二维河网系统分形动力学研究

河网系统是一个远离平衡态的、开放的复杂系统。现阶段认为河流的演变机理包括外在宏观形状表现以及内在微观动力学机制,而河流的演变也是二者之间的平衡转化。目前,使用分形理论对河流的特征及河床的演变发展研究已经成为一种重要的手段。鉴于分形理论运用的局限性,特别是算法有宏观形状而无微观机制的弊病,应用线宽和线面积这两个可以直接与河流动力学衔接的概念,推导了可以直接用绘制图形(河流)的线宽计算维数的线维数和线面积计算维数的面维数,实现了维数计算由点到线、面的突破,为河网分形发育程度与河流动力学及最小能耗等理论衔接提供了可能,即为构建河网外在形状和内在动力学的新理论,以及最终实现河流的宏观外在特征和微观内在特征的衔接提供了两种理论途径。

裂隙化岩体不连续面密度的分形研究

不连续面密度是表征岩体内部不连续面分布特征的重要参数之一,但是岩体内不连续面的分布是随机的、不规则的,要想准确获得岩体不连续面密度的真实值是不可能的。基于现场调查的岩体露头不连续面特征,借助计算机模拟技术建立岩体不连续面分布的二维、三维随机裂隙网格模型,从数理统计学的角度计算岩体不连续面密度数值。并基于分形理论计算岩体不连续面分布的二维、三维分布特征,尝试建立岩体不连续面密度与分维数的数学关系。计算结果表明,岩体不连续面密度与分维数具有相同的变化趋势,随着不连续面分维数的增大,不连续面密度增大,不连续面密度与分维数之间存在线性关系。研究结果表明,不连续面分布的体密度和三维分形维数,可以更加综合地反映岩体内部不连续面的分布特征和空间信息及对岩体强度参数的影响,对工程应用具有更好的实际作用。且在此基础上,提出基于不连续面分布的体密度和三维分形维数的岩体等效抗剪强度指标的折减计算。

基于小波变换的精密测量点云多尺度分解

为了减小多源跨尺度点云数据尺度与数据量上的差异,提出了一种基于小波变换的点云多尺度分解方法。对细节丰富的小尺度点云数据进行多尺度分解,以及尺度分解在跨尺度点云数据配准中的应用进行研究。首先,对小尺度点云进行栅格建模,建立全局点云二值表达函数。根据离散小波变换理论,对栅格点云进行多次的三维小波分解,利用小波尺度函数的低通特性,保留低频信息来获取原始小尺度点云的近似尺度数据。然后,基于面维数和差体维数差表征与原始数据的相似度,确定有效的小波分解级数。最后,将各级分解得到的点云数据与大尺度点云数据进行精确配准,并将配准关系应用于原始点云,提高跨尺度点云的配准精度。实验结果表明:本文提出的多尺度分解方法能够对数据进行有效分解,应用于某航空发动机叶片多尺度测量中,将显微测量的局部气膜孔小尺度点云数据与整体叶片结构光数据配准,配准精度提升了61.36%。该分解方法应用于叶片边缘与栅格零件多尺度测量中,配准精度分别提升了48.59%,43.86%。所提的点云多尺度分解方法能够有效分解小尺度点云数据,大幅提升跨尺度数据的配准精度。

THEORETICAL VERIFICATION OF THE SCALING RELATION TO DETERMINE SURFACE FRACTAL DIMENSION OF POROUS MEDIA

A simplified procedure is developed to acquire the surface fractal dimension of porous media utilizing the PSD information from mercury porosimetry or other analyses.The self similarity of the inner surface of Sierpinski sponge is analyzed,the result of which demonstrates that the inner surface of Sierpinski sponge is not scale invariant over the whole range of scale transformations.By applying the simplified procedure to analyze and treat the PSD information of Sierpinski sponge over the scale invariant range,it is found that the surface fractal dimension calculated by the scaling relation is in very good agreement with its theoretical value,which virtually provides a theoretical affirmation of the method.

