulsion using the distributions of both the pseudorapidity intervals and the azimuthal angle intervals of the shower particles emitted in a central rapidity region. The scaled factorial moments, reduced scaled factorial moments and multifractal moments as functions of the bin size in pseudorapidity and in azimuthal angle have been calculated and have revealed the presence of an intermittent behaviour which may be due to the random cascading property of the reaction. The anomalous fractal dimension has been found to increase with the increase of rank of the moment.     

Multifractal dimensions in QCD cascades

Particle production in small rapidity or angular intervals have fractal structures similar to a Cantor dust. In this paper we present analytical result for multifractal dimensions valid for high energies. For high moments the dimension is given by \(\sqrt {6\alpha _s /\pi } \) . The scaling properties seen in the partonic state are not so well reflected in the hadronic multiplicity moments or factorial moments. We show how to define new observables on the final hadronic state, which do scale well. This means that the multifractal dimensions can be well determined and compared with results from QCD.     

potential theory and analytic properties of self-similar fractal and multifractal distributions

By the use of recursion relations and analytic techniques we deduce general analytic results pertaining to the electrostatic potential, moments, and Fourier transform of exactly self-similar fractal and multifractal charge distributions. Three specific examples are given: the binomial distribution on the middle-third Cantor set, which is a multifractal distribution, the uniform distribution on the Menger sponge, which illustrates the added complication of higher dimensionality, and the uniform distribution on the von Koch snowflake, which illustrates the effect of rotations in the defining transformations.     

Fractal behaviour and correlations in rapidity particle distributions at high energies

Recent arguments of Sarcevic and Satz for multifractal behaviour in rapidity particle distributions are shown to have a simple explanation in terms of multisource production in hadron collisions as it happens in the negative binomial approximation. The arguments for strict fractal behaviour may, however, still be justified if use is made of the correlation Mueller moments instead of the factorial moments.     

SIMULATION OF MULTIPLE FRACTAL AND COMPACT GROWTH OF ULTRA-THIN FILMS ON HEXAGONAL SUBSTRATE

The multiple cluster growth of ultra-thin films with different deposition rate and different substrate temperature has been studied by kinetic Monte-Carlo simulation. With increasing diffusion rate along cluster edges (corresponding to an increasing substrate temperature), pattern structures change smoothly from fractal islands, compact islands with random shapes, to regular islands, and the average branch width of clusters increases continuously up to some constant value in the compact island limit. The formation of the multiple fractal and compact clusters can be described quantitatively by multifractal. The results of multifractal analysis show that with pattern change from fractal to compact islands, the Hausdorff dimension D₀, the information dimension D₁, and the correlation dimension D₂ decrease, while the width and height of the multifractal spectra increase.     

海杂波背景下小目标检测的分形方法

针对海杂波背景下小目标检测对海情依赖性强的问题, 本文采用分数布朗运动模型对实测海杂波建模, 结合多重分形去势波动分析法确定分形参数, 分析了海杂波的单尺度、多重分形特性. 在单尺度分形的基础上, 利用表征海杂波分形特征的分数维和Hurst指数构建了分形差量, 提出了基于分形差量的小目标检测方法;在多重分形基础上, 比较了两种海杂波的高尺度多重分形特性. 结果表明, 当尺度q > 10时, 纯海杂波的多重分形参数H(q) < 0, 而存在小目标的H(q) > 0, 此差异性为高尺度分形参数的海杂波背景小目标检测提供了判定依据. 所研究的两种方法均能实现不同海情下的小目标检测.     

MULTIPLE CLUSTER GROWTH OF ULTRA-THIN FILMS WITH ANISOTROPIC EDGE DIFFUSION

The multiple cluster growth of ultra-thin films on a hexagonal substrate with fractal, dendritic and compact morphology has been studied by computer simulation. The influence of the different diffusion processes along island edges on the island shape has been investigated. The results show that the anisotropic corner diffusion induces the dendritic growth, and the anisotropic step diffusion can promote the anisotropic growth and cause the ramified islands growing in three directions. In the case of compact growth, the island shape is mainly determined by the anisotropic corner crossing process. The nonuniform distribution of the multiple cluster formation can be described quantitatively by multifractal. With patterns changing from fractal to compact islands, the width and height of the bell-like or hook-like multifractal spectra increase, while the top f(α) decreases.     

Performance comparison of detection methods for weak target based on two-dimensional fractal sea surface

A detection method of the weak radar target is studied by applying fuzzy theory and multifractal correlation theory based on a two-dimensional fractal sea surface model. Firstly, a two-dimensional fractal sea surface model and its backscattering coefficient are introduced, the backscattering coefficient is a universal model affected by seawater permittivity, electromagnetic wave incidence angle, incident frequency, wind speed and wind direction factors. A novel two-dimensional wideband radar echo model, which is considered as a time-domain convolution of the stepped frequency signal radiated by airborne radar and the backscattering coefficient, is derived. Secondly, multifractal correlation theory is elaborated and a computation method of a membership degree of multifractal correlation spectrum is proposed, fuzzy theory and the AdaBoost algorithm are applied to the target detection. Finally, several target detection methods are compared with CA-CFAR and works of the predecessors. The results of the comparative study show its rationality of the two-dimensional wideband radar echo model and the superiority of wideband radars in detection performance, it is also seen that the multifractal correlation spectrum outperforms the multifractal spectrum in the probability of detection.