山地城市的分形美学特征

分形美学以一种新观念和方法研究城市美学,通过建立简单分形模型探讨和度量城市的不规则性和复杂性,使山地城市美学研究从定性走向定量,从模糊走向科学。山地城市与平原城市比较,在地形地貌、空间形态和景观格局等方面表现出了独特的分形美学特征。     

分形城市引力模型的一般形式和应用方法--关于城市体系空间作用的引力理论探讨

基于分形思想和城市规模-产出关系推导出城市引力模型的一般形式Iij=GijMaiiMajjR-bij,论证了参数a和b的分维性质,并将引力系数定义为Gij=G|Rij,|/(1+Sij),式中Rii为i、j两城市的相关系数,Sij为二者的相似系数,G为量纲转换系数.以长春城镇体系和郑、汴、洛点-轴系统为实例说明了模型的应用方法,并指出了城市引力数值的相对性特征.作者发现,城镇体系各要素的引力之和Fi=∑Iij,在一定时空条件下满足位序-规模法则F(k)=F1K-q(k=1,2,…,n);这也表明,借助引力计算可以揭示城市体系某些隐含的地理规律.     

城市系统的异速生长关系与位序-规模法则——对Steindl模型的修正与发展

基于Steindl模型的建模思想，设置一个时间－年龄变量T，将城市规模（P）－数目（f)异速生长的假设条件重新构造为dP(T)/dT=gP(T),df(T)/dT=-rf(T)，据此导出反映城市等级－规模关系的Beckmann-Davis模型：P（m)-P1λ^m-1,f(m)=f1δ^1-m，进而导出三参数Zipf定律：P（r)=C(r-a)^-dx,式中g=lnλ，r=lnδ,C=p1[δ/(δ-1)]^dx，α=1/(1-δ),dz=g/r=lnλ/lnδ。根据几何测度关系建立分维方程：dz=Dp/Df，从而揭示：城市规模分布的分维D＝1／dz在本质上乃是城市体系空间结构的分维Df与各城市人口空间分布的平均维数Dp之比。     

Fractal models for the fragmentation of rocks and soils: a review

Fragmentation, the process of breaking apart into fragments, is caused by the propagation of multiple fractures at different length scales. Such fractures can be induced by dynamic crack growth during compressive/tensile loading or by stress waves during impact loading. Fragmentation of rocks occurs in resoonse to tectonic activity, percussive drilling, grinding and blasting. Soil fragmentation is the result of tillage and planting operations. Fractal theory, which deals with the scaling of hierarchical and irregur systems, offers new opportunities for modeling the fragmentation process. This paper reviews the literature on fractal models for the fragmentation of heterogeneous brittle earth materials. Fractal models are available for the fragmentation of: (1) classical aggregate; (2) aggregates with fractal pore space; and (3) aggregates with fractal surfaces. In each case, the aggregates are composed of building blocks of finite size. Structural failure is hierarchical in nature and takes place by multiple fracturing of the aggregated building blocks. The resulting number-size distribution of fragments depends on the probability of failure, P(1/bⁱ) at each level in the hierarchy. Models for both scale-invariant and scale-dependent are reviewed. In the case of scale-invariant P(1/bⁱ)< 1, theory predict: D_f = 3 + log [P(1/bⁱ)]/log[b] for classical aggregates; D_f=D_m+log[P(1/bⁱ)]/log[b] for aggregates with fractal pore space; and D_f=D_s for aggregates with fractal surfaces. where b is a scaling factor and D_f, D_m and D_s are the fragmentation, mass and surface fractal dimensions, respectively. The physical significance of these parameters is discussed, methods of estimating them are reviewed, and topics needing further research are identified.     

Elastic-wave velocities for porous media with power-law distribution of pore sizes

 A system consisting of an elastic matrix with randomly distributed pores of uniform shapes but with sizes governed by a power-law distribution is investigated in a theoretical way. The velocities of elastic waves propagating through such a system are calculated. The obtained results are that the velocities decrease with increasing total porosity and for a given porosity velocities moderately decrease with increasing absolute value of the exponent D in a power-law distribution of pore sizes. Received: 3 July 1995 / Accepted: 2 August 1996     

西北地区城市规模分形结构的研究

本文利用分形理论和相空间概念，从理论的角度演绎推导出城市规模分形结构的一般模式，并以此为基础，结合西北地区自然，经济，社会状况，对五省萄城市规模分形结构进行初步分析，为深入研究其城市体系，制定城市，区域发展战略提供一定的参考。     

泥石流的分形特征及其意义

分析了泥石流流体和堆积物粒度分布的分形结构特征，其分维值介于２￣３之间，平均值分别为２．７１和２．６５左右。研究了泥石流沟水系的分形特征及其在不同观察尺度下分维的变化特征，结果表明，分维可作为描述泥石流粒度成分和泥石流沟水系的参数，反映了泥石流活动的形成演化特征，在此基础上，论述了分维的研究意义。     

岩石断面的分形测量及其分维的计算

在实验室内使岩石单轴压缩直至破裂,用位移传感器测量其断面高度,用显微镜观测断面切片的剖线,所得数据用尺度法计算其分维,各种岩石的不同曲线的分维在1.002-1.028之间,与野外断层主迹线分维值相同.用切岛法计算整个断面的分维约为2.05左右.有关分析和计算认为,分维的大小与岩石破裂时所受力的方向有关,与采样步长有关,而与岩石样品的大小无关.     

研究地震和岩石破裂现象的非线性科学方法

本文以地震孕育和岩石破裂过程的阶段(包括裂纹系形成、变形局部化和断层形成、断层活动和松弛)为线索,阐述了非线性科学方法(包括分形几何学,自组织临界现象和混沌动力学)的应用,提出了地震孕育过程和岩石破裂各阶段的普适性特征、机理和要着重研究的课题.     

初探地震活动的时间分维特征

本文运用分维的概念和方法,对我国部分强震前地震活动时间分维,前震震群活动时间分维,7级以上大地震的余震活动时间分维和小震群活动时间分维进行了计算。初步结果表明,同一类型的地震活动(如强震前较大时空范围内地震活动、强震的余震、前震震群、小震群等类型)的时间分维十分相近,而不同类型地震活动的时间分维存在着差异,一般说来,强震前的地震活动比较普遍地存在降维现象,表现出临近强震时,震源及附近地区地震活动时间结构的有序性增强。这为地震预报开辟了一个新的途径。