Fundamental biological and biomimetic processes, from tissue morphogenesis to
soft robotics, rely on the propagation of chemical and mechanical surface waves
to signal and coordinate active force generation. The complex interplay between
surface geometry and contraction wave dynamics remains poorly understood, but
will be essential for the future design of chemically-driven soft robots and
active materials. Here, we couple prototypical chemical wave and
reaction-diffusion models to non-Euclidean shell mechanics to identify and
characterize generic features of chemo-mechanical wave propagation on active
deformable surfaces. Our theoretical framework is validated against recent data
from contractile wave measurements on ascidian and starfish oocytes, producing
good quantitative agreement in both cases. The theory is then applied to
illustrate how geometry and preexisting discrete symmetries can be utilized to
focus active elastic surface waves. We highlight the practical potential of
chemo-mechanical coupling by demonstrating spontaneous wave-induced locomotion
of elastic shells of various geometries. Altogether, our results show how
geometry, elasticity and chemical signaling can be harnessed to construct
dynamically adaptable, autonomously moving mechanical surface wave guides.Comment: text changes abstract and intro, new results on self-propelled
elastic shells added; 5 pages, 3 figures; videos available on reques
