测井曲线盒维数在松辽盆地火山岩岩性识别中的应用

大庆徐家围地区火山岩地层天然气储量丰富,不同类型火山岩之间抗钻特性差别较大,为此有必要确定该地区深层火山岩岩性分布规律和物理特性.本文利用分形几何理论,从测井资料的自相似性出发,提出利用测井资料盒维数了解火山岩岩性分布的方法.在此基础上,运用窗口技术,计算了大庆徐深1井相关测井资料盒维数,岩性识别率达到90%以上;同时探讨了分维值与火山岩岩性之间的关系及影响分维值大小的因素.     

煤微孔表面的分形维数及其变化规律的研究

本文利用气体吸附数据确定了各种煤阶煤（从褐煤到无烟煤）和煤焦气化反应过程中微孔表面的分形维数及其变化规律。这有助于进一步认识煤的孔结构特征。     

基于分形维数的分析信号自适应中值滤波

提出一种面向分析仪器谱图信号处理的分形维自适应中值波方法（AMeFFD）。该法延拓运用分形理论，定义了相对点盒维数概念，由此建立建立判定脉冲型噪声的特异性指标，从而可自动调节中值滤波窗口宽度，有效地滤除脉冲型噪声及其它类噪声。对仿真色谱信号及实测色谱图的处理结果表明：AMeFFD法克服了经典中值滤波算法的缺陷，无论在信号的均方根偏差还是谱峰差等指标上，均明显优于后者，能在确保谱峰不畸变的同时更有效地滤除脉冲型常见噪声，是处理化学谱图信号的有力工具。     

煤焦分形维数及其对比热容的影响研究

比热容是煤炭热物理性质之一,在煤矿的矿井防火、防止煤与瓦斯突出、井下降温设计及煤炭加工利用(如煤炭的燃烧、气化、焦化、液化等)等方面是关键参数之一,对提高煤炭热能利用率、提高经济效益、减少环境污染等,具有非常重要的意义。比热容的影响因素很多,如煤化程度、水分质量分数、热解温度等,煤焦微观结构的影响也是其中很重要的一方面。分形几何由Mandelbrot 1982年创立,是定量描述自相似或自相关等不规则形体的工具。研究表明,煤焦微观结构具有分形特征。在煤焦分形的研究中,常用的实验技术方法为吸附法、小角度X射线散射法和孔度法,采用扫描电子显微镜和数字图象处理方法研究煤焦的分形结构,能更加深入地理解其分形维数与性能的关系。     

钛基氧化物电极的分形维数和电催化性能

分形几何学是近十几年来发展起来的新的数学理论,它对研究自然科学中的不规则几何行为具有独特的优势,尤其对材料的表面结构与性能研究有着重要的理论和实际意义。多相催化反应的一个显著特征就是在整个反应的一个显著特征就是在整个反应过程中都存在着反应界面,而界面的结构性质对反应过程有重要的影响。十几年前,有关这类界面的研究几乎都基于欧氏几何模型,在简单情况下视之为平面,在较复杂的情况下视之为曲面,即总是把表面视为二维面,但在很多情况下,这种做法与实际情况并不相符,例如,催化剂是多孔的,表面极不规则,存在各种晶体缺陷,而这些缺陷一般又是活性中心的集中处,面对这类粗糙的表面,经典的夫整几何学已显得无能为力,近年来,由Mandelbrot建立起来的分形几何学给人们解决诸多粗糙表面的复杂问题提供了新的途径和思路,本文计算了几种电极材料的表面分形维数,并对其催化性能进行了讨论。     

冲洗色谱特征点法测定表面分形维数初探

在用非线性气相色谱测填料表面分形维数中,首次运用气固色谱（ＥＣＰ法（ｅｌｕｔｉｏｎ ｂｙ ｃｈａｒａｃｔｅｒｉｓｔｉｃ ｐｏｉｎｔｓ ｍｅｔｈｏｄ）,测定了正戊烷、正已烷、正庚烷３种烷烃在不同颗粒大小的硅胶表面的吸附等温线,通过拟合Ｌａｎｇｍｕｉｒ方程,求出单分子饱和吸附容量,并采用单分子层吸附的分形模型,求得硅胶的发形维数,提供了一种测定表面分形维数的新方法。     

