Contact Angle Prediction Model for Underwater Oleophobic Surfaces Based on Multifractal Theory

Traditional microstructure scale parameters have difficulty describing the structure and distribution of a roughmaterial’s surface morphology comprehensively and quantitatively. This study constructs hydrophilic and underwateroleophobic surfaces based on polyvinylidene fluoride (PVDF) using a chemical modification method, and the fractaldimension and multifractal spectrum are used to quantitatively characterize the microscopic morphology. A new contactangle prediction model for underwater oleophobic surfaces is established. The results show that the fractal dimension ofthe PVDF surface first increases and then decreases with the reaction time. The uniformity characterized by the multifractalspectrum was generally consistent with scanning electron microscope observations. The contact angle of water droplets onthe PVDF surface is negatively correlated with the fractal dimension, and oil droplets in water are positively correlated.When the fractal dimension is 2.0975, the new contact angle prediction model has higher prediction accuracy. Themaximum and minimum relative deviations of the contact angle between the theoretical and measured data are 18.20%and 0.72%, respectively. For water ring transportation, the larger the fractal dimension and spectral width of the materialsurface, the smaller the absolute value of the spectral difference, the stronger the hydrophilic and oleophobic properties, andthe better the water ring transportation stability.

Fractal and Multifractal Modeling of Hydrothermal Mineral Deposit Spectrum: Application to Gold Deposits in Abitibi Area, Ontario, Canada

A number of fractal/multifractal methods are introduced for quantifying the mineral deposit spectrum which include a number-size model, grade-tonnage model, power spectrum model, multifractal model and an eigenvalue spectrum model. The first two models characterize mineral deposits spectra based on relationships among the measures of mineral deposits. These include the number of deposits, size of deposits, concentration and volume of mineral deposits. The last three methods that deal with the spatial-temporal spectra of mineral deposit studies are all expected to be popularized in near future. A case study of hydrothermal gold deposits from the Abitibi area, a world-class mineral district, is used to demonstrate the principle as well as the applications of methods proposed in this paper. It has been shown that fractal and multifractal models are generally applicable to modeling of mineral deposits and occurrences. Clusters of mineral deposits were identified by several methods including the power spectral analysis, singularity analysis and the eigenvalue analysis. These clusters contain most of the known mineral deposits in the Timmins and Kirkland Lake camps.

Variable bit rate video traffic modeling by multiplicative multifractal model

Multiplicative multifractal process could well modal video traffic. The multiplier distributions in the multiplicatire multifractal model for video traffic are investigated and it is found that Gaussian is not suitable for describing the multipliers on the small time scales. A new statistical distribution-symmetric Pareto distribution is introduced. It is applied instead of Gaussian for the multipliers on those scales. Based on that, the algorithm is updated so that symmetric pareto distribution and Gaussian distribution are used to model video traffic but on different time scales. The simulation results demonstrate that the algorithm could model video traffic more accurately.

Markov-Switching Time-Varying Copula Modeling of Dependence Structure between Oil and GCC Stock Markets

This paper proposes a Markov-switching copula model to examine the presence of regime change in the time-varying dependence structure between oil price changes and stock market returns in six GCC countries. The marginal distributions are assumed to follow a long-memory model while the copula parameters are supposed to evolve according to the Markov-switching process. Furthermore, we estimate the Value-at-Risk (VaR) based on the proposed approach. The empirical results provide evidence of three regime changes, representing precrisis, financial crisis and post-crisis, in the dependence structure between energy and GCC stock markets. In particular, in the pre- and post-crisis regimes, there is no dependence, while in the crisis regime, there is significant tail dependence. For OPEC countries, we find lower tail dependence whereas in non-OPEC countries, we see upper tail dependence. VaR experiments show that the Markov-switching time- varying copula model performs better than the time-varying copula model.

A Multifractal Detrended Fluctuation Analysis of the Ising Financial Markets Model with Small World Topology

We present a multifractal detrended fluctuation analysis （MFDFA） of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors： broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series.

