Abstract
In a bearing state, touching spheres (disks in two dimensions) roll on
each other without slip. Here we frustrate a system of touching spheres
by imposing two different bearing states on opposite sides and search
for the configurations of lowest energy dissipation. If the dissipation
between contacts of spheres is viscous (with random damping constants),
the angular momentum continuously changes from one bearing state to the
other. For Coulomb friction (with random friction coefficients) in two
dimensions, a sharp line separates the two bearing states and we show
that this line corresponds to the minimum cut. Astonishingly, however,
in three dimensions intermediate bearing domains that are not
synchronized with either side are energetically more favorable than the
minimum-cut surface. Instead of a sharp cut, the steady state displays a
fragmented structure. This novel type of state of minimum dissipation is
characterized by a spanning network of slipless contacts that reaches
every sphere. Such a situation becomes possible because in three
dimensions bearing states have four degrees of freedom.
