Mathematical Sciences: Dynamics of Galaxies/Order and Chaos

这项提议将使用模态法将银河盘作为非线性动力系统来研究。为了确保模式方法是现实和可行的，将对选定星系的螺旋结构进行研究。因此，该理论将首先应用于已有观测数据的M81星系和银河系，并对螺旋模式进行了某些初步研究。接下来，我们将考虑与两组分基本平衡态(由恒星和星际气体组成)相关的微不稳定模之间的非线性相互作用。这一过程预计将受到气体成分的很大影响，其强烈的非线性响应、自引力和耗散特性将使螺旋结构趋于稳定。最后，在对各种物理过程进行数学处理后，将对这些过程进行分析研究。

This proposal will study the dynamics of galactic disks as nonlinear dynamical systems using the modal approach. To assure that the modal approach is realistic and viable, a study will be made of the spiral structure of selected galaxies. Thus, the theory will first be applied to the galaxy M81 and the Milky Way for which observational data are already available and certain preliminary studies of spiral modes have also been carried out. Next, the nonlinear interactions of the mildly unstable modes associated with a two-component basic equilibrium state (consisting of stars and interstellar gas) will be considered. This process is expected to be greatly influenced by the gaseous component whose strong nonlinear response, and self-gravitating and dissipative character would tend to stabilize the spiral structure. Finally analytical studies will be made of the various physical processes after these processes have been formulated for mathematical treatment.