基于分形理论的尖-板电极短空气隙放电现象

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,最后运用计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的情况下,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.     

气体放电随机现象的图像智能化分析

本文采用高速相机记录气体放电信息,获得高分辨率的空间与时间的视频数据.通过分析其放电图案,发现其为树状分形结构,其单个放电点和多个放电点的分形维数分别为1.64和1.71.利用课题组采用python编写的软件,对获取的大量的图像信息进行智能化的轮廓识别和质心标记,获取了每个放电条件下,5911张相邻时间间隔为0.5 ms的图像的放电点的位置分布信息.结果显示,放电点数在空间内出现的位置概率接近高斯分布,其出现的时间间隔分布接近指数衰减.     

二维logistic映射的动力学行为和奇怪吸引子的分形特征

研究了二维logistic映射的动力学行为和奇怪吸引子的分形特征.利用分岔图、相图和Lyapunov指数谱分析系统的分岔过程,研究系统通向混沌的道路并确定系统处于混沌运动的参数区间;采用G-P算法计算奇怪吸引子的关联维数和Kolmogorov熵,对奇怪吸引子的分形特征定量刻画;采用逃逸时间算法构造奇怪吸引子的彩色广义M-J集,对奇怪吸引子的分形特征定性表征.结果表明,这些分析方法的配合使用可以更全面、形象地描述奇怪吸引子的分形特征.     

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...     

新的具有光滑二次函数混沌系统的构建与实现

拓展和改变Lorenz混沌系统的非线性函数,构建一个新的具有光滑二次函数的自治混沌系统,系统包含3个系统变量乘积的非线性函数项和5个平衡点,详细讨论了平衡点的性质并计算了分形维数.利用分岔图和Lyapunov指数谱对系统随参数变化的情况进行分析后得出,系统会发生倍周期分岔.用数字信号处理芯片对混沌系统进行硬件实现,实验结果表明理论分析的正确性以及系统具有较为复杂的动力学行为. 关键词： 混沌系统 分岔图 Lyapunov指数 数字信号处理     

纳秒脉冲电压下同轴场畸变开关多通道放电特性

使气体开关形成多通道放电是减小开关电感、通道电阻、电极熔蚀,提高开关寿命和稳定性的有效措施。设计了一种同轴场畸变气体火花开关,研究了开关在纳秒脉冲电压下的多通道放电现象。研究了脉冲电压上升速率与多通道放电特性的关系,比较了两种体积比的SF6/Ar混合气体多通道放电特性。实验结果表明:一定气压下,平均通道数随着脉冲电压上升率增加而增多,电流分布趋向均匀;相同脉冲峰值与气压比值,不同气压下,高气压下的通道数较多;SF6/Ar混合气体中,氩气含量较高情况下多通道放电特性较好。最后,结合J.C.Martin的多通道放电理论对实验结果作出了初步解释。     

气体吸附法测定二氧化硅干凝胶的分形维数

提出了一种方便、科学有效的利用气体吸附法测定二氧化硅干凝胶等多孔材料分形维数（表面分形维数和孔分布分形维数）的方法，不需要进行一系列的吸附/脱附实验，只需要利用单一气体的一次吸附/脱附实验得出的样品孔分布、比表面数据，与不同的标尺进行关联，即可同时获得表面分形维数和孔分布分形维数.通过误差分析和校正，保证了结果的可靠性.用上述方法测定了二氧化硅干凝胶的分形维数，以FHH法和SAXS法对所得结果进行了比较和验证，并对吸附/脱附过程所得结果的差异进行了初步分析. 关键词： 分形维数 气体吸附 二氧化硅 干凝胶     

分形聚集逾渗性质的计算机模拟

提出3种模型——小尺寸随机逐次成核生长模型和二维及三维代代聚集生长模型,在不同的近邻条件下和不同尺寸的网格中,通过蒙特卡罗模拟,系统地研究了一维、二维和三维分形聚集的逾渗性质.计算结果显示,分形聚集的逾渗阈值仅取决于空间维数和近邻条件,与模型的网格大小无关,是分形系统固有的临界属性;生长概率等于逾渗阈值时,聚集体可以无限生长并保持分形维数恒定,此时的分形维数只是空间维数的线性函数.     