An Analytical Model for Multifractal Systems

Previous multifractal spectrum theories can only reflect that an object is multifractal and few explicit expressions of f(α) can be obtained for the practical application of nonlinearity measure. In this paper, an analytical model for multifractal systems is developed by combining and improving the Jake model, Tyler fractal model and Gompertz curve, which allows one to obtain explicit expressions of a multifractal spectrum. The results show that the model can deal with many classical multifractal examples well, such as soil particle-size distributions, non-standard Sierpinski carpet and three-piece-fractal market price oscillations. Applied to the soil physics, the model can effectively predict the cumulative mass of particles across the entire range of soil textural classes.

Multifractal Simulation of GeochemicalMap Patterns

Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.

基于组合预测模型的滑坡变形趋势研究

为实现滑坡变形的高精度预测,基于滑坡变形监测成果,先以支持向量回归、RReliefF算法、鲸鱼优化算法及Arima模型为基础,构建滑坡变形组合预测模型;再利用多重分形消除趋势波动分析和Spearman秩次检验,研究滑坡变形的多标度特征。结果表明,通过不断组合优化处理,能显著提高滑坡变形预测精度,且经外推预测,D1~D3监测点的现有速率相对更大,且预测速率较现有速率的减小幅度依次为21.61%、12.95%和6.54%,D4监测点的预测预测速率相对更大,其较现有速率的增加幅度为19.85%,说明滑坡前缘稳定性进一步趋于不利;4个监测点具有不同的分形谱宽度和大波形所占比例,但D4监测点在分形谱宽度及大波形所占比例上均为最不利;4个监测点变形的分形谱宽度均为增加趋势,且只有D2监测点的大波动所占比例为增加特征,其他监测点均为减小趋势,说明滑坡变形的波动性会更加剧烈,但大波动总体趋于减弱,只在局部为增加趋势,建议尽快进行滑坡防治处理。

Multifractal modelling and spectrum analysis: Methods and applications to gamma ray spectrometer data from southwestern Nova Scotia, Canada

Multifractal spectrum, autocorrelation/semivariogram and power spectrum are three dif- ferent functions characterizing a field or measure from different aspects. These functions are interre- lated in such that the autocorrelation/semivariogram and power spectrum are related to the low order statistical moments (0 to 2 nd) which may determine the local multifractality (τ ″(1)) of a multifractal measure. A better understanding of the interrelationships among these three functions is important because, on one hand, the multifractal modelling characterizes a multifractal measure in a more de- tailed manner since it involves moments of all orders. On the other hand, the commonly used semivariogram and power spectrum functions can be used as alternatives to study the dominant mul- tifractal properties around the mean measure. Moreover, semivariogram and power-spectrum func- tions provide spatial and spectral information, which is highly valued in geological applications. A new fractal relation found between area and power-spectrum will be useful for investigation of new meth- ods of spatial-spectral analysis for pattern recognition, anomaly separation, classification, etc. These results have been demonstrated with the case study of modelling gamma ray spectrometer data from the mineral district, southwestern Nova Scotia, Canada. The results have shown that the values of uranium (U), thorium (Th) and potassium (K) may possess monofractal properties whereas the ratios of these values show high multifractality. The values of the ratios U/K and U/Th show relatively large variances and may provide more information for distinguishing the distinct phases of the granites, country rocks as well as possible gold mineralization-associated regional hydrothermal alteration zones. In addition, the power spectra for U, Th, K, U/Th and U/K consistently show two distinct power-law relationships for two ranges of wave number 12≤ω ≤160 km and 0≤ω ≤12 km. These properties might provide useful thresholds for separating the power-spectrum values into two types of patterns to reflect different influences of possible geological processes such as hydrothermal altera- tion in the study area.

Multifractal spectrum and spectral behavior of calcium and titanium isotopes based on nuclear shell model

We investigate the effect of valence space nucleons on the multifractal analysis(MFA)and spectral analysis of calcium and titanium isotopes.The multifractality of wavefunctions is characterized by its associated singularity spectrum f(α)and generalized dimension Dq.The random matrix theory(RMT)has been employed in the study of properties of the distribution of energy levels.In particular,we find that the number of nucleons and two-body residual interactions particularly affect the singularity and energy level spectra.

