On Hamiltonian particle dynamics

This paper focuses on Hamiltonian description of phenomena and presents a m ethod of analyzing various kinds of scale phenomena from a unified viewpoin t. The method is based on both the Hamiltonian formulation of a system and the particle methods, and is therefore called Hamiltonian Particle Dynamics (HPD). In this paper, the background and the elementary concepts of HPD ar e explained and an example of HPD applications, namely the behavior of inco mpressible inviscid fluid, is solved. In order to improve accuracy of HPD w ith respect to space, it is combined with CIVA, a highly accurate interpola tion method, but the combined method is subject to problems in that the inv ariants of the system are not conserved in a long-time computation. For sol ving the problems, symplectic time integrators are introduced and the effec tiveness is confirmed by mathematical and numerical analyses.