Bifurcation instructed design of multistate machines

Geometric Control and Memory in Networks of Hysteretic Elements

The response of driven frustrated media stems from interacting hysteretic elements. We derive explicit mappings from networks of hysteretic springs to their abstract representation as interacting hysterons. These mappings reveal how the physical network controls the signs, magnitudes, symmetries, and pairwise nature of the hysteron interactions. In addition, strong geometric nonlinearities can produce pathways that require excess hysterons or even break hysteron models. Our results pave the way for metamaterials with geometrically controlled interactions, pathways, and functionalities, and highlight fundamental limitations of abstract hysterons in modeling disordered systems.

Non-reciprocal topological solitons in active metamaterials

From protein motifs1 to black holes2, topological solitons are pervasive nonlinear excitations that are robust and can be driven by external fields3. So far, existing driving mechanisms all accelerate solitons and antisolitons in opposite directions3,4. Here we introduce a local driving mechanism for solitons that accelerates both solitons and antisolitons in the same direction instead: non-reciprocal driving. To realize this mechanism, we construct an active mechanical metamaterial consisting of non-reciprocally coupled oscillators5-8 subject to a bistable potential9-14. We find that such nonlinearity coaxes non-reciprocal excitations-so-called non-Hermitian skin waves5-8,15-22, which are typically unstable-into robust one-way (anti)solitons. We harness such non-reciprocal topological solitons by constructing an active waveguide capable of transmitting and filtering unidirectional information. Finally, we illustrate this mechanism in another class of metamaterials that shows the breaking of 'supersymmetry'23,24 causing only antisolitons to be driven. Our observations and models demonstrate a subtle interplay between non-reciprocity and topological solitons, whereby solitons create their own driving force by locally straining the material. Beyond the scope of our study, non-reciprocal solitons might provide an efficient driving mechanism for robotic locomotion25 and could emerge in other settings, for example, quantum mechanics26,27, optics28-30 and soft matter31.