Effects of fractal surface on rheological behavior and combustion kinetics of modified brown coal water slurries

The paper reports the effects of surface fractal structures on the rheological behavior and combustion kinetics of raw brown coal and three modified coal water slurries （CWSs）. The results show that the fractal structures and physicochemical properties of samples are dependent on various modification processes. The apparent viscosities of the coal water slurries increase with increasing surface fractal dimensions （D）, especially with decreasing shear rates. Fur- thermore, it has been proved that the ignition temperatures and apparent activation energies of modified CWSs are lower than that of raw coal water slurry. Compared with the traditional qualitative analysis of the effect of pore structures on CWSs properties, D can more efficiently indicate the quantificational effect of pore structures on the rheological behavior and combustion kinetics of CWSs.

Implication of Surface Fractal Analysis to Evaluate the Relative Sensitivity of Topography to Active Tectonics,Zagros Mountains, Iran

Fractal geometry is increasingly becoming a useful tool for modeling and quantifying the complex patterns of natural phenomena. The Earth's topography is one of these phenomena that have fractal characteristics. This paper investigates the relative sensitivity of topography to active tectonics using ASTER Global Digital Elevation Model. The covering divider method was used for direct extraction of surface fractal dimension(D surf) to estimate the roughness-surface of topography with aid of geographic information system(GIS)techniques. This evaluation let us highlight the role of the geomorphic and tectonic processes on the spatial variability of fractal properties of natural landforms.Geomorphic zones can be delineated using fractal dimension mapping in which variability of surface fractal dimension reflects the roughness of the landform surface and is a measure of topography texture. Obtained results showed this method can be a quick and easy way to assess the distribution of land surface deformation in different tectonic settings. The loose alluvial deposits and irregularities derived by tectonic activity have high fractal dimensions whereas the competent formations and higher wavelength folded surfaces have lower fractal dimensions.According to the obtained results, the Kazerun Fault Zone has a crucial role in the separation of the Zagros Mountain Ranges into the different lithological,geomorphological and structural zones.

A numerical simulation of seepage structure surface and its feasibility

According to Cubic law and incompressible fluid law of mass conservation, the seepage character of the fracture surface was simulated with the simulation method of fractal theory and random Brown function. Furthermore, the permeability coefficient of the single fracture was obtained. In order to test the stability of the method, 500 simulations were conducted on each different fractal dimension. The simulated permeability coefficient was analyzed in probability density distribution and probability cumulative distribution statistics. Statistics showed that the discrete degree of the permeability coefficient increases with the increase of the fractal dimension. And the calculation result has better stability when the fractal dimension value is relatively small. According to the Bayes theory, the characteristic index of the permeability coefficient on fractal dimension P（Dfi｜ Ri） is established. The index, P（Dfi｜ Ri）, shows that when the simulated permeability coefficient is relatively large, it can clearly represent the fractal dimension of the structure surface, the probability is 82%. The calculated results of the characteristic index verify the feasibility of the method.

Numerical Calculation of Channel Dredging Volume Using 3D Digital Stratum Model

Prediction of channel dredging volume is critical for project cost estimation. However, many proposed approximate methods are not accurate. This paper presents a novel numerical method to accurately calculate the dredg- ing volume using a 3D stratum model (DSM) and a channel surface model. First, the 3D DSM is constructed rapidly yet accurately from non-uniform rational B-splines (NURBS) surfaces through Boolean operation between a physical terrain model and a stratum surfaces model. Then, a parametric channel surface model is built from cross-section data and a channel center line using code implemented in the VC++ programming language. Finally, the volumes of different types of physical stratums can be calculated automatically and hierarchically to determine the dredging volume. Practical application shows that the DSM method is more precise and faster compared to the section method, and that the implementation of the developed software provides an interactive graphical user interface and visual presentation.