常压下气体放电等离子体振荡的实验与理论研究

在实验上研究了高压交流电弧发生器电极间隙的气体放电及等离子体振荡, 观察到了气体放电过程中的纳秒脉冲.以电子的流体运动方程和麦克斯韦方程为理论基础, 利用δ函数来描述交变外电场作用下电极处的电子堆积现象,建立了常压下气体放电时等离子体在外电场中振荡的理论模型,通过Laplace变换求解出电极间的放电电压.理论与实验结果基本符合, 从而可估算出实验中等离子体的电子数密度为1.3× 10¹²/m³.     

近地层大气光学湍流的分形和间歇性特征分析

利用光纤湍流测量系统获得了合肥西郊科学岛上气象观测场内下垫面平坦的水面上方0.48m、草地上方1.8m和23m高处的大气折射率起伏的观测数据,采用R/S分析法计算了近地层大气光学湍流的赫斯特指数和分形维数,统计分析了分形维数的日变化特征及概率分布特征。结果表明:对于一天的不同时段,分形维数在一定范围内动态变化,且中午时段相对稳定;在三种下垫面条件下,全天分形维数的值大多在1.3~1.4之间,其最可几概率位于1.35处,从均值来看,草地上方1.8m的分形维数最大,水面上方0.48m次之,草地上方23m处最小。最后,初步探讨了近地层大气光学湍流分形维数、间歇性指数和湍流发展程度的相关性。     

Fractal dimension of long electrical discharges

The fractal dimension of 500 mm long electrical discharges is presented by analyzing a set of photographic images. Three popular fractal dimension estimation techniques, box counting, sandbox and correlation function methods were used to estimate the fractal dimension of the discharge channels. To remove the apparent thickness due to varying magnitudes of current in the discharge channels, edge detection algorithms were utilized. The estimated fractal dimensions for box counting, sandbox and correlation function for long laboratory sparks were 1.20 ± 0.06, 1.66 ± 0.05 and 1.52 ± 0.12 respectively. Within statistical uncertainties, the estimated fractal dimensions of positive and negative polarities agreed very well.     

分形理论在碳化材料三维烧蚀热防护计算中的应用

烧蚀过程中的传热传质对烧蚀防护工程具有重要意义,准确的温度评估可以为高超声速飞行器的热防护结构和烧蚀材料的设计提供有效的支持.由于材料烧蚀形成的碳化物是一种典型的多孔介质,其结构具有自相似性,可以用分形理论来描述.在烧蚀计算中引入了分形渗透率张量模型进行计算.针对烧蚀过程中热解气体在碳化层中的扩散方程、温度、材料等参数...     

悬浮颗粒计数信号等效体积的分形测度

提出悬浮颗粒质量子集的概念,并将其推广为与计数测量信号幅度档对应的等效质量子集概念.根据统计学原理,进一步建立了悬浮颗粒质量子集颗粒平均体积的分形测度模型.基于悬浮颗粒群不同质量子集的几何形貌结构分布具有统计自相似性的特征,推导出计数法颗粒质量测量中与信号幅度档对应的颗粒等效质量计算公式,建立起计数法悬浮颗粒质量测量的基础理论模型. 关键词： 分形测度 形貌参数 质量测量 质量子集     

The Relation Between Elastic and Total Scatterings from Fractals

The ratio of the elastic and total scattering intensities η(q) = I:(q)/I_t²(q) is studied for fractals of dimension range widely. The results show that it oscillatorily decays with a quantity qR_o where q is the absolute value of the momentum transfer q and R_o the average distance between the nearest neighbor sites of scatters in fractal objects. The locations of valleys and peaks of η are only dependent on fractal dimensions. However, the dependence is very beak and η is almost a constant varying in the range of only several percent for widely different fractal dimensions.     

