Extremal collision sequences of particles on a line: optimal transmission of kinetic energy

The transmission of kinetic energy through chains of inelastically colliding spheres is investigated for the case of constant coefficient of restitution \epsilon=const and impact-velocity dependent coefficient \epsilon(v) for viscoelastic particles. We derive a theory for the optimal distribution of particle masses which maximize the energy transfer along the chain and check it numerically. We found that for \epsilon=const the mass distribution is a monotonous function which does not depend on the value of \epsilon. In contrast, for \epsilon(v) the mass distribution reveals a pronounced maximum, depending on the particle properties and on the chain length. The system investigated demonstrates that even for small and simple systems the velocity dependence of the coefficient of restitution may lead to new effects with respect to the same systems under the simplifying approximation \epsilon=const.