Effects of AlN hydrolysis on fractal geometry characteristics of residue from secondary aluminium dross using response surface methodology

The effects of aluminium nitride(AlN)hydrolysis on fractal geometry characteristics of residue from secondary aluminium dross were studied using response surface methodology.The results show that the fractal dimensions of the residue can be significantly influenced by the AlN hydrolysis from secondary aluminium dross.The hydrolysis of AlN in the dross was spontaneous under temperatures of303-373K.The actual fractal dimensions of residue were significantly affected by the liquid-solid ratio(p<0.05)and changed from1.16to1.80,which accurately aligned with those from the calculations.Moreover,the fractal dimensions of residue were significantly affected by the interactions between hydrolysis temperature and hydrolysis time,liquid-solid ratio and hydrolysis time,respectively(p<0.01).The minimum fractal dimensions of the residue reached1.15under the optimized conditions,which included a hydrolysis temperature of30℃,liquid-solid ratio of5mL/g and hydrolysis time of10min.The results suggest that response surface methodology can guide in optimizing the conditions of AlN hydrolysis in order to obtain the minimum fractal dimensions of residue for improving the reutilization of the dross.

A Lifting Line Theory for a Three-dimensional Hydrofoil

Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.

Barotropic current fluctuations coupled with sea level drawdown in Yellow and Bohai Seas

Sub-tidal barotropic current variations coupled with residual sea level fluctuation in the Bohai and Yellow Seas during wintertime are addressed in this study.The temporal evolution and spatial distribution of current fluctuation are investigated using moored acoustic Doppler current profiler data in a three-dimensional numerical model.It is found that a southward current followed by a northward current occurred in the northern Yellow Sea during the fluctuation,concurrent with a significant outflow followed by inflow through the Bohai Strait.The process is consistent from surface to bottom and is coupled with remarkable residual sea level fluctuation.This quasi three-day fluctuation with amplitude 0.2-0.3 m/s leads to 1 m/1.2 m drawdown in the northern Yellow and Bohai Seas,respectively,strongly influencing water exchange between those seas.Because this a prominent feature in the seas,it is necessary to evaluate its effect on fluctuation during winter in future studies,in particular,the northward current during the recovery phase of sea level in the Bohai and Yellow Seas regarding seasonal variation.

A Research for a Division of Regular Polyhedron by Rhombic Dodecahedron

Abstract：A space-filling polyhedron is a polyhedron which ＇tile＇ space, analogous to the way of certain polygons tiled the plane. The cube is the unique space-filling platonic solid. If we make line connections the center with the vertices in the certain cube, the cube is divided into six pyramids. And if we glued six pyramids to the faces of the cube, we obtain a ＇rhombic dodecahedron＇. Since cubes are packing a space, rhombic dodecahedra are also space-filling polyhedra and a rhombic dodecahedron is divided into two regular tetrahcdra and one regular octahedron. In this study, we present how rhombic dodecahedron can be split into tetrahedra and octahedron. In this process, we can research a variety of divisions of regular polyhedron.

Mitigation of floor heave in West Kentucky Coal Mine

A West Kentucky mine operation in No. 11 seam encountered floor heave, due to the localized increase in the thickness of the fireclay mine floor. Floor heave has overridden seals installed in two mined out panels. The third seal's location was planned for isolating that area from the Mains. A plan of support has been developed to prevent repetition of the floor heave and related problems outby the seals. The applied ground control measures were successful. An attempt of a 3D numerical modeling was made; thus, it would match the observed behavior of the mine floor and could be used as a design tool in similar conditions. The paper describes sequence of events, an applied mitigation ground control system, and the first stage of numerical modeling.

Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schrodinger Equation

Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.

