Abstract
Failing to satisfy Liouville's theorem, the dynamics of granular materials is affected by the attractors in their phase spaces. Motion of inelastic hard disks in a thin pipe with energy sources at both ends of the pipe is simulated and the statistical steady state is studied. We investigate the probability distribution function of the spacing $l$ between neighboring particles, and find that the attractors can lead to a phase of the cluster of particles with structures different from that of an ideal gas.
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