Description
Wave propagation in a one-dimensional lattice of spherical beads, which serves as a prototype for granular media, is investigated. We review the theory of bead-lattice systems and show that it is possible to transform the Newtonian differential equations into the Korteweg-de Vries (KdV) equation. In order to observe directed-ratchet transport (DRT), we then consider a system where the trajectory of the central bead is prescribed by a biharmonic forcing function. By comparing the mean impulse of beads equidistant from the forcing bead, two distinct types of directed transport can be observed -- spatial and temporal DRT. Based on the value of forcing function's frequency relative to the system's cutoff frequency, bead-lattice systems can be categorized by the presence and magnitude of each type of DRT. Furthermore, we investigate how varying the forcing function's frequency and biharmonic weight affects DRT velocity and magnitude. Finally, friction is introduced into the system, which significantly inhibits one type of DRT. For low forcing frequencies, the friction also induces a switching of the DRT direction
