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Thus, we described the master equation approach to the earthquakelike model with a continuous distribution of static thresholds, which is much more efficient than simulations and can be solved analytically in cases which are particularly relevant. It provides a deeper understanding of friction analyzed at the mesoscale in terms of the statistical properties of the contacts. Our approach splits the study of friction in independent parts:
(i) the study of the contacts, which needs inputs from the microscopic scale, e.g., from MD simulations and/or AFM/FFM experiments,
(ii) the calculation of the friction force given by the master equation provided the statistical properties of the contacts are known,
(iii) the incorporation of other aspects such as the temperature effects and aging of contacts,
(iv) the incorporation of the interaction between the contacts within the λc2 area to find parameters of the λ-contacts, and
(v) the study of the collective behavior of the λ-contacts taking into account the elasticity of the sliding block.on the mesoscopic scale.
The proposed approach describes the stick-slip and smooth sliding regimes of tribological systems as well as transitions between these regimes when the system parameters, such as the sliding velocity or the temperature, are changed. On the mesoscale, our approach allows us to find the screening length λs, and to clarify when a concerted (avalanche-like) motion of contacts (a self-healing crack) appears, what is its velocity and the propagation length Λ.
Note, however, that the ME approach is to be applied to meso- or macroscopic systems, where the contacts between the substrates is due to a large number of microcontacts; it cannot be used to explain the AFM/FFM tip-based experiments, except if there is a multi-contact through several tip atoms.
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tribology pageLast updated on April 28, 2014 by Oleg Braun