Nonlinear Waves And Phase Transition In Dust Crystals

In recent years, dusty plasma has become a fast-growing branch of the plasma sci-ence. It reveals very strong coupling characteristics due to the strong coulomb interaction and low temperature. It was found that there were a considerable number of, and ordered structural dust particles floating on the top of discharging plate, which exhibit a similar hexagonal crystal structure (the so-called dust lattice) such as plane, face-centered cubic and body-centered cubic under certain conditions. Dust lattice is a prosperous research direction not only because it can provide a realistic, easy-to-control experimental proto-type for the strongly-coupled plasma theory, but also it can be used as a bridge connecting the dust plasma physics and condensed matter physics. The dust lattice can contribute the understanding of some processes in the solid state physics. The main purpose of this thesis is to study the solitary wave interaction in the dust lattice and the measure synchronization and phase transitions in one-dimensional Frenkel-Kontorova (FK) model systems.The thesis is divided into four chapters:in ChapterⅠ, we gave a brief introduction of the fundamentals of the plasma and its applications; in ChapterⅡ, the Korteweg-de Vries(KdV) equation which describes the behaviors of solitary waves and the phase shift and the track has been obtained by studying the collision of the two solitary waves in any angle of the hexagonal lattice in two different directions based on the Poincare-Lighthill-Kuo(PLK) perturbation method. The dependence of the phase shift on the system pa-rameters was also studied; in chapterⅢ, we use the Frenkel-Kontorova(FK) model to study the measure synchronization and phase transition of two coupled particles. It was found that the two orbits have the same average phase space when the coupling strength is greater than a critical value defined in the measure synchronization,, Furthermore, we studied the relationship between the measure synchronization and the system parameters. Finally, a summary of this article and future work in this field were discussed.