Pattern Formation in Robotic Mechanical Metamaterial

TL;DR

This paper introduces a robotic mechanical metamaterial platform to study and control pattern formation in non-equilibrium systems, linking small-scale interactions to macroscopic behavior through analytical modeling.

Contribution

It demonstrates how a robotic mechanical metamaterial can be used to experimentally explore and prescribe pattern formation, bridging the gap between phenomenological models and real systems.

Findings

The platform exhibits spatial and temporal oscillations in response to feedback parameter variations.

Analytical models accurately predict pattern behaviors and link them to system parameters.

The system provides a controllable environment for studying non-equilibrium pattern formation.

Abstract

Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be explored. As the underlying dynamics are typically complex, pattern formation is often theoretically analyzed and understood via phenomenological models, which effectively represent the causal mechanisms, but obscure the link between the small-scale interactions/processes and the observed macroscopic behavior. Moreover, efforts to prescribe the patterning response are often undercut by the experimental inaccessibility of the small-scale constituents/processes. This article demonstrates an artificial system (i.e., a robotic mechanical metamaterial) as an accessible and versatile platform within which to explore and prescribe the patterning response of non-equilibrium systems. Specifically, in varying a feedback parameter within the prescribed reaction kinetics, the robotic mechanical metamaterial alternately develops spatial and temporal oscillations in the displacement field following a perturbation of the initial quiescent, uniform state. The platform is amenable to a first-principles analytical description so that corresponding theoretical results possess qualitative and quantitative significance, and maintain connection to the specific system parameters.