Collective Friction of an Array of Particles: A Crucial Test for Numerical Algorithms

Abstract
Using different simulation techniques, we study the influence of the friction law governing interparticle and particle-plane contacts on the dynamics of a regular array of rigid parallel cylinders moving on a plane. We find that the evolution of the system depends strongly on the simulation method. But both in simulations with a Contact Dynamics algorithm, which prescribes the basic Coulomb's law of friction, and in simulations with molecular dynamics, which prescribes a regularized form of Coulomb's law, a steady state with very similar collective rotation modes is reached. As long as the static and dynamic friction coefficients are equal, the rotation modes are independent of the initial conditions. We show that in all cases, the global steady-state coefficient of friction between the array and the plane is a function of the driving force and the system size, and hence is not Coulombian.