格子玻尔兹曼方法研究激发介质中的非线性波-理论物理专业论文.docxVIP

PAGE PAGE IV Lattice Boltzmann Method For Nonlinear Waves In Excitable Media Graduate student: Chen chao Advisers: Vice-Prof. DengMinYi Prof. KongLingJiang Specialty: Theoretical Physics Direction: Computation Physics Grade: 2007 Abstract The characteristic of nonlinear waves in excitable media is one of the current research focus. The spiral wave and its fragmentation usually do harm to the practical systems. Therefore, it has greatly practical significance to study the characteristic of the nonlinear wave. With many merits such as higher precision, simple code and excellent stability, Lattice Boltzmann method has become an effective tool for studying the nature of nonlinear wave. In this paper, we studied the nonlinear wave in the Selkov reaction-diffusion system by using Lattice Boltzmann method. First of all, we established the 9-speed square lattice model for the reaction-diffusion equations and deduced the reaction-diffusion equations from the Lattice Boltzmann equation. Next, we divided the two-dimensional system into 300 × 300 grids and simulated it under the no-flow boundary condition by using computer. The main works of this paper include three parts as follow: First, when taking the parameters as a = 0.76 ， b = 0.02 ， χ = 0.1 ， κ = 5.0 , DX = DY = 0.1, the numerical simulation results show that the system is excitable. Under the same parameters, the system can evolve to different nonlinear waves starting from different initial states, and the system can evolve into three different states such as the spiral wave state, spatiotemporal chaos state and uniform state starting from the same state with different parameters. It is also found that the spiral wave instability in the Selkov reaction system is the Doppler instability. The system phase diagrams within a certain range of parameters are shown through the simulation of the system evolution under a variety of parameters. Second, based on the theory of the lattice Boltzmann method, it i