FRACTAL VISCOUS FINGERING AND ITS SCALING STRUCTURE IN RANDOM SIERPINSKI CARPET

Viscous fingering (VF) in random Sierpinski carpet is investigated by means of successive over-relaxation technique and under the assumption that bond radii are of Rayleigh distribution. In the random Sierpinski network, the VF pattern of porous media in the limit M→∞ (M is the viscosity ratio and equals to η₂/η₁ where η₁ and η₂ are the viscosities of the injected and displaced fluids, respectively) is found to be similar to the diffusion-limited aggregation (DLA) pattern. The interior of the cluster of the displacing fluid is compact on long length scales when M=1, and the pores in the interior of the cluster have been completely swept by the displacing fluid. For finite values of M such as M≥10, the pores in the interior of the cluster have been only partly swept by the displacing fluid on short length scales. But for values of M in 1f(α) sites have velocites scaling as L^-α; and the scaling function f(α) is measured and its variation with M is found.     

沉积岩中的分形及其在石油勘探和开发中的应用

介绍了沉积岩的分形性质，简述了沉积岩中的分形在石油勘探和开发中的应用．     

Scaling Behaviour of Diffusion Limited Aggregation with Linear Seed

We present a computer model of diffusion limited aggregation with linear seed. The clusters with varying linear seed lengths are simulated, and their pattern structure, fractal dimension and multifractal spectrum are obtained. The simulation results show that the linear seed length has little effect on the pattern structure of the aggregation clusters if its length is comparatively shorter. With its increasing, the linear seed length has stronger effects on the pattern structure, while the dimension D f decreases. When the linear seed length is larger, the corresponding pattern structure is cross alike. The larger the linear seed length is, the more obvious the cross-like structure with more particles clustering at the two ends of the linear seed and along the vertical direction to the centre of the linear seed. Furthermore, the multifractal spectra curve becomes lower and the range of singularity narrower. The longer the length of a linear seed is, the less irregular and nonuniform the pattern becomes.     

圆锥复数及其在物理学中的应用

圆锥复数是一种泛复数,由它可以非常方便地导出伽里略变化、洛伦兹变换和欧几里得变换,以及相应的速度变换规律,而这些规律分别是研究低速运动、高速运动和超光速运动的基础.下面简要地介绍圆锥复数的性质及其在物理学中的应用. 考虑某虚单位ω,它可用来定义泛复数 a=α+βω,(1)这里α,β均为实数.若ω分别取i,j,κ 且满足以下诸式 a=α+βi(i满足 i~2+1=0),(2) a=α+βj(j满足j~2-1=0),(3) a=α+βK(K满足K~2=0,(4)我们把(2),(3),(4)式的α分别称为椭圆数(简记为C)、双曲数(简记为H)和抛物数(简记为P),并统称为平面泛复数或圆锥复数. …     

自仿射Sierpinski地毯中的粘滞指进

构造了自仿射Sierpinski地毯.在自仿射Sierpinski地毯中,认为喉管半径服从截断瑞利分布,采用逐次超松弛技术,模拟了自仿射Sierpinski地毯中的粘滞指进.计算了粘滞指进分维,结果表明,当粘滞比M→∞时,指进图样与在自仿射Sierpinski地毯中DLA模拟的结果类似：当M=1时,驱替流体在长标度范围内具有紧凑的结构,且具有稳定的位移. 关键词：     

各向异性扩散DLA集团的豪斯道夫维数与标度性质

讨论了DLA集团的各向异性扩散效应.计算机模拟证实了具有各向异性扩散规则的DLA集团有严格的菱形结构.导出了一个粒子的各向异性扩散的新方程，计算了各向异性扩散DLA集团的豪斯道夫维数，结果表明，有效外半角β_eff=min(β_ix,β_iy).讨论了各向异性扩散DLA集团的广义维数，使用修改的楔模型得到了广义维数D_q的表达式. 关键词：     

Pattern Structure and Properties of Invasion Percolation in Porous Media

The percolation clusters with varying occupy probability are constructed.Invasion percolation(IP)in percolation cluster is investigated by means of IP alporithm without trapping.The pattern constructions of IP in percolation clusters are obviously different from that of visocous fingering(VF) in percolation clusters.The fractal dimension Df of IP increases with increasing the percolation probability P.The geometry and the topology of the porous media have strong effects on the pattern structure of IP.For large M(the node numbers occupied by the injected fluid),the rescaled value is Rg/M^1/Df,which asymptotically approaches a constant value,and Rg is the gyration radius of IP cluster,Moreover,the chemical dimension Dl and the shortest path exponent dmin are obtained.     

THE IMMISCIBLE DISPLACEMENT IN PERCOLATION CLUSTER

The percolation clusters with varying occupy probability were constructed in this paper. Viscous fingering (VF) in percolation cluster, based on the assumption that bond radii are Rayleigh distribution, is investigated by means of successive over-relaxation technique. The fractal dimension for VF in percolation cluster is calculated. The result shows that it can increase fractal dimension of VF as increase of percolation probability of reduce of viscous ratio. VF's fractal dimension of porous media in the limit viscous ratio →∞ is found to be identical with that in diffusion limited-aggregation. We have found that the topology and the geometry of the porous medium have strong effects on the displacement processes and the structure of the VF. We find that the sweep efficiency of the displacement processes mainly depends upon the length of the network system and also on the viscosity ratio. Moreover, the fractional flow of injected fluid as a function of mean saturation is obtained.