相变演化Suliciu模型中波的相互作用

基金项目: 国家重点基础研究计划“非线性科学”项目;自然科学基金资助项目(10002002,90407021)

Wave Interactions in Suliciu Model for Dynaimc Phase Transitions

LTCS, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China

摘要: 描述相变演化的Suliciu模型，其基本波可由行波分析得到．对于任何给定分两段常值的初始状态，相应的Riemann解是某些基本波的组合．对分三段常值的初始状态，解由上述Riemann解构成，其中相邻两状态间以基本波连接．当基本波发生碰撞时，新的Riemann问题形成．通过研究这些Riemann问题，可以在适当的参数空间中对基本波之间复杂的相互作用加以分类．
- 相变 /
- Suliciu模型 /
- 波的相互作用
Abstract: Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis.For any given initial data with two pieces of constant states,the Riemann solutions are constructed as a combination of elementary waves.When the initial profile contains three pieces of constant states,the solution may be constructed from the Riemann solutions,with each two adjacent states connected by elementary waves.A new Riemann problem forms when these two waves collide.Through the exploration of these Riemann problems,the outcome of wave interactions may be classified in a suitable parametric space.
- phase transition /
- Suliciu model /
- wave interaction

[1]	Wilson K G.The renormalization group and critical phenomena[J].Reviews of Modern Physics,1983,55(3):583—600. doi: 10.1103/RevModPhys.55.583
[2]	Hsieh D Y,Tang S,Wang X P.On hydrodynamic instability, chaos, and phase transition[J].Acta Mechanica Sinica,1996,12(1):1—14. doi: 10.1007/BF02486757
[3]	Faciu C,Suliciu I.A maxwell model for pseudoelastic materials[J].Scripta Metallurgica et Materialia,1994,31(10):1399—1404. doi: 10.1016/0956-716X(94)90125-2
[4]	Natalini R, Tang S. Discrete kinetic models for dynamical phase transitions [J].Communication on Applied Nonlinear Analysis,2000,7(2):1—32.
[5]	Qian J.非线性数值分析中的两个问题[D].硕士论文.北京：北京大学2003，1—35.