General Mechanical Energy Landscape in Two-Dimensional Interacting Systems

Domain systems composed of individual entities, cells, or particles commonly exhibit complex mechanical energy landscape with a plethora of metastable states. Recent studies on a class of domain systems governed by dominant interfacial energy show that an equivalent foam energy (the sum of interfacial lengths), is a strong predictