Dynamics that trigger/inhibit cluster formation in a one-dimensional granular gas

We present a study of a one-dimensional granular gas of point-like particles not subject to gravity between two walls at granular-temperatures T− and T+, with T−<T+ and submit a physical picture of the mechanism that triggers or inhibits cluster formation. It is known that, depending on the normalized temperature difference Δ=(T+−T−)/(T++T−), the system may be completely fluidized, or in a mixed state in which a cluster coexists with the fluidized gas. We devise and explain in detail a method for integrating the one-dimensional dissipative Boltzmann equation in the test-particle limit for the stationary case. The behavior of the system in its fluid phase is dominated by characteristic lines which are trajectories of particles subjected to a force which attracts them to a fixed point. If this point lies between the two walls a cluster forms, if not then the system remains fluidized.