Numerical simulation by N-body gravitational algorithm employing analytical Kepler's solutions in two- and three-dimensional systems

Yasutaro Nishimura^1*

¹College of Sciences, National Cheng Kung University, Tainan, Taiwan

* Presenter:Yasutaro Nishimura, email:nishimura@pssc.ncku.edu.tw

An N-body numerical simulation tool is developed in two- and three-dimensional systems. Instead of employing conventional softening parameters at the binary collisions, we have employed the analytical Kepler solutions when the kinetic energy and potential energy of the central force became comparable, which are successfully connected to the numerical solutions of the N-body simulation. The work is extended to a three-dimensional system. At the binary collisions, reminding Kepler's law, we find out local planes where the two orbits reside. In charged particle system, having both the ions and electrons (and thus both the attractive and repulsive forces), Debye shielding is inherent. We seek for particles' diffusion and how the irreversibility comes into play to the system. This work is supported by Taiwan MOST 109-2112-M-006-009- and
MOST 110-2112-M-006-0013-.

Keywords: N-body simulation, Kepler's solution, Central force, Debye shielding, Origin of irreversibility