Number and universality of transition waves in tristable metamaterial lattices

Determine the number of distinct transition wave types supported by one-dimensional metamaterial lattices with tristable onsite potential energy landscapes created by localized external magnetic fields, and ascertain whether a universal law governs the characteristics of these transition waves.

Background

Transition waves in systems with nonconvex energy landscapes have been extensively studied in bistable settings, but tristable configurations remain comparatively unexplored. The authors design a magnetoelastic lattice whose onsite potential can be tuned to be monostable, bistable, or tristable by adjusting an external magnetic field produced by fixed magnets. In such tristable lattices, understanding what kinds of transition waves can exist is essential to controlling phase switching dynamics and leveraging multistability for applications.

Prior theoretical work suggested possible scaling relations for transition waves, but whether a universal law governs wave characteristics in tristable, magnetically tunable lattices—such as amplitude, profile, and velocity—remained an explicit open question posed by the authors.