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Wave coarsening drives time crystallization in mechatronic metamaterials

Published: 10/14/2026, 12:00 AM

Nature (2026) Cite this article When metals are magnetized1, emulsions phase separate2, or galaxies cluster3, domain walls and patterns form and irremediably coarsen over time. This coarsening is universally driven by diffusive relaxation towards equilibrium. Here we discover a vibrational counterpart—wave coarsening—in active elastic media4,5,6,7,8,9,10,11,12,13: vibrations emerge and spontaneously grow in wavelength, period and amplitude, before a globally synchronized state called a time crystal14,15,16,17 forms. We observe wave coarsening in one- and two-dimensional mechatronic metamaterials and capture its dynamical scaling. We further arrest the process by breaking momentum conservation and reveal a far-from-equilibrium nonlinear analogue to chiral topological edge modes18,19,20,21,22,23,24. Our results open new questions about the transient physics of systems with non-potential interactions15,25,26,27,28 and suggest an organizing principle for nonlinear waves in acoustics29,30, optomechanics31,32, living matter6,33 and soft robotics9. This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription Prices may be subject to local taxes which are calculated during checkout All the data supporting this study are available on the public repository at Zenodo69 (https://doi.org/10.5281/zenodo.17398589). The code supporting this study is available on the public repository at Zenodo69 (https://doi.org/10.5281/zenodo.17398589). Bray, A. J. Theory of phase ordering kinetics. Physica A 194, 41–52 (1993). Article ADS Google Scholar