Rate and State Dependent Friction Law Showing Convex Velocity Dependence and Vanishing Static Friction Force Derived from Microscopic Point of View.

Rate and state dependent friction law, which describe the behavior of the friction force in terms of the sliding velocity and the state varible, is well employed in the study of earthquake and so on. I derive new type of rate and state dependent friction law from microscopic point of view. It turns out that the static fricion force vanishes in generall. The kinetic friction force grows from zero with increasing sliding velocity. Under some condition the kinetic friction force shows maximun as a function of the sliding velocity in the stedy state. The physical mechanism of these behavior of the friction force is explained. The relation with the earthquake is also discussed.