Relaxation Process of Gravitational N-body System its Application

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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.