The Study Of Anisotropy Diffusion Fractal Growth

The study of anisotropy fractal growth is an international topic, which has greatsignificance. The first chapter introduces the current status of research on this subject at homeand abroad; the second chapter explains the basic concepts and the research methods of fractal,including definition, classification, fractal dimension and multifractal theory and algorithms;the third chapter explained the full conditions and the physical mechanisms of fractal growth,and then for the diffusion limited aggregation model, we studied its patterns structure andanalysis on the scale properties by computer simulation.The forth chapter studies the fractal coagulation of particles in Euclidean space. Firstly,we simulate growth of DLA model in two-dimensional plane by using Monte Carlo methods,and analysis the fractal dimension and multifractal spectrum. What’s more, we discussed thescaling property of the anisotropic diffusion aggregation group, respectively when "seeds"were "point seed" and "line seed". We did computer simulation of this two cases, got patternsstructure of both cases, and calculated the multifractal spectrum. From simulation results wefound the relationship between DLA growth and line length L : The growth patterns of DLAstructure takes on "+" type as L increasing; The fractal dimension D continue to decreaseand so area min，a max; And the quality of DLA growth is more uniformity.The fifth chapter studies how uniform external field influent on the DLA growth of agroup in the two-dimensional plane. We fulfilled DLA growth patterns of a component intwo-dimensional plane when plus the outfield, by using Monte Carlo methods, analyzed of itsnature, and calculated its fractal dimension and multifractal spectrum. When comparing withthat without outfield, we found outfield will effect on homogeneity and symmetry of DLAgrowth, and increasing the field strength will reduce homogeneity and symmetry. Then, forvariable size seeds, we simulated its diffusion aggregation fractal growth in two-dimensionalspace and three-dimensional space, and analyzed its fractal dimension and multifractalspectrum. We got result is the concentration and diameter of particle have effects onhomogeneity and symmetry of the fractal growth. As the concentration increasing, thesymmetry of DLA growth first increase and then decrease, but when particle diameterincrease, the growth group will lose its symmetry.In chapter six, we designed two different Sierpinski carpets by the Mapping DilationMethod, simulated DLA fractal growth by computer, received the pattern structures, andcalculated the fractal dimension and the multifractal spectrum. Then, when pipe radius abbeynon-uniform distribution, for immiscible displacement in the Sierpinski carpet, we designed adeterministic model algorithm, simulated the fractal viscous fingering in the grid by usingsuccessive super relaxation technique, and got some new properties. The result indicated thatthe ratio of viscous and geometric topology structure of porous media had effects on thestructure of VF, fractal dimension and drive sweep efficiency. When the ratio ofviscous M reduces or parameter k increases, displacement fluid sweep range will increase,that is to say the space effectiveness of viscous fingering will increase, and will lead to fractal dimension and flood sweep efficiency increase.