Statistical Mechanics of Self Gravitating Systems

自引力系统的统计力学

基本信息

批准号：
11640263
负责人：
MORIKAWA Masahiro
金额：
$ 1.28万
依托单位：
Department of Physics, Ochanomizu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640263/
关键词：
self gravitating systems saddle point method non-additive statistical mechanics stable distributions negative specific heat fractal scale dependent dispersions gamma ray bursts Tsallis統計力学 CfAII南フラクタル自己臨界組織化

项目摘要

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.

1. 自引力/系统的鞍点法。通过分析自交互系统，我使用鞍点法评估了配分函数。 1-暗淡。相变是二阶的，并且是 3 维的。相变是一级相变。2． Tsallis/Renyi 统计力学和 CfA-II-South 数据。事实证明，非相加性是自引力系统的本质。推广 Tsallis 统计力学中的欧拉关系，我得到了负参数 q, 。这反映了自引力系统的不稳定性。3．分形结构的起源（负比热和宇宙膨胀）。研究约束在圆上的自引力粒子，寻找分形结构的起源。力的短距离奇异性产生的负比热是非高斯速度分布的根源。 4．拉斯坎帕纳斯星系红移 deta 的多重分形分析。从 2 维。拉斯坎帕纳斯数据；我提取了v3-dim。信息并得出结论，星系的分形分布持续到几个10Mpc.5。伽马射线伤害的时序分析。我研究了突发剖面功率谱中幂律结构的起源。结果证明，起源是镜头的特殊形式，而不是脉冲的自相似结构。6．稳定分布的统计力学。我发现 Tsallis 分布是稳定分布的良好近似，并且数学上发散的离散度包含尺度依赖性的相关信息。