A Markov-switching predator-prey model with Allee effect for preys

This paper concerns with a Markov-switching predator-prey model with Allee effect for preys.The conditions under which extinction of predator and prey populations occur have been established.Sufficient conditions are also given for persistence and global attractivity in mean.In addition,stability in the distribution of the system under con-sideration is derived under some assumptions.Finally,numerical simulations are carried out to illustrate theoretical results.

基于“元素含量—面积”模型方法的地球化学场的多重分形模式分析

从多重分形理论出发,在赤峰地区的2个区域应用“元素含量—面积(C-A)”模型方法。对“元素含量—面积”双对数图的形态进行分析,将地球化学异常多重分形特征模式分为3种类型:模式Ⅰ为可拟合为2条直线段的简单多重分形模式,具有该模式的元素在研究区内没有成矿富集的趋势,不存在实质性的致矿异常;模式Ⅱ为可以拟合为3条直线段的高富集多重分形模式,它在模式Ⅰ的基础上叠加有高含量的异常场,具有该模式的元素在研究区内存在较强的局部富集,成矿的可能性很大;模式Ⅲ为可拟合成3条直线段的低富集多重分形模式,它在模式Ⅰ的基础上叠加的是较弱的异常场,具有该模式的元素在研究区内有较弱的矿化作用。在此基础上,分析了元素的成矿富集规律和空间分布特征,确定了区域异常和局部异常的异常下限,划分了地球化学背景、区域异常和局部异常。

矩分析法及其在粤北韶关地区金属成矿作用研究中的应用

采用多重分形矩分析法探讨了粤北韶关地区4292km2内1448个基岩样品的25项元素的分形分布规律。结果表明,金属地球化学场元素的多重分形谱函数上凸且连续,其多重分形谱函数的开口大小在某种程度上能反映地球化学场的浓集程度。地球化学场中元素在空间上的分布具有连续多重分形特征,与成矿密切相关的微量元素一般服从左侧开口明显大于右侧开口的连续多重分形左偏模式,而非主要成矿元素则对应右侧开口大的连续多重分形右偏模式。

基于多维分形模型与指示克里格方法的地球化学异常识别研究

指示克里格方法是一种不依赖于分布假设条件的非参数估值方法,对于异常值和偏态分布都具有良好的稳健能力,因此可以作为地球化学异常研究的理想工具。阈值作为指示克里格方法最重要的参数,对于插值结果具有很大影响。该文从多维分形理论出发,利用浓度-面积(C-A)模型计算地球化学异常下限值,并将其作为阈值参与指示克里格法插值计算。为了解决多维分形测度时的不确定性,利用Voronoi图的唯一性对C-A模型进行了改进,并通过安徽省某铜矿区大比例尺化探Cu元素地球化学数据对上述方法进行了实例研究。结果显示,较之反距离加权插值法、普通克里格插值法,指示克里格法获取的最高累计概率范围与已知矿体的空间吻合程度更高,具有更好的地球化学异常识别能力。对于地球化学数据空间变异性强烈的地区,指示克里格方法在稳定变异函数形状和高值信息重建能力方面具有很大的优势。

面向城市热环境格局时空演变的多重分形模式--以郑州市为例

与单分形相比,多重分形模型赋予了更多描述客观世界中复杂现象和事物的参数和手段,为更加准确和精细地刻画自然界中普遍存在的非线性现象和过程提供了一种有效途径。以河南省郑州市为研究对象,选取三期Landsat5-TM影像反演城市地表温度,并采用多重分形的理论与方法定量地探讨和研究城市热环境场纹理结构及其在时空中的分布特征,以及在不同的标度区间内热环境场与NDVI之间的关系。研究结果表明:20年间郑州市热场景观的多重分形谱奇异性指数最大值与最小值之差"α由0.6716减小为0.6419,奇异性指数最小值αmin和最大值αmax分别由1.4644、2.136减小为1.4304和2.0723,背景场奇异值α(fmax)由2.0111减小为2.0083,纹理测度最大值与最小值的分维数f(αmin)和f(αmax)分别由0.2354、1.4877增大为0.3412和1.734,意味着随着近20年经济的发展和城镇化率的提高,研究区域的热场纹理信息量不断减少,结构趋于简单,而纹理测度最大值、最小值和研究区温度有增大的趋势。对于位于郑州市不同位置且由不同景观斑块类型构成的区域,市区区域纹理测度波动幅度最小,而水体区域最大;市区纹理测度最大值和最小值的分维数最大,不同等级纹理像元数量分布比较均匀,空间簇聚程度高,而水体则相反,另从市区样本的多重分形参数来看,新开发的区域比老市区具有更小的αmin值和D2值。区域温度均值与多重分形参数之间呈现较强的线性相关性,而区域标准差与多重分形参数之间的相关性更强,线性变化的顺序依次为水体、农业用地、城郊和市区。另外,还利用C-A(浓度-面积)模型把2011年热场图像纹理结构分割为3个标度不变性区间,在此基础上讨论了奇异性指数α对区域温度与NDVI(归一化植被指数)之间关系的影响,发现斑块边缘的地表温度对NDVI最为敏感,且奇异性指数对不同标度区间的地表温度的本底值贡献是正向的,这些结论对热环境场的尺度转换研究具有一定的参考意义。

