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。

Three-dimensional interpretation of sparse survey line MT data: Synthetic examples

Currently, most of MT （magnetotelluric） data are still collected on sparse survey lines and interpreted using 2D inversion methods because of the field work cost, the work area environment, and so on. However, there are some 2D interpretation limitations of the MT data from 3D geoelectrical structures which always leads to wrong geological interpretations. In this paper, we used the 3D inversion method to interpret the MT sparse lines data. In model testing, the sparse lines data are the MT full information data generated from a test model and processed using the 3D conjugate gradients inversion code. The inversion results show that this inversion method is reasonable and effective. Meanwhile, we prove that for inversion results with different element parameters, the results by joint inversion of both the impedance tensor data and the tipper data are more accurate and closer to the test model.

NOTE ON FORMULATION OF GEOMETRIC PROPERTIES OF A POLYNOMIAL SYSTEM

This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.

Polar Functions for Fractional Brownian Motion

Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the class of polar functions are studied. Our theorem 1 improves the previous results of Graversen and Legall. Theorem2 solves a problem of Legall (1987) on Brownian motion.

SPEEDING-UP RE-SAMPLED ALGORITHM IN RAY CASTING VOLUME RENDERING OF MEDICAL IMAGES

Ray casting algorithm can obtain a better quality image in volume rendering, however, it exists some problems, such as powerful computing capacity and slow rendering speed. How to improve the re-sampled speed is a key to speed up the ray casting algorithm. An algorithm is introduced to reduce matrix computation by matrix transformation characteristics of re-sampling points in a two coordinate system. The projection of 3-D datasets on image plane is adopted to reduce the number of rays. Utilizing boundary box technique avoids the sampling in empty voxel. By extending the Bresenham algorithm to three dimensions, each re-sampling point is calculated. Experimental results show that a two to three-fold improvement in rendering speed using the optimized algorithm, and the similar image quality to traditional algorithm can be achieved. The optimized algorithm can produce the required quality images, thus reducing the total operations and speeding up the volume rendering.

Effects of nonlinear strength parameters on stability of 3D soil slopes

Actual slope stability problems have three-dimensional(3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.

Linear manifold clustering for high dimensional data based on line manifold searching and fusing

High dimensional data clustering,with the inherent sparsity of data and the existence of noise,is a serious challenge for clustering algorithms.A new linear manifold clustering method was proposed to address this problem.The basic idea was to search the line manifold clusters hidden in datasets,and then fuse some of the line manifold clusters to construct higher dimensional manifold clusters.The orthogonal distance and the tangent distance were considered together as the linear manifold distance metrics. Spatial neighbor information was fully utilized to construct the original line manifold and optimize line manifolds during the line manifold cluster searching procedure.The results obtained from experiments over real and synthetic data sets demonstrate the superiority of the proposed method over some competing clustering methods in terms of accuracy and computation time.The proposed method is able to obtain high clustering accuracy for various data sets with different sizes,manifold dimensions and noise ratios,which confirms the anti-noise capability and high clustering accuracy of the proposed method for high dimensional data.

Imperfect preventive maintenance for numerical control machine tools with log-linear virtual age process

Based on the log-linear virtual age process, an imperfect preventive maintenance policy for numerical control(NC)machine tools with random maintenance quality is proposed. The proposed model is a combination of the Kijima type virtual age model and the failure intensity adjustment model. Maintenance intervals of the proposed hybrid model are derived when the failure intensity increase factor and the restoration factor are both random variables with uniform distribution. The optimal maintenance policy in infinite time horizon is presented. A numerical example is given when the failures of NC machine tools are described by the log-linear process. Finally, a discussion is presented to show how the optimal results depend on the different cost parameters.

Characterization of surface EMG signals using improved approximate entropy

An improved approximate entropy (ApEn) is presented and applied to characterize surface electromyography (sEMG) signals. In most previous experiments using nonlinear dynamic analysis, this certain processing was often confronted with the problem of insufficient data points and noisy circumstances, which led to unsatisfactory results. Compared with fractal dimension as well as the standard ApEn, the improved ApEn can extract information underlying sEMG signals more efficiently and accu- rately. The method introduced here can also be applied to other medium-sized and noisy physiological signals.

Analytical Algorithms for the Blend Ratios by Fibre-bundle Tensile Curves Part Ⅱ: Calculations of the Modulus Method and the Percentage Method

The principles for the modulus method and the percentage method are established and discussed in the part following Part Ⅰ of the series papers, in which we proposed the various algorithms of the strength method and the work method. The samples of Wool/PET blended fibre bundles, the method of fibre-bundle tensile tests and the typical specific stress-extension curves from the fibre bundles with different blend ratios are the same as in Part Ⅰ. It can be found that the theoretical results estimated by the modulus and percentage methods accord with the experimental values highly though the calculations of the two methods are slightly more complex than those of the strength and work methods. Especially, using the modulus method can not only avoid the influence of the error caused by the determination of the tensile curve of no fibre breaking in stretching, Y(e), but also need not to know the tensile curves of mono-component fibre bundles in certain calculation. The latter advantage of the modulus method exists in the percentage method too, but it should adopt the improved calculation of ones.

Spectral Method for Three-Dimensional Nonlinear Klein-Gordon Equation by Using Generalized Laguerre and Spherical Harmonic Functions

In this paper,a generalized Laguerre-spherical harmonic spectral method is proposed for the Cauchy problem of three-dimensional nonlinear Klein-Gordon equation. The goal is to make the numerical solutions to preserve the same conservation as that for the exact solution.The stability and convergence of the proposed scheme are proved.Numerical results demonstrate the efficiency of this approach.We also establish some basic results on the generalized Laguerre-spherical harmonic orthogonal approximation,which play an important role in spectral methods for various problems defined on the whole space and unbounded domains with spherical geometry.

