基于分形理论的尖-板电极短空气隙放电现象研究

气体放电的发展过程非常复杂, 实验观测结果表明非均匀场短空气隙放电过程中经常产生随机并伴有分岔现象的放电通道. 由于这些放电现象的整体结构表现出一定的自相似性, 因此, 结合经典流注放电与分形理论而建立的介质击穿模型成为描述气体中放电通道分岔现象的一种有效的分析方法, 而放电通道的复杂程度可以用分形维数表征. 为了明确此模型参数中发展概率指数的取值, 本文对直流高压作用下的10 mm针板电极空气隙放电通道图像进行了分析、处理和分形计算, 并与理论模型的仿真结果对比. 由于空气隙主放电通道的亮度明显高于其他弱分支, 导致各放电通道的宽度各异, 需要对所拍摄图像进行灰度变换和边界识别处理, 最后运用盒维数法计算出分形维数. 研究结果表明在其他参数与实验条件相同条件下, 调整理论模型中的发展概率指数, 使得仿真结果与实验结果相吻合, 依据本文实验条件下和理论模型分析, 发展概率指数η 在0.04-0.05范围. 本文的研究印证了尖-板电极短空气隙放电复杂现象的可测性并提供了一种分析方法.     

Structural properties of silver nanoparticle agglomerates based on transmission electron microscopy: relationship to particle mobility analysis

In this work, the structural properties of silver nanoparticle agglomerates generated using condensation and evaporation method in an electric tube furnace followed by a coagulation process are analyzed using Transmission Electron Microscopy (TEM). Agglomerates with mobility diameters of 80, 120, and 150 nm are sampled using the electrostatic method and then imaged by TEM. The primary particle diameter of silver agglomerates was 13.8 nm with a standard deviation of 2.5 nm. We obtained the relationship between the projected area equivalent diameter (d _pa) and the mobility diameter (d _m), i.e., d _pa = 0.92 ± 0.03 d _m for particles from 80 to 150 nm. We obtained fractal dimensions of silver agglomerates using three different methods: (1) D _f = 1.84 ± 0.03, 1.75 ± 0.06, and 1.74 ± 0.03 for d _m = 80, 120, and 150 nm, respectively from projected TEM images using a box counting algorithm; (2) fractal dimension (D _fL) = 1.47 based on maximum projected length from projected TEM images using an empirical equation proposed by Koylu et al. (1995) Combust Flame 100:621–633; and (3) mass fractal-like dimension (D _fm) = 1.71 theoretically derived from the mobility analysis proposed by Lall and Friedlander (2006) J Aerosol Sci 37:260–271. We also compared the number of primary particles in agglomerate and found that the number of primary particles obtained from the projected surface area using an empirical equation proposed by Koylu et al. (1995) Combust Flame 100:621–633 is larger than that from using the relationship, d _pa = 0.92 ± 0.03 d _m or from using the mobility analysis.     

Identification of two simultaneous partial discharge sources in an oil-pressboard insulation system using acoustic emission techniques

Insulation failure is one of the major causes of catastrophic failure of transformers. It is established that partial discharge (PD) causes insulation degradation and premature failure of insulation. In power apparatus, more than one PD source may be active simultaneously. The nature of insulation degradation for multiple PD sources is different from that due to single PD source. Therefore, it will be helpful for severity assessment of insulation degradation, if the number of active PD sources are identified and classified. This paper presents a method for identification and classification of two simultaneously active PD sources using acoustic emission techniques. The acoustic emission (AE) signals are measured for laboratory simulated PD in an oil-pressboard insulation system for three different electrode systems. The measurements of partial discharge acoustic emission (PDAE) signals are carried out for single PD source and for two simultaneous PD sources. The measured signals are analyzed using discrete wavelet transform (DWT), box counting fractal dimension and lacunarity. Box counting fractal dimension and lacunarity are calculated for DWT decomposed signal of major frequency band. Energy distribution in different frequency bands of DWT decomposed signal along with box counting fractal dimension and lacunarity is used for classification of two simultaneous PD sources.     

树状分形结构形成过程的实验研究

对大量金属小球在强电场作用下运动形态的演化全过程用联机摄像装置进行了实时拍摄,通过用Sandbox方法计算其稳定状态的分维数,系统地研究了分维数随电压的变化关系.结果表明：在一定电压范围内金属小球聚集体通过自组织过程形成稳定的树状分形结构,其分维数随外加电压的增加而减小.该结果对研究耗散结构的形成机理和外界动力对耗散结构的形貌影响具有参考价值. 关键词： 分形生长 自组织过程 树状结构 分维数     

Self-consistent development and fractal structure of leader discharges along a water surface

Ideas regarding the development of single-and multichannel leader discharges over water surfaces are generalized on the basis of experimental data. The Ohmic conductivity of water is found to be manifested in the self consistency of their dynamics and fractal structure. The fractal dimensionality of a single-channel leader discharge is found to be 0.96±0.05 and that of a multichannel discharge to be 1.85±0.05. Mechanisms are proposed for the branching of leader discharge channels and for the development of bifurcations from branches and channels. Zh. Tekh. Fiz. 69, 35–40 (April 1999)     

a-Ge/Au双层膜退火后分形区的形成

本文用透射电子显微镜观察了a-Ge/Au双层膜在不同退火温度后出现的分形区域,并计算了它们的分数维数。100℃退火时,触发分形结晶区的成核位较少,形成良好的具有无规分叉、自相似的分形区,分数维数为1.785±0.01。200℃退火时,成核位迅速增加,除了分数维数为:1.818±0.008的分形区外,还出现孤立的无枝叉结构的岛状区域。300℃退火时,只出现尺寸很不相同的两种岛状区域,对上述枝叉伏、岛状区域的出现以及a-Ge膜的晶化和Au膜缩聚之间的关系进行了讨论。 关键词：     

Measurement of Aggregate Fractal Dimensions Using Static Light Scattering

Aggregates formed from colloidal particles will vary in shape according to the aggregation regime prevalent. Compact structures are formed when the aggregation is slow, whilst loose tenuous structures are formed when rapid (or diffusion limited) aggregation prevails. These structures can be fractal in nature, that is, there is a relationship between porosity and the number of primary particles making up the aggregate, and is described by the fractal dimension, d_F. Fractal dimensions of hematite aggregates have been measured experimentally using the static light scattering technique. Fractal dimensions varied with aggregation regimes; for the rapid aggregation regime, d_F was found to be 2.8, whilst for conditions in which aggregation was slow (retardation forces prevail), d_F's of 2.3 were measured. For conditions which lead to aggregation in which both diffusion and retardation forces play a part, structures with fractal dimensions such that 2.3 < d_F < 2.8 were found. The effects of adsorbed fulvic acid, a naturally occuring organic acid, on the kinetics of hematite aggregation and on the resulting structure of hematite aggregates were also investigated. The study of aggregate structure shows that the fractal dimensions of hematite aggregates which are partially coated with fulvic acid molecules are higher than those obtained with no adsorbed fulvic acid. The scattering exponents obtained from static light scattering experiments of these aggregates range from 2.83 ± 0.08 to 3.42 ± 0.1. The scattering exponents of greater than 3 indicate that the scattering is the result of objects that contains pores which are bounded by surfaces with a fractal structure, and can be related only to surface fractal dimension. The high fractal dimensions are due to restructuring within the aggregates, which only occured at low coverage by the organic acid.     

Fractal structure of digital speckle patterns produced by rough surfaces

We report on the fractal analysis of digital speckle patterns experimentally generated using an optical setup to record the light scattered from metallic rough surfaces in the normal direction. Using the differential box counting technique, we have calculated the fractal dimension of digital speckle patterns for six samples with different roughness. Our results show a quadratic dependence between the surface roughness and the fractal dimension of the corresponding digital speckle pattern. As an application a method to determine the surface roughness of metallic surfaces is proposed.     

