Clustering motions in N-body systems - Computer experiments of kinetic laws -

The dynamical process of cluster formation is numerically studied by carrying out with 2-dimensional N-body systems under short-range interactions. First, we give a theoretical definition of cluster boundaries by use of a scalar field of the Gauss-Riemann curvature. Based on this lucid definition, we can obtain much reliable information regarding statistical aspects of clustering motion. The energy dependence of the cluster size exhibits phase-transition-like behavior, as predicted by the cell model, and the velocity distribution function obeys the Maxwell-Boltzmann statistics not only in the gaseous phase but also in the cluster. However, it is pointed that the fluctuations of the cluster's shape reveal very long time memories, even in the equilibrium state. Secondly, the kinetic aspects of each particle are analyzed from the residence time distribution. The residence time in the gaseous phase obeys a Poisson distribution, but in the droplet phase it obeys a Negative-Weibull distribution with the exponent α (≃ 1.7) within a certain scaling regime. Also, it is elucidated that the intrinsic long time behavior obeys the universal law of nearly integrable Hamiltonian dynamics, and that the symbolic dynamics of one particle display 1/f spectra very stably. Lastly, it is pointed out that these two regimes, i.e., the Negative-Weibull regime and the universal long time regime, correspond to different phases coexisting in a cluster, and the interdependence between both phases is discussed in relation to the stochastic theory of nucleation.