Higher-Dimensional Integrable Systems Arising from Motions of Curves on S^2(R)and S^3(R)

We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).

The Four Intersection-and-Difference Model for Line-Line Topological Relations

The description of line-line topological relations is still an unsolved issue although much effort has been done. The problem is involved in many practical applications such as spatial query, spatial analysis and cartographic generalization. To develop a sound and effective approach to describe line-line relations, it is first necessary to define the topology of an individual line, i.e., local topology. The concept of connective degree is used for the identification of topological differences in the geometric structure of a line. The general topological definition of a line is given, i.e., endpoints set and interior point set. This definition can be applied to the embedded spaces of different dimensions, whether co-dimension is equal to or larger than zero. On this basis, a generic model called the 4 intersection-and-difference is set up for the description of basic line-line topological relations, upon which a conceptual neighborhood graph is built with consideration of topological distance, it is concluded that the proposed model can represent the property of topological changes, and basic relations between line segments in IR^1 and IR^2.

Yarn Architecture Analysis of Two-step 3D Braided Composites

A comprehensive study of yarn architecture of two-step rectangle 3D braided composites is presented. Firstly, the braided surface, the shapes of yarns and the intertwining between braider yams and axial yams are analyzed from experimentation. With the microstructure being defined, three levels of unit cell structure are identified, i.e. large unit cell, second unit cell and minimal unit cell. Secondly, based on the minimal unit cell in the interior and on the boundary of the entire cross-section, the deformations of axial yams squashed by braider yams contribute to the increase of the fiber packing factors of axial yams. Finally, the predicted fiber volume fraction of the composites decreases with the increase of linear density of the braider yam and the pitch length. Favorable correlations between the predicted and the experimental results arc found for six groups of the composites.

Coordinated Multi-User Spectrum Sharing in Distributed Antenna-Based Cognitive Radio Systems

Spectrum sharing for efficient reuse of licensed spectrum is an important concept for cognitive radio technologies.In a spectrum-sharing system(SSS),deploying the antennas in a distributed manner can offer a new spatial dimension for the efficient reuse of licensed frequency bands.To improve the whole performance of multiple secondary users(SUs),this paper addresses the problem of coordinated multi-SU spectrum sharing in a distributed antenna-based SSS.By adopting the Hungarian method,the primal decomposition method and pricing policy,we propose a coordinated multi-user transmission scheme,so as to maximize the sum-rate of SUs.Simulation results show that the proposed method can significantly enhance the system performance,and the computational complexity is low.

Numerical Simulation of Two-dimensional Nonlinear Sloshing Problems

Numerical simulation of a two-dimensional nonlinear sloshing problem is preceded by the finite element method. Two theories are used. One is fully nonlinear theory; the other is time domain second order theory. A liquid sloshing in a rectangular container subjected to a horizontal excitation is simulated using these two theories. Numerical results are obtained and comparisons are made. It is found that a good agreement is obtained for the case of small amplitude oscillation. For the situation of large amplitude excitation, although the differences between using the two theories are obvious the second order solution can still exhibit typical nonlinear features of nonlinear wave.

Numerical simulation of tire/soil interaction using a verified 3D finite element model

The compaction and stress generation on terrain were always investigated based on empirical approaches or testing methods for tire/soil interaction.However,the analysis should be performed for various tires and at different soil strengths.With the increasing capacity of numerical computers and simulation software,finite element modeling of tire/terrain interaction seems a good approach for predicting the effect of change on the parameters.In this work,an elaborated 3D model fully complianning with the geometry of radial tire 115/60R13 was established,using commercial code Solidwork Simulation.The hyper-elastic and incompressible rubber as tire main material was analyzed by Moony-Rivlin model.The Drucker-Prager yield criterion was used to model the soil compaction.Results show that the model realistically predicts the laboratory tests outputs of the modeled tire on the soft soil.

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.

Enhancement of Microcalcifications Based on Fractal Techniques in Mammograms

Microcalcification clusters in mammograms are an important early sign of breast cancer. The enhancement of mieroealcifications in mammograms is one of the most important preprocessing techniques for the extraction of cluster mierocalcifications. In this paper, we present a novel method for the enhancement of microcalcifications. Firstly, the initial microcaleification edges were extracted by using kirsch edge operator, and the diseontinouse edges were linked by employing fi＇aetal teehnique, Then, the continuous closed edges of microcalcifications were filled by using seed filling algorithm. The pixel values of the filled region were replaced by the corresponding pixel values in the original image. Finally, the enhancement of microcalcifications in mammograms was achieved by adding the filled image to the original image. We evaluated the performance of our algorithm by using 50 regions of interesting （ROIs） with microcalcification clusters from DDSM database. The experiment results demonstrate that our CAD system can give better enhancement effect compared with other methods.

GPU Accelerated Marine Data Visualization Method

The study of marine data visualization is of great value. Marine data, due to its large scale, random variation and multiresolution in nature, are hard to be visualized and analyzed. Nowadays, constructing an ocean model and visualizing model results have become some of the most important research topics of ‘Digital Ocean'. In this paper, a spherical ray casting method is developed to improve the traditional ray-casting algorithm and to make efficient use of GPUs. Aiming at the ocean current data, a 3D view-dependent line integral convolution method is used, in which the spatial frequency is adapted according to the distance from a camera. The study is based on a 3D virtual reality and visualization engine, namely the VV-Ocean. Some interactive operations are also provided to highlight the interesting structures and the characteristics of volumetric data. Finally, the marine data gathered in the East China Sea are displayed and analyzed. The results show that the method meets the requirements of real-time and interactive rendering.