Analysis of fractals with dependent branching by box counting, P-adic coverages, and systems of equations of P-adic coverages

Concept of the dimension of space-time in the general relativity theory and quantum theory is discussed. It is emphasized that the dimension of a discrete space can be defined based on the Hausdorff measure. The noninteger dimension is a typical characteristic of a fractal. The process of hadron formation in interactions between high-energy particles and nuclei is supposed to possess fractal properties. The following methods for analyzing fractals are considered: box counting (BC), method of P-adic coverages (PaC), and method of systems of equations of P-adic coverages (SePaC), for determining the fractal dimension. A comparative analysis of fractals with dependent branching is performed using these methods. We determine the optimum values of parameters permitting one to determine the fractal dimension D _F , number of levels N _lev, and the fractal structure with maximal efficiency. It is noted that the SePaC method has advantages in analyzing fractals with dependent branching.     

A new information dimension of complex networks

The fractal and self-similarity properties are revealed in many complex networks. The classical information dimension is an important method to study fractal and self-similarity properties of planar networks. However, it is not practical for real complex networks. In this Letter, a new information dimension of complex networks is proposed. The nodes number in each box is considered by using the box-covering algorithm of complex networks. The proposed method is applied to calculate the fractal dimensions of some real networks. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks.     

The Use of Small Angle Light Scattering to Study Structure of Flocs

In this paper, a new approach using small angle light scattering to study the structure of large micron sized flocs is described. The flocs were made up from uniformly sized, approximately spherical hematite particles, induced to aggregate using 250 mM KCl to ensure that growth was governed by diffusion limited aggregation alone. The fractal dimensions of the hematite aggregates changed from 1.73 to 2.23 ± 0.05 as the aggregation proceeded, indicating that restructuring occurred during aggregation. The fractal dimensions obtained from the small angle light scattering technique are compared with those obtained from the combination of volume fraction and floc size measurement. The steady state fractal dimensions (2.23 ± 0.05) obtained by small angle light scattering are comparable to the fractal dimensions obtained from determining the slope of the relationship between floc volume fraction and floc size (2.09 and 2.14 ± 0.05). The discrepancy between the fractal dimensions obtained by these techniques during the initial stages of aggregation is due to the fact that the latter method measures the average fractal dimensions, whilst the former method measures the fractal dimensions at any particular instant.     

Off lattice simulations of cluster-cluster aggregation in dimensions 2–6

Cluster-cluster aggregation has been simulated in dimensions two to six using both linear and brownian cluster trajectories. Relatively efficient off lattice algorithms have allowed large clusters to be generated and values for the fractal dimensionalities of the aggregates have been obtained without finite concentration effects. The values for the fractal dimensionality are in good aggreement with lattice model simulations for euclidean dimensionalities 2–4. The effective dimensionality (D_β) obtained from the dependence of the radius of gyration on cluster size increases with increasing cluster size for all of our models (particularly for d ≥ 4). For clusters in the accessible size range (up to 10³-10⁴) D_β is slightly larger for cluster-cluster aggregation via linear trajectories than for brownian trajectories. For cluster-cluster aggregation via brownian trajectories, the limiting (large cluster size) fractal dimensionality is estimated to be 1.46 ± 0.04 for d=2,1.82 ± 0.10 for d = 3, 2.10 ± 0.15 for d = 4, 2.35 ± 0.15 for d = 4, 2.65 ± 0.25 for d = 6. For cluster- cluster aggregation via linear trajectories, the limiting fractal dimensionality is estimated to be 1.55 ± 0.04 for d = 2, 1.91 ± 0.10 for d = 3≥ 2.5 ± 0.06 for d = 5 and ≥2.64 ± 0.05 for d = 6.     

Comparison of fractal analysis methods in the study of fractals with independent branching

The notion of dimension as a quantitative characteristic of space geometry is discussed. It is supposed that hadrons created in interactions between particles and nuclei can be considered sets of points possessing fractal properties in the three-dimensional phase space (p _T , η, ?). The Hausdorff-Besicovich dimension D _F is considered the most natural characteristic for determining the fractal dimension. Different methods for determining the fractal dimension are compared: box counting (BC), P-adic coverage (PaC), and system of equations of P-adic coverage (SePaC). A procedure for choosing optimum values of parameters of the considered methods is presented. These parameters are shown to be able to reconstruct the fractal dimension D _F , number of levels N _lev, and fractal structure with maximal efficiency. The features of the PaC- and SePaC-methods in the analysis of fractals with independent branching are noted.     

