Analysis of a Statistical Stick-Slip Model

We study mathematical details of a statistical stick-slip model of a group of springs. We present the conditions for the steady shear stress σ ̄ to be N-shaped and obtain a general view-point of the linear stability analysis for a slip model coupled with macroscopic elasticity. Our model can be reduced to an ordinary differential equation under an approximation, and the reduced slip equation is found to be equivalent to a slip equation of a more phenomenological slip model. In a previous paper, 1) we presented a stick-slip model which is composed of two parallel plates and a group of springs being stochastically adsorbed or desorbed to one of the plates. This model has been successfully applied to the stick-slip phenomena of polymer liquids, especially to the periodic spurt flow caused by th