结合多重分形的网络流量非线性预测

通过分析树型多重分形结构的相关性发现,多重分形可以把非平稳且具有长相关(LRD)和分形特性的网络流量序列转化为可用短相关(SRD)模型表示的序列组。利用多重分形这种将时间序列分解为多层的能力,提出了一种结合多重分形的FIR神经网络流量预测模型(MF-FIR,multifractal FIR network)。MF-FIR合理地利用了流量序列的LRD信息,具有很好的多步预测性能,可以满足通信系统在线预测的要求。

多分形波动率预测模型及其MCS检验

以上证综指的5 min高频数据为例,在已有的多分形波动率(multifractal volatility)测度方法基础上,提出了新的波动率测度方法及模型.运用滚动时间窗的样本外预测技术以及比SPA检验更具优势的"模型信度设定检验"(model confidence set,MCS),对比了新的波动率测度模型和主流的GARCH族以及已实现波动率(realized volatility)模型的预测精度.实证结果显示:不论是短记忆模型还是长记忆模型,多分形波动率模型的预测精度明显优于GARCH族模型,且长记忆模型的预测能力要好于短记忆模型.同时,在多数损失函数下,新提出的多分形波动率测度方法及其动力学模型的预测效果都是最优的.

多重分形与地质统计学方法在粤北刘家山地区矿化指示中的应用

为了解地球化学元素在岩石等介质中的局部富集和贫化规律,采用多重分形和地质统计学方法来分析其空间自相关性及奇异性,多重分形方法通过多重分形模型来刻画,地质统计学方法通过变异函数来实现。应用这两种方法处理粤北刘家山地区1∶5万水系沉积物地球化学各元素数据表明,地球化学数据的局部奇异性在该区可反映铅锌铜矿化蚀变带等局部成矿有利部位。为进一步研究异常与奇异性区的关系采用分形滤波技术(S-A法)对该区成矿主元素Pb、Zn进行分析,发现由S-A法分解得到的异常区与奇异性区一致,并且得出由S-A法分解的异常具有局部奇异性的结论。研究区内具有明显奇异性的地区也即元素富集区域是铅锌矿异常区域,它们与铅锌矿成矿作用和已知矿床的赋存密切相关,这也为该地区元素的成矿潜力评价提供了重要的线索。

中天山乌拉斯台地区矿化异常提取及评价

以多重分形理论为基础,对中天山乌拉斯台地区铜多金属元素的岩屑测量数据,采用C-A法获得铜多金属的异常下限值,将其作为阈值进行指示克里格插值,绘制研究区的铜多金属地球化学异常图。研究显示,基于该方法获得的Cu矿化异常高值区主要集中在华力西早期第三侵入次的石英闪长岩和花岗闪长岩岩体中,受北西向和次级北东向断裂构造控制明显,该异常区可以作为寻找热液型铜多金属矿产的重要远景区。该方法对于地球化学数据空间变异性强烈的地区,较之普通克里格插值法具有更好的地球化学异常识别能力和高值信息重建能力,所得结果的最高累计频率值范围与已知矿化点的空间位置吻合度更高,在地球化学异常信息提取工作中具有推广意义。