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Analysis And Control Of Diffusion Limited Aggregate Growth

Posted on:2009-02-13Degree:MasterType:Thesis
Country:ChinaCandidate:S L ShenFull Text:PDF
GTID:2120360245994663Subject:Control theory and control engineering
Abstract/Summary:PDF Full Text Request
Fractal growth is a very important research direction in fractal theory and its application. Diffusion limited aggregation is a typical fractal growth process, which has been applied widely in biology, physics, mathematics, engineering and other fields. It provides a basic understanding for many other growth process and also it can be used to predict the relationship between growth rate and time of actual random cohesion, as well as their physical mechanism and transport properties. Especially, it is used to simulate the spread of cancer cells cohesion in recent years, making fractal growth become a hot research in the field of nonlinear science. At present, most of the research focuses on computer simulation. Therefore the study of the mathematical mechanism and physical mechanism becomes more important. Starting with the mathematical model of diffusion limited aggregation, the growth process is analyzed in detail in this paper. The main contents and results are as follows:Based on the simulation of Laplace equation, the growth model is improved and the growth process is simulated, which provides a base for the next step of this research.Iterative steps are introduced in Laplace equation based on the meaning of random walk. And the impact on fractal structures and dimensions about the changing of the iterative steps is analyzed. Especially, it shows that the fractal has a property of anisotropic growth when steps are unequal on all directions.The heat conduction equation is applied to the field of fractal. The impact of different source terms on concentration distribution which determines the fractal growth is analyzed by studying the discrete diffusion equation. The fractal growth is controlled affectively. And a method is also provided as a paradigm for reasonable selection of control parameters and control region, which makes the complicated dynamic behavior of diffusion limited aggregation growth become predictable and controllable.Conclusions and forecast are given at the end of the paper.
Keywords/Search Tags:fractal growth, diffusion limited aggregate, iterative step, source term
PDF Full Text Request
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