Controlling dissipation: from vibrated granular matter to rate- and state-dependent friction

Abstract:

Understanding how the interplay between energy input and dissipation mechanisms influences the dynamical properties of physical systems is a central problem that bridges fundamental science and practical applications. In thermal systems, the situation is simplified because thermodynamic equilibrium allows the kinetic energy to be set independently of microscopic details by coupling the system to a heat reservoir. However, at length scales where thermal fluctuations are negligible and frictional forces dominate, such a powerful framework no longer applies.

In my talk, I will present two examples where specific external driving can be used to control energy dissipation in driven athermal systems.

First, I will examine the rheology of vibrated granular materials. I will discuss how the effective viscosity of a dense granular packing—measured via vane rheometry—relates to the driving parameters of the mechanical vibrations applied to the system [1]. Through numerical analysis and a simple oscillator model, I will show that the macroscopic rheological behavior of the system can be attributed to internal dissipation mechanisms within the granular dynamics [2].

In the second part of the talk, I will present a recent theoretical study where we apply optimal control techniques to the rate- and state-dependent law for solid-on-solid friction [3]. We demonstrate how swift state-to-state protocols can drive the system between two arbitrary stationary velocities within a set time, while also avoiding stick-slip instabilities that typically arise during sudden velocity changes. Using variational methods, we further address the problem of finding the optimal driving protocol that minimizes the work done by friction when connecting these stationary states.

[1]: Gnoli et al. Phys. Rev. Lett. 120, 138001 (2018)

[2]: Plati et al. Phys. Rev. Research 3, 013011 (2021)

[3]: Plati et al. European Journal of Mechanics – A/Solids 111, 105550 (2024)