The development of real time data driving multi-axis linkage and synergic movement control system of 3D variable cross-section roll forming machine

The three dimensional variable cross-section roll forming is a kind of new metal forming technol- ogy which combines large forming force, multi-axis linkage movement and space synergic movement, and the sequential synergic movement of the ganged roller group is used to complete the metal sheet forming according to the shape of the complicated and variable forming part data. The control system should meet the demands of quick response to the test requirements of the product part. A new kind of real time data driving multi-axis linkage and synergic movement control strategy of 3D roll forming is put forward in the paper. In the new control strategy, the forming data are automatically generated according to the shape of the parts, and the multi-axis linkage movement together with cooperative motion among the six stands of the 3D roll forming machine is driven by the real-time information, and the control nodes are also driven by the forming data. The new control strategy is applied to a 48 axis 3D roll forming machine developed by our research center, and the control servo period is less than 10ms. A forming experiment of variable cross section part is carried out, and the forming preci- sion is better than ＋ 0.5mm by the control strategy. The result of the experiment proves that the control strategy has significant potentiality for the development of 3D roll forming production line with large scale, multi-axis ganged and svner^ic movement

Fermionic Zero Modes in Gauge and Gravity Backgrounds on a Sphere

In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two-dimensional compact manifold S2 as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under quite general assumptions about these backgrounds on the bulk. Several special cases of gauge background on the sphere axe discussed and some simple fermionic zero modes are obtained.

Fractal characteristics of cracks and fragments generated in unloading rockburst tests

True triaxial rockburst experiments with four different unloading rates were performed on four prism specimens of granite sampled from Beishan, China. The damage evolution in the rockburst test was investigated from two aspects including fracture surface crack and fragment characteristics. The scanning electron microscopy was used to observe the micro crack information on fragment surface. Combing binarization and box counting dimensions, the fractal dimensions of cracks were obtained. Meanwhile,the fragments were collected and a sieving experiment was conducted. We weighed the fragments qualities, counted the amount of fragments and measured the fragments length, width and thickness.Utilizing four methods to calculate damage fractal dimensions of fragments, the trend of fractal value changing with unloading rates can be roughly described. It can be concluded from these experiments that the fractal dimension either for crack or for fragment holds a decreasing trend with the decreasing unloading rate, indicating a reduction of damage level.

Experimental and theoretical analysis of fiber Bragg gratings under Transverse Force to a Small Grating Section

Fiber Bragg grating under transverse force on a small grating section is studied by numerical simulation and experimentation. A numerical simulation based on the transfer matrix method is used to calculate the consequent changes in reflected spectrum. The reflected spectra of the FBG subjected to the transverse force split into two main peaks, and the split point shifted linearly and periodically versus the applied force. The split point is shifted in the bandwidth with the period of 11N, and the sensitivity of the split point wavelength shift versus the applied force is 0.05 nm/N in one period. The experimental results show good agreement with the simulation analysis.

A Method for Calculating Fractal Dimension of Amicrons and Fractal Simulation of Boundary Micro-Topography

A simple and practical method to calculate the fractal dimension （FD） of amicron＇s projective surface profile based on fractal theory is proposed. Taking AI（OH）3 material particles as an example, the scanning electron microscope （SEM） photos of particles were processed using an image.processing software （IPS） Photoshop. Taking the pixel as a fixed yardstick with the enlargement of the size of the particle image, the box-dimension and circumference-area （C-S） methods were used to calculate the FD of the surface profile of the particle. The FD of 1.2623 of the classic Koch curve is obtained, which approximates the true value of 1.2628. The complexities of the object＇s boundary and surface micro-topography are simulated successfully by a generator method.

Simulating Deposition of Aerosol Particles on Single Fiber Surface

The stochastic simulation method, based on the concept of control window and the numerical solution of the Langevin equation, is applied to solve the deposition problem of particles from the flowing suspensions onto a fiber collector. Using the Kuwabara model to characterize the flow field, the effects of Stokes number, interception parameter, packing density, particle size distribution on the collection efficioncy, and the deposition morphology of particles onto a collector are i examined. The morphology of deposit obtained in the simulated results agrees Well with experimental observations. The estimation of the initial coUection efficiency through the simulations considers that the deposited particles are in good agreement with published experimental data. In addition, the collection efficiency of particles increases in a wider particle size distribution region.