再生催化剂表面的变维分形表征

基于分形几何理论，以失活的催化剂化催化剂的再生为研究对象，用静态重量吸附法测定了经历不同再生阶段催化剂表面的单层饱和吸附量，计算得到了不同再段催化剂表面的分形维数，考察了其表面形貌在再生过程中的变化规律，研究结果表明，整个再生过程中，催化剂表面的分形维数在2．5－3．2之间有规律的发生变化，即从再生开始到结束，表面的分形维数由小变大，再由大变小然后趋于稳定。催化剂颗粒的电镜分析结果与实验数据一致。     

小波包去噪信号的分形特征

将分形理论与小波包滤波相结合，用盒维数的大小来评判信号曲线的滤波情况。随着小波包分解尺度的增大，滤波后信号曲线的盒维数逐渐减小，并最后趋于稳定值。因此可以根据盒维数-分解尺度曲线来选择最佳分解尺度。对仿真含噪信号进行了滤波实验，结果表明：即使在信噪比低至0．5时仍能得到较好的结果，并且该法用于毛细管电泳实验数据的处理结果同样令人满意。     

分形理论在催化剂研究中的应用

介绍了分形和分形维数在催化剂研究中的应用.概述了催化剂研究中常用的分形维数测定方法,包括盒子维法、散射强度法和吸附法.从四个方面分析了近年来催化剂分形研究的方向和进展:分形维数与催化剂评定和筛选,催化剂分形孔结构,分形与反应动力学,模型建立.从分形维数的测量、催化剂分形生长模型以及多重分形研究三个方面对分形在催化剂方面的应用进行了评价和展望.     

基于分形理论分辨重叠峰的新算法

将分形理论用于仪器分析信号的解析,提出一种面向分析谱图中重叠信号处理的分形分辨算法.通过对信号进行分形分析,采用分形维数可有效地反映信号的特征,准确地得到谱峰个数和位置的信息,避免人为判断的误差,实现重叠复合信号的分辨.实验表明,这种新的重叠谱峰分辨法能用于光谱、电化学、色谱等仪器分析数据的处理     

Fractal Dimension of Microbead Assemblies Used for Protein Detection

We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1 μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest–Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70–1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles.     

基于靶向多肽探针的蛋白质分析检测新方法

高选择性、高灵敏度的蛋白质分析检测方法是复杂生命体系研究的有力工具,能为疾病的发现、治疗以及分子机制研究提供新的、有价值的思路和手段.该文围绕蛋白质与多肽的分子识别,针对疾病相关多肽、蛋白质的分离、分析与检测新方法,综述了近几年取得的研究进展,可为复杂生命体系中生理活性分子的结构与功能研究提供借鉴.     

用化学动力学方法估算颗粒表面的分维

A chemical kinetic method based on the kinetic expression of the second-order reaction on fractals is used to determine the spectral dimension of fractal surfaces. The method can conveniently give the spectral dimension by analyzing the relation between reactant concentration and reaction time (ct～t). The spectral dimension of the Diffusion-Limited Aggregate (DLA) is obtained by Monte Carlo simulation of the desorption process of chemisorbed hydrogen from DLA, and it is in agreement, with that in literature. Also, the spectral dimension of a real catalyst 12% Ni/Al2O3 is obtained by the method.     

