Using the fractional interaction law to model the impact dynamics of multiparticle collisions in arbitrary form

Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional calculus we proposed an expression for the repulsive force, which is the so-called fractional interaction law. We then illustrate and discuss how to control (correlate) the energy dissipation and the collisional time for an individual particle within multiparticle collisions. We included in the multiparticle collisions the friction mechanism needed for the transition from coupled torsion-sliding friction through rolling friction to static friction. Analyzing simple simulations we found that binary collisions dominate in the strong repulsive state. However, weak repulsion is observed to be much stronger within multiparticle collisions. The presented numerical results can be used to realistically model the impact dynamics of an individual particle in a group of colliding particles.