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We generalize the collisions rules of the Sinai billiard to mimic collisions of two wet disks. The dissipative interaction of the disks leads to cooling and eventually to clustering. To work against this energy loss we shear the system by applying Lees-Edwards boundary conditions.
For sufficiently high shear rates the energy input due shearing overcompensates the dissipative interaction such that the ensemble average < E > of the particle energy increases linearly. We find that the energies are distributed according to an exponential function that scales with < E >. This has unexpected consequences: Due to the very large energy fluctuations the system may cluster even when starting from very high energies. Irrespective of shear rate the driven wet billiard system has a leak. Due to the non-compact phase space of the accelerating system we find an algebraic distribution of lifetimes: While the size of the leak is independent of < E > the size of the average occupied phase space grows with < E >. Hence the escape rate decreases with time which results in the algebraic decay of lifetimes. In the outlook we discuss how this mechanism to generate very long chaotic transients might also appear in systems with many degrees of freedom. |
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