Tailoring the Morphology and Fractal Dimension of 2D Mesh-like Gold Gels

As there is a great demand of 2D metal networks, especially out of gold for a plethora of applications we show a universal synthetic method via phase boundary gelation which allows the fabrication of networks displaying areas of up to 2 cm². They are transferred to many different substrates: glass, glassy carbon, silicon, or polymers such as PDMS. In addition to the standardly used web thickness, the networks are parametrized by their fractal dimension. By variation of experimental conditions, we produced web thicknesses between 4.1 nm and 14.7 nm and fractal dimensions in the span of 1.56 to 1.76 which allows to tailor the structures to fit for various applications. Furthermore, the morphology can be tailored by stacking sheets of the networks. For each different metal network, we determined its optical transmission and sheet resistance. The obtained values of up to 97 % transparency and sheet resistances as low as 55.9 Ω/sq highlight the great potential of the obtained materials.     

On the Concentration Dependence of the Cluster Fractal Dimension in Colloidal Aggregation

We have undertaken the task to calculate, by means of extensive numerical simulations and by different procedures, the cluster fractal dimension (d) of colloidal aggregates at different initial colloid concentrations. Our first approach consists in obtaining d from the slope of the log-log plots of the radius of gyration versus size of all the clusters formed during the aggregation time. In this way, for diffusion-limited colloidal aggregation, we have found a square root type of increase of the fractal dimension with concentration, from its zero-concentration value: d = d⁰ _f + a , with d⁰ _f = 1.80 ± 0.01, a = 0.91 ± 0.03 and = 0.51 ± 0.02, and where is the volume fraction of the colloidal particles. In our second procedure, we get the d via the particle-particle correlation function g_cluster(r) and the structure function S_cluster(q) of individual clusters. We first show that the stretched exponential law g_cluster(r) = Ar^{d –3}e^–(r/) gives an excellent fit to the cutoff of the g(r). Here, A, a and are parameters characteristic of each of the clusters. From the corresponding fits we then obtain the cluster fractal dimension. In the case of the structure function S_cluster (q), using its Fourier transform relation with g_cluster(r) and introducing the stretched exponential law, it is exhibited that at high q values it presents a length scale for which it is linear in a log-log plot versus q, and the value of the d extracted from this plot coincides with the d of the stretched exponential law. The concentration dependence of this new estimate of d, using the correlation functions for individual clusters, agrees perfectly well with that from the radius of gyration versus size. It is however shown that the structure factor S(q) of the whole system (related to the normalized scattering intensity) is not the correct function to use when trying to obtain a cluster fractal dimension in concentrated suspensions. The log-log plot of S(q) vs. q proportions a value higher than the true value. Nevertheless, it is also shown that the true value can be obtained from the initial slope of the particle-particle correlation function g(r), of the whole system. A recipe is given on how to obtain approximately this g(r) from a knowledge of the S(q), up to a certain maximum q value.     

基于XRD曲线分形维度的丝光沸石晶化动力学行为分析

丝光沸石;水热晶化;分形维度;化学混沌;晶化动力学     

中药色谱指纹图谱的小波变换及分形表达方法

提出一种基于小波变换的色谱指纹图谱分形表达方法。该法运用小波变换将色谱谱线分解至不同分辨尺度，然后计算各尺度分量的分形维数，用色谱的小波基分形参量替代色谱指纹图谱的采样值。仿真实验结果表明，色谱小波基分形参量对谱峰保留时间漂移具有较好的抗干扰能力。以当归和川芎两种中药材的品种及道地性鉴别分类问题为实例，比较研究色谱采样值与小波基分形参量，k-近邻法的交叉验证计算结果表明，小波基分形参量的分类效果优于色谱采样值。     

基于分形动力学过程的腐蚀预测模型

腐蚀是一种复杂随机现象,可以用分形理论更好地描述。本文根据分形动力学过程,以一组基于不同表面条件下的腐蚀发生概率为参数,建立计算机模型来预测大气、土壤环境的金属腐蚀过程。计算结果和实际腐蚀特征吻合一致。此外,本文还讨论了幂函数腐蚀模型中指数n和各种腐蚀概率之间的定量关系,揭示了腐蚀发展规律。