核爆与雷电电磁脉冲识别

用经验模态分解和分形分析相结合的方法对核爆和雷电电磁脉冲信号进行了识别研究。计算了核爆和雷电电磁脉冲原始信号的盒维数,以及原始信号经验模态分解后前4阶固有模态分量（IMF）的盒维数。用最近邻法对核爆和雷电进行了识别,实验结果表明:原始信号经验模态分解后一阶、二阶IMF盒维数的识别率要略高于三阶、四阶IMF盒维数的识别率;原始信号盒维数的识别率高于经验模态分解后各阶IMF盒维数的识别率;二维和三维特征的识别率要高于一维特征的识别率,另外二维和三维特征的识别率更加趋于稳定,并且三维特征的识别率都在90%以上。     

Method of systems of equations of P-adic coverages for fractal analysis of events

Self-similarity in high-energy multiparticle production processes is discussed. A parton shower and hadronization are assumed to give rise to a set of particle with a fractal structure. It is noted that the box counting (BC) and P-adic coverage (PaC) methods determine the fractal dimension with permissible 1/k ranges. A new method of systems of equations of P-adic coverages (SePaC) is proposed that extends the PaC method to fractals with permissible m/k ranges. The SePaC method is shown to determine the fractal dimension of a shower with a prescribed accuracy, the number of fractal levels, the type of the cascade (random or regular), and its structure.     

Dimension of fractal growth patterns as a dynamical exponent

We consider a conformal theory of fractal growth patterns in two dimensions, including diffusion limited aggregation (DLA) as a particular case. In this theory the fractal dimension of the asymptotic cluster manifests itself as a dynamical exponent observable already at very early growth stages. Using a renormalization relation we show from early stage dynamics that the dimension D of DLA can be estimated, 1.69相似文献   

Near space radiation dosimetry in Australian outback using a balloon borne energy compensated PIN diode detector

This paper reports the near space ballooning experiment carried out at Australian outback town West Wyalong (33°51′S, 147°24′E) on 19 July 2015. Several dedicated electronic detectors including digital temperature and acceleration (vibration) sensors and an energy compensated PIN-diode gamma ray dosimeter were installed in a thermally insulated Styrofoam payload box. A 9 V Lithium-Polymer battery powered all the devices. The payload box was attached to a helium-filled latex weather balloon and set afloat. The balloon reached a peak burst altitude of 30 km and then soft-landed aided by a self-deploying parachute 66.2 km away form the launch site. The payload box was retrieved and data collected from the electronic sensors analysed. The integrated cosmic ray induced photon ambient dose equivalent recorded by the PIN diode detector was evaluated to be 0.36 ± 0.05 μSv. Furthermore, a high-altitude extended version of commercially available aviation dosimetry package EPCARD.Net (European Program package for the Calculation of Aviation Route Doses) was used to calculate the ambient dose equivalents during the balloon flight. The radiation environment originated from the secondary cosmic ray shower is composed of neutrons, protons, electrons, muons, pions and photons. The photon ambient dose equivalent estimated by the EPCARD.Net code found to be 0.47 ± 0.09 μSv. The important aspects of balloon based near-space radiation dosimetry are highlighted in this paper.     

An Extended Correlation Dimension of Complex Networks

Fractal and self-similarity are important characteristics of complex networks. The correlation dimension is one of the measures implemented to characterize the fractal nature of unweighted structures, but it has not been extended to weighted networks. In this paper, the correlation dimension is extended to the weighted networks. The proposed method uses edge-weights accumulation to obtain scale distances. It can be used not only for weighted networks but also for unweighted networks. We selected six weighted networks, including two synthetic fractal networks and four real-world networks, to validate it. The results show that the proposed method was effective for the fractal scaling analysis of weighted complex networks. Meanwhile, this method was used to analyze the fractal properties of the Newman–Watts (NW) unweighted small-world networks. Compared with other fractal dimensions, the correlation dimension is more suitable for the quantitative analysis of small-world effects.