Abstract
One of the most intensively discussed subjects in the dynamics of dissipative hard sphere systems is the effect of inelastic collapse, where the entire kinetic energy of the relative motion of a set of particles is dissipated in finite time due to an infinite sequence of collisions. The known collapse scenarios imply two preconditions: inertia of the particles and at least some degree of elasticity. For completely inelastic particles, collapse scenarios degenerate to a single sticky contact. By considering the overdamped motion of a frictional particle along the steepest descent in a rigid landscape, here we show that there exist collapse scenarios of novel type even if neither of these preconditions hold true. By means of numerical simulations we show that such collapses are no rare events due to particular particle shape and/or initial conditions and, thus, may be considered as an alternative scenario of granular cluster formation.
Highlights
One of the most intensively discussed subjects in the dynamics of dissipative hard sphere systems is the effect of inelastic collapse, where the entire kinetic energy of the relative motion of a set of particles is dissipated in finite time due to an infinite sequence of collisions
The problem of inelastic collapse of identical, ideally hard, purely repulsive, and dissipatively colliding spheres reads as follows: given N particles in force-free space, are there initial conditions for the positions and velocities such that the entire energy of their relative motion will be dissipated? If dissipation is quantified by the coefficient of restitution, ε, relating the pre-collisional and post-collisional normal velocity, the question implies that there occurs an infinite sequence of collisions resulting in a cluster where each particle is in permanent contact with at least one neighbor
The infinite sequence of collisions leading to a collapse occurs in finite time[1,3] which lead to severe problems for event-driven molecular dynamics where time progresses in steps of collisions
Summary
One of the most intensively discussed subjects in the dynamics of dissipative hard sphere systems is the effect of inelastic collapse, where the entire kinetic energy of the relative motion of a set of particles is dissipated in finite time due to an infinite sequence of collisions. T = 33, the particle enters a cycling motion, at three contact points in periodic sequence, and eventually experiences a collapse (dashed line) such that the simulation comes to rest.
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