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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。通过对自相互作用系统的分析，利用鞍点法求出了配分函数。一维相变为二级相变，三维相变为一级相变. Tsallis/Renyi统计力学和CfA-II-South数据。非加性是自引力系统的本质。推广了Tsallis统计力学中的欧拉关系，得到了负参数q，。这反映了自引力系统的不稳定性.分形结构的起源（负比热和宇宙膨胀）。研究了被约束在圆周上的自引力粒子，寻找分形结构的起源。由力的短程奇异性引起的负比热是非高斯速度分布的根源. Las Campanas星系红移数据的多重分形分析。从2维的Las Campanas数据中提取了3维的信息，得出星系的分形分布延续到几十兆秒差距的结论.γ射线损伤的时间序列分析我调查的起源的幂律结构的功率谱的爆发配置文件。结果表明，这一现象的根源是弹丸的特殊形状，而不是弹丸的自相似结构.稳定分布的统计力学。我发现，Tsallis分布是一个很好的近似的稳定分布，和数学发散的分散体包括相关的信息的规模依赖。