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。自我引力/系统的马鞍poit方法。分析自相互作用系统，我使用鞍点方法评估了分区功能。 1-dim。相变是二阶，而3-dim。相变是一阶的2。 Tsallis/Renyi统计力学和CFA-II - 南数据。非促进性是自我重力系统的本质。在tsallis统计力学中概括了Euler的关系，我获得了负参数Q。这反映了自我引力系统的不稳定。3。分形结构的起源（负比热和宇宙膨胀）。研究了在一个圆圈上限制的自着引力颗粒，以寻求分形结构的起源。负比热来自力的短距离奇异性，事实证明是非高斯速度分布的起源。4。 Las Campanas Galaxy Redshift Deta的多骨分析。来自2二键。 Las Campanas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。伽马射线的时间序列分析受伤。我研究了爆发轮廓功率谱中幂律结构的起源。原来原来是镜头的特殊形式，而不是Burts.6的自相似结构。稳定分布的统计力学。我发现tsallis分布是稳定分布的良好近似值，并且数学上不同的分散体包括量表依赖性的相关信息。