Prandtl–Tomlinson (PT) model can be used to explain nanoscale friction in a variety of
situations, except when a nanoscale object undergoes rolling. To alleviate this problem, we
generalize the PT model as a collection of interacting point particles arranged on a ring of
radius R⁠. The center of mass of the ring is connected to a spring of stiffness k⁠, whose
other end is attached to a fictitious mass that moves with a constant velocity v⁠. The entire
assembly is driven in a composite force field, which is a product of (i) the familiar sinusoidal …