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Relaxation Process of Gravitational N-body System its Application

引力N体系统的弛豫过程及其应用

基本信息

批准号：
02452062
负责人：
NAKAZAWA Kiyoshi
金额：
$ 4.8万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (B)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1992
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-02452062/
关键词：
Planetary Growth Statistical Behavior of Planetesimal N-body Simulation Origin of the Solar System Gravitational scattering Origin of the Solar System Gravitational Nーbody Simulation origin of the Solar System Gravitational Scattering

项目摘要

The main aim of this project is to achieve the following three themes:(1) Development of a new algorithm by which the relaxation processes in the gravitational N-body system can be simulated numerically, (2) Development of theoretical analysis on the statistical behavior of the gravitational N-body system, and (3) Formulation and development of a new method by which the planetary growth can persuade numerically. The results obtained in the three years are as follows:(1) We succeeded in developing a our new computational code by which the gravitational N-body system can be simulated efficiently. As a result we found that our code can simulate stably the time evolution of a system which is composed of 300 gravitational bodies or so. The basic concept and algorithm of our code will be presented in Publ. Astron. Soc. Jpn. in near future.(2) We succeeded in formulating the transport equation of Fokker-Planck type which describes the statistical behavior of gravitational bodies with two kinds of masses. Furthermore, by calculating numericallya number of scattering orbits we found the coefficients of deffusioned and dynamical friction. By the use of this formulation we will be able to study in detail the statistical behavior of a swarm of gravitating bodies orbiting under the solar gravity.(3) In place of the ordinary statistical coagulation equation which breaks down in describing the coagulation process in some cases, we succeeded in deriving an alternative equation which is exact stochastically. Solving the stochastic equation in various physical conditions, we studied the limit of the ordinary equation. The results are already summerized as a paper. We are now trying to develope a new computational code which can simulate the planetary growth on the basis of our stochastic coagulatin equation.

本项目的主要目标是实现以下三个主题：（1）开发一种新的算法，通过该算法可以数值模拟引力N体系统中的弛豫过程，（2）开发引力N体系统统计行为的理论分析，以及（3）制定和开发一种新的方法，通过该方法可以数值模拟行星生长。三年来取得的主要成果如下：（1）我们成功地开发了一个新的计算程序，可以有效地模拟引力N体系统。结果表明，我们的程序可以稳定地模拟由300个左右引力体组成的系统的时间演化。我们的编码的基本概念和算法将在Publ. Astron. Soc. Jpn中介绍。在不久将来。(2)我们成功地建立了描述两种质量引力体统计行为的Fokker-Planck型输运方程。此外，通过计算散射轨道的数目，我们得到了扩散摩擦系数和动力学摩擦系数。利用这个公式，我们将能够详细地研究在太阳引力作用下绕轨道运行的一群引力天体的统计行为。(3)本文成功地导出了一个精确的统计混凝方程，以代替在某些情况下不能描述混凝过程的常规统计混凝方程。在各种物理条件下求解随机方程，研究了常方程的极限。结果已经总结为论文。我们正在尝试开发一个新的计算程序，可以模拟行星增长的基础上，我们的随机凝聚方程。