岩石节理粗糙面的分形几何特性与剪切强度关系的实验研究

自然形成的岩石节理面的表面形状具有分形特性，利用分形理论来描述岩石节理的粗糙特性，并确立与岩石节理面的剪切力学特性间的关系对于指导岩体工程设计，和管理具有重要一研究利用开发设计的三维激光测距仪在精确测定岩石节理面的表面形状４ 基础上，依据变量图法建立了 岩石节理面的     

动态裂纹扩展中的分形效应

假设裂纹顶端沿着分形轨迹运动，建立了裂纹扩展的分形弯折（ｋｉｎｋｉｎｇ）模型来描述裂纹的动态扩展。根据这个模型，我们推导了分形裂纹扩展对劝态应力强度和裂纹速度的影响．动态应力强度因子与表观应力强度因子之比Ｋ（ｌ（ｔ），Ｖ）／Ｋ（Ｌ（ｔ），Ｏ）是表观裂纹速度Ｖ＿Ｏ，材料微结构参数（ｄ／Δａ），分维Ｄ和裂纹扩展路径的弯折角θ的函数。本文研究结果表明：在分形裂纹扩展中，表观（或量测）的裂纹速度Ｖ＿Ｏ很难接近Ｒａｙｌｅｉｇｈ波速Ｃ＿ｒ．动态断裂实验中Ｖ＿Ｏ明显低于Ｃ＿ｒ的原因可能是分形裂纹扩展效应所致。材料的微结构，裂纹扩展路径的分维和弯折角均很强地影响动态应力强度因子和裂纹扩展速度。     

结合部切向接触刚度分形模型研究

根据球体与平面接触的切向接触刚度和粗糙表面的接触分形理论，从理论上首次建立了结合部切向接触刚度分形模型，该模型具有尺度独立性。通过对所建模型的数字仿真，直观地给出了结合部切向接触刚度与其影响因素之间的非线性关系，并与实验研究结果具有较好的一致性，从而说明了该模型是合理的。     

Attractors of non-Newtonian fluids

The existence of global attractors is demonstrated for the dynamical systems generated by motions of nonlinear bipolar and non-Newtonian viscous fluids and upper bounds are obtained for the Hausdorff and fractal dimensions of the attractors for the bipolar case.     

从具体例子看惯性流形概念的推广

惯性流形的概念要求所有轨道指数收敛于唯一吸引子[5],这对于很多物理问题,例如sine-Gordon方程是很难满足的[4],本文中给出的人工例子建议了惯性流形的推广形式,这个推广形式去掉了整体吸引子是唯一的预先要求,该推广概念使用于sine-Gordon方程。     

Percolation theory approach to transport phenomena in porous media

The percolation theory approach to static and dynamic properties of the single- and two-phase fluid flow in porous media is described. Using percolation cluster scaling laws, one can obtain functional relations between the saturation fraction of a given phase and the capillary pressure, the relative permeability, and the dispersion coefficient, in drainage and imbibition processes. In addition, the scale dependency of the transport coefficient is shown to be an outcome of the fractal nature of pore space and of the random flow pattern of the fluids or contaminant.     

Bifurcations and chaos in parametrically excited single-degree-of-freedom systems

The behavior of single-degree-of-freedom systems possessing quadratic and cubic nonlinearities subject to parametric excitation is investigated. Both fundamental and principal parametric resonances are considered. A global bifurcation diagram in the excitation amplitude and excitation frequency domain is presented showing different possible stable steady-state solutions (attractors). Fractal basin maps for fundamental and principal parametric resonances when three attractors coexist are presented in color. An enlargement of one region of the map for principal parametric resonance reveals a Cantor-like set of fractal boundaries. For some cases, both periodic and chaotic attractors coexist.     

锡基巴氏合金磨损表面的分形与磨损率

利用结构函数分析法研究了滑动摩擦学系统中金属磨损表面轮廓线的分形特性。结果表明：磨损表面轮廓线在小于Ｓｍ的尺度上具有分形结构。采用结构函数法可以方便地确定粗糙表面轮廓线的分形参数，即垂直于滑动方向上磨损表面轮廓线的分维Ｄ可作为磨损表面分维的特征值，它与金属磨损率的变化有着密切的关系，最佳分维Ｄｏｐｔ值对应于材料的最低磨损率。     

Mean field calculation of effective permeability based on fractal pore space

Effective permeability for porous rocks is calculated using mean field theory. We make two simplifying assumptions about the internal conductances in a network representation of the porous rock: (i) Pore space is characterized by a uniform fractal scaling; (ii) the internal conductances depend only on the characteristic pore sizes. Within these approximations, it is possible to derive a simple probability density for the internal conductances which is used for calculating effective permeability. Good agreement between calculations and experimental data of permeability vs. porosity is achieved.     

Representation of discrete sequences with high-dimensional iterated function systems

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is self-affine or piece-wise self-affine in R ² or R ³ (R is the set of real numbers). In this paper, the piece-wise hidden-variable fractal model is extended from R ³ to R ⁿ (n is an integer greater than 3), which is called the high-dimensional piece-wise hidden-variable fractal model. This new model uses a “mapping partial derivative” and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the hidden variables. Therefore, the result is very general.