The Simulation And Research Of Self-organizing Phenomenon In Two Reactive-diffusion Systems Based On Cellular Automaton

Most of the systems involved in nature and industry are complex systems,and the complexity of these systems has been paid attention to for years.The reaction-diffusion system is a complex system,as reaction and diffusion are coupled with other in this process,among which self-organization phenomenon is particularly prominent in many complex phenomena.For simulation,the traditional method to establish partial differential equations is limited to the high coupling of the system.The cellular automaton has the advantages of an automatic decoupling system and is easy to display,which is suitable for the self-organization phenomenon of the reaction-diffusion system.On this basis,the two reaction-diffusion system,Belousov-Zhabotinsky(B-Z)reactiondiffusion system and crystallization system,self-organization phenomenon,including chemical wave,diagram,crystal,crystal morphology and the structure of a cellular automata model,can display the appearance of crystals and the distribution of the crystal particles.Specifically,this thesis is divided into three parts.The first part is the research method.Cellular Automata has grid-induced anisotropy when it is used to simulate reaction-diffusion systems.Therefore,the cause of the problem and the method to eliminate it are first discussed.It also includes how to display the anisotropy imposed by the simulation model itself on the basis of eliminating the grid-induced anisotropy.Different from solving partial differential equations,cellular automata considers a subsystem instead of a particle.Its disadvantage is that the geometric shape of the bottom grid and the selected neighborhood can strongly affect the evolution results of cellular automata,which limits the application of cellular automata in accurate quantitative problems.In order to improve the universality of the cellular automata model,a suitable cellular automata model is not selected according to the anisotropy of the system.On the basis of eliminating the anisotropy of the grid,the anisotropy of the model is added to the evolution rule of the square grid.In the second part,the self-organization phenomena in two kinds of reaction-diffusion systems are simulated from the time and space levels by using the characteristics of cellular automata algorithm.This part includes two aspects,the chemical pattern in the B-Z reaction-diffusion system and the different crystal morphologies in the crystallization process.B-Z reactiondiffusion system is a relatively simple complex system with rich selforganization behavior and relatively clear mechanism.By analyzing the stability of the B-Z reaction-diffusion system,the different parameter conditions of self-organization phenomenon and self-organization behavior of the B-Z reaction-diffusion system are obtained.The effects of different reaction parameters and different diffusion parameters on the self-organization phenomenon are simulated by cellular automata,and the state of selforganization phenomenon in different media,including the effects of different diffusion media and different reactant composition,is discussed.Based on the B-Z reaction-diffusion system simulated by cellular automata,the cellular automata model of crystallization process is established.Taking the snowflake process produced by water crystallization as an example,the influence of different crystallization conditions on crystal morphology is discussed,especially the influence of the difference between reaction speed and diffusion speed on crystal morphology.The third part is to simulate the crystallization process in industry by using cellular automata.Because the crystal morphology and particle size distribution have a great influence on the quality of crystal products,these two kinds of information are very important for fine production.In this paper,cellular automata is used to describe the growth process of each crystal from the mesoscopic scale,and a cellular automata model is established,which can not only show the crystal morphology,but also show the crystal size distribution,and then a cellular automata simulation framework for guiding industrial production can be established.The crystallization process of potassium nitrate and potassium dihydrogen phosphate is simulated,and the particle size distribution of the simulation results is compared with that of the highresolution finite volume method,which proved the feasibility of the simulation method.The simulation speed is not only faster than that of the high-resolution finite volume method,but also the crystal morphology can be displayed.Through these three parts,the cellular automata simulation framework of reaction-diffusion system is established,the self-organization phenomenon in reaction-diffusion systems is shown,and the influence of reaction-diffusion on self-organization morphology is discussed.Compared with the traditional method of establishing partial differential equations in numerical discrete solutions,cellular automata can display the whole evolution process of the system only with an initial value.It does not need to solve complex boundary conditions,the calculation speed is fast,and it can be arbitrarily put together.It can not only provide guidance for industrial production,but also provide method reference for further study of more complex phenomena of reactiondiffusion system simulation.