Hierarchical clustering and formation of a power law correlation in a one-dimensional self-gravitating system

Abstract

The process of formation of a power law correlation structure ina one-dimensional self-gravitating system is examined numerically.It is clarified that structures created in small spatial scalegrow up to larger scale through clustering of clusters, and form apower law correlation. With the help of the Lyapunov vector, the relationbetween the instability in small spatial scale and the particle-like(non-fluid) behavior of the system is discussed.