Non-linear rheology of layered systems - a phase model approach

We study non-lineax rheology of a simple theoretical model developed to mimic layered systems such as lamellar structures under shear. In the present work we study a 2-dimensional version of the model which exhibits a Kosterlitz-Thouless transition in equilibrium at a critical temperature T-c While the system behaves as Newtonain fluid at high temperatures T > T-c it exhibits shear thinning at low temperatures T < T-c. The non-linear rheology in the present model is understood as due to motions of edge dislocations and resembles the non-linear transport phenomena in superconductors by vortex motions.