Formation of inhomogeneous spatial structures in the boundary near-surface layer of ice

A nonlinear model of boundary ice sliding is proposed to describe two atomically smooth surfaces separated by an ultrathin premelted ice layer. The model is based on a Lorenz-type system of equations parameterized by shear strain, stress, and temperature of the near-surface ice layer. The spatial inhomogeneity of these parameters is taken into account, and it is shown that during sliding, a domain structure with two types of domains emerges along the contact plane. The temporal evolution of the fractal dimensions of these domain distributions over the contact plane is calculated, and the existence of a characteristic time when the fractal dimensions attain their minimum values is demonstrated. It is found that during evolution, the system tends toward a homogeneous state, in which a fixed value of shear strain is realized over the entire contact area, determining the relative sliding velocity of the rubbing blocks.