We numerically investigate the supratransmission phenomenon in an active nonlinear system modeled by the 1D/2D discrete sine-Gordon equation with non-local feedback. While, at a given frequency, the typical passive system exhibits a single amplitude threshold marking the onset of the phenomenon, we show that the inclusion of non-local feedback manifests additional thresholds that depend upon the specific boundary from which supratransmission is stimulated, realizing asymmetric (i.e., non-reciprocal) dynamics. The results illustrate a new means of controlling nonlinear wave propagation and energy transport for, e.g., signal amplification and mechanical logic.

In this Letter, we consider the dynamics of a multi-stable metamaterial with an elastic substrate to realize a mechanical system within which the position of a transition wavefront can be precisely controlled and remotely determined. This ability is enabled, in part, by a (strain-)tunable potential energy landscape that conveys the wavefront from one stabilizing defect site to another. In separating two acoustically distinct domains, the wavefront reflects small-amplitude waves of appropriate frequency back toward the source whereupon the time interval between excitation and echo reveals the position of the front. In a numerical study, we exploit these mechanisms for mechanical multi-level memory, which may find applications, e.g., in soft robots as a flexible alternative to current rigid memory technologies. More generally, we anticipate that the concepts presented here toward a command of the transition wave position will enhance the development and applicability of multi-stable metamaterials.