Deterministic stick-slip dynamics in a one-dimensional random potential

In physics, engineering and other settings, it is important to understand the macroscopic behaviour of systems whose evolution is determined by microscale effects. It seems natural to consider these microscale effects to be random in nature (and, therefore, beyond the scope of classical averaging and homogenization theory) and to constitute some perturbation of a well-understood smooth structure. In the case of rate-dependent viscous systems, analysis of how the random microstructure determines the macroscopic behaviour can be found in the Green-Kubo relations and many further developments since their introduction in the 1950s [2] [4]. In the realm of rate-independent plasticity theory, there is a large literature (see, for example, [7]) surrounding ordinary differential inclusions such as