Rotating Matter: The Bearing State*

Granular materials are characterized by an additional degree of freedom, rotations,
which become particularly relevant for spherical particles.
A packing of spheres is called bi-chromatic if every loop formed by contacts is even.
In three dimensions, bi-chromatic bearings have many different sliding-free configurations,
so called bearing states. Packings with bearing states can even be made space-filling.
Their bearing states can be viewed as a realization of solid turbulence exhibiting Kolmogorov
scaling and anomalous heat conduction. In three dimensions a continuum of such configurations
can be obtained as cuts through four-dimensional space-filling bearing states. Bearings states can be
perceived as physical realizations of networks of oscillators with asymmetrically weighted couplings.
These networks can exhibit optimal synchronization properties through tuning of the local
interaction strength as a function of node degree or the inertia of their constituting rotor disks
through a power-law mass-radius relation . Under this condition, the average participation per disk is
maximized and the energy dissipation rate is homogeneously distributed among elementary rotors.
The synchronization of rotations occurs in avalanches following a broad size distribution.