Research On Model Design And Application Of Fractal Aggregation And Dispersion

Fractal is an important part of nonlinear science,and agglomeration and dispersion are the two basic processes of fractal growth.These two processes are often random,but they often have self-organization and self-similarity behind the random processes.Many things in nature and society show up agglomeration and dispersion process obviously,such as formation of snowflake,growth of crystalline thin films,formation of soil aggregates,proliferation of cancer cells,expansion of urban scale and evolution of social network and so on.Because of the randomness of the nonlinear process,it is difficult to get the law behind the random phenomenon by the ordinary test method.However,we can break through some limitations through computer simulation,and reasonably adjust the control parameters according to needs,and get some related information about aggregation and dispersion quickly,then achieve the analysis and evaluation of the fractal growth phenomenon.The process of fractal growth is often from scratch,from small to large.So,most of the traditional studies paid more attention to the construction of the cohesive model and ignored or disregarded the dispersal process consciously or unintentionally.In fact,the development of things has never been achieved overnight.The process of fractal growth is also accompanied by dispersion in cohesion,with agglomeration in dispersion.Therefore,establishing a fractal growth model based on condensation and dispersion coupling is of great theoretical and practical significance for a deep understanding of fractal phenomena in nonlinear science.The main work and results of this paper are as follows:(1)Constructing a unified model of fractal agglomeration based on the lattice model.This model unifies all the growth models in the traditional sense,which means the results of the cohesive models in the traditional sense can be obtained by this model with the modification of some corresponding control parameters.This unified model not only provides convenience for the simulation research,but also makes a unified form of other cohesive models,which provides a possibility for revealing the essential law behind the condensation process.(2)Constructing a unified model of fractal dispersion based on lattice mode.The traditional dispersion model is based on the change of the external shear flow field,which leads to the deformation of the aggregate firstly,and then causes the disintegration.In fact,there are often explosive dispersion,split dispersion and erosive dispersion in the form of dispersion.In terms of dispersion,explosive dispersion often means "one is more than one",and split dispersion often means "one is a few",while the erosion type is often "from outside and inside".The decentralized model established in this paper can integrate these three kinds of dispersion.The control parameter is just the choice of the dispersed location and the determination of the dispersion probability,and this model is also a useful tool to explore the rule of the dispersion process(3)Constructing a unified model for fractal growth based on lattice model.The fractal growth model is the organic coupling of fractal agglomeration and fractal dispersion.The particle has diffusion model,collision model,process model or aggregation model.It is a key link of fractal growth model,and based on the theory of stochastic process,and it can reveal self-organization and self-similar characteristics behind the random process by using the related curves.With such a unified model of fractal growth,the work of fractal growth will not only stay on some interesting pictures,more importantly,the growth process of fractal can be controllable,and reveal the dynamics of fractal growth.In this paper,the basic rules and relationship of aggregation,dispersion and growth are revealed from the fractal characteristics of aggregates,cluster concentration,cluster distribution and so on.(4)This paper uses the Java programming language to develop the simulation software of fractal aggregation,fractal dispersion and fractal growth in the Eclipse programming environment,and realize the visualization of fractal aggregation,fractal dispersion and fractal growth process using Java3 D technology.(5)The fractal aggregation model,fractal dispersion model and fractal growth model have been verified in the field of soil colloids.This paper discusses the formation and dispersion and evolution process of soil aggregate,and researches the stability of soil aggregate from the point of computer simulation of soil aggregate,and gets some coincident result compared with some related tests.This test provides a strong support for the later research of soil erosion and soil crust research.In conclusion,the model established in this study has important theoretical significance for in-depth study of fractal growth.At the same time,it has practical application value in discussing the stability of soil aggregate and offering supplement to traditional experimental research.