Statistical Mechanics of Self Gravitating Systems

1. 自重力系统的鞍点法。在分析自相互作用系统时，用鞍点法求配分函数。1-dim。相变是二阶的，3-dim。相变是一阶的。Tsallis/Renyi统计力学和CfA-II-South数据。非可加性是自引力系统的本质。推广Tsallis统计力学中的欧拉关系，得到负参数q，。这反映了自重力系统的不稳定性。分形结构的起源（负比热与宇宙膨胀）。研究了约束在圆上的自引力粒子，寻求分形结构的起源。负比热来源于力的近距离奇点，是非高斯速度分布的起源。拉斯坎帕纳斯星系红移数据的多重分形分析。从2-dim开始。Las Campanas数据；我提取了v3-dim。得出的结论是，星系的分形分布可以持续到几个10Mpc.5。伽玛射线损伤的时间序列分析。我研究了爆炸剖面功率谱中幂律结构的起源。事实证明，其起源是镜头的特殊形式，而不是镜头的自相似结构。稳定分布的统计力学。我发现，Tsallis分布是稳定分布的一个很好的近似值，数学上的发散色散包含了尺度依赖的相关信息。

1. Saddle poit method for the self gravitating/systems. Analyzing the self interacting systems, I evaluated the partition function by using the saddle point method. The 1-dim. phase transition is of second order, and the 3-dim. phase transition is of first order.2. Tsallis/Renyi statistical mechanics and the CfA-II-South data. The non-additivity turnd out to be the essence of the self gravitationg systems. Generalizing Euler relation in Tsallis statistical mechanics, I obtained negative parameter q,. which reflects the instability of the self gravitating systems.3. The origin of the fractal structure (negative specific heat an the cosmic expansion). Self gravitating particles constrained on a circle is investigated seeking for the origin of fractal structure. The negative specific heat, which comes from the short-distance singularity of the force, turned out to be the origin for the non-Gaussian velocity distributions.4. Multi-fractal analysis of Las Campanas galaxy redshift deta. From the 2-dim. Las Campanas data ; I extracted thev3-dim. information and concluded that the fractal distribution of galaxies continue upto several 10Mpc.5. Time sequence analysis of Gamma-ray hurts. I investigated the origin of the power-law structure in the power spectrum of the burst profile. The origin turned out to be the special form of the shots and not the self-similar structures of the burts.6. Statistical mechanics of the stable distributions. I found that the Tsallis distribution is a good approximation of the stable distributions, and the mathematically divergent dispersions include relevant information of the scale dependence.