Fractal microstructures of light-emitting porous silicon films

By means of scanning electron microscopy and computer simulation, we have investigated the microstructures of a 23-μm-thick porous silicon (PS) film and a 6-μm-thick PS film. The two films give off strong visible emissions when excited by the 254 nm light. For the 23-μm-thick PS film, both of its cross-sectional and top-surface morphologies exhibit self-similarity whose small-scale and large-scale microstructures resemble one another. For the 6-μm-thick PS film, self-similar cracks are developed on its top surface. Our results have demonstrated that the microstructures of PS films exhibit the characteristics of fractals. With box counting method, the fractal dimensions of the PS films are calculated to be about 2.3-2.6. Based on the model of diffusion-limited aggregation, the fractal growth processes have been simulated for the PS films.     

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.     

空温式翅片管气化器结霜模型及数值模拟

以分形理论的DLA模型为基础,建立了空温式翅片管气化器深冷表面上霜晶生长的二维模型,模拟了深冷表面上的霜晶生长过程.采用计盒维数法对模拟出的霜晶生长图像进行了分形维数的计算,结果表明深冷表面上霜晶的分形维数较一般冷表面上的分形维数大,从而说明深冷表面上的霜晶具有更加复杂的结构,充满空间的能力更大.这对进一步理解空温式深...     

Effects of fractal gating of potassium channels on neuronal behaviours

The classical model of voltage-gated ion channels assumes that according to a Markov process ion channels switch among a small number of states without memory, but a bunch of experimental papers show that some ion channels exhibit significant memory effects, and this memory effects can take the form of kinetic rate constant that is fractal. Obviously the gating character of ion channels will affect generation and propagation of action potentials, furthermore, affect generation, coding and propagation of neural information. However, there is little previous research on this series of interesting issues. This paper investigates effects of fractal gating of potassium channel subunits switching from closed state to open state on neuronal behaviours. The obtained results show that fractal gating of potassium channel subunits switching from closed state to open state has important effects on neuronal behaviours, increases excitability, rest potential and spiking frequency of the neuronal membrane, and decreases threshold voltage and threshold injected current of the neuronal membrane. So fractal gating of potassium channel subunits switching from closed state to open state can improve the sensitivity of the neuronal membrane, and enlarge the encoded strength of neural information.     

Tortuosity for streamlines in porous media

An analysis of tortuosity for streamlines in porous media is presented by coupling the circle and square models. It is assumed that some particles in porous media do not overlap and that fluid in porous media is incompressible. The relationship between tortuosity and porosity is attained with different configurations by using a statistical method. In addition, the tortuosity fractal dimension is expressed as a function of porosity. Those correlations do not include any empirical constant. The percolation threshold and tortuosity fractal dimension threshold of porous media are also presented as: c = 0.32, D T c = 1.07. The predicted correlations of the tortuosity and the porosity agree well with the existing experimental and simulated results.     

Transport properties of saturated and unsaturated porous fractal materials

Inviscid, irrotational flow through fractal porous materials is studied. The key parameter is the variation of tortuosity with the filling fraction phi of fluid in the porous material. Altering the filling fraction provides a way of probing the effect of the fractal structure over all its length scales. The variation of tortuosity with phi is found to follow a power law of the form alpha approximately phi (-E) for deterministic and stochastic fractals in two and three dimensions. A phenomenological argument for the scaling of tortuosity alpha with filling fraction phi is presented and is given by alpha approximately phi(D_{w}-2/D_{f}-d_{E}), where D_{f} is the fractal dimension, D_{w} is the random walk dimension, and d_{E} is the Euclidean dimension. Numerically calculated values of the exponents show good agreement with those predicted from the phenomenological argument for both the saturated and the unsaturated model.