Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 13: Granular Matter/ Contact Dynamics II

DY 13.6: Talk

Wednesday, March 24, 2010, 11:00–11:15, H47

Acceleration, Clustering and Superlong Transients in a Billiard Model for Wet Granular Matter — Franziska Glaßmeier, Diego Fregolente, Martin Brinkmann, and •Jürgen Vollmer — MPI for Dynamics and Self-Organization, Bunsenstr. 10, 37073 Göttingen, Germany

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 to shearing overcompensates the dissipative interaction such that the ensemble average of the particle energy ⟨ E⟩ increases linearly. 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 has a leak for all shear rates. Consequently, the disks may cluster even when started from very high energies.

Suprisingly, we observe an algebraic distribution of lifetimes. It is due to the non-compact phase space of the accelerating system. A relation of this phenomenon to Fermi acceleration in time-dependent billiards, and generalizations to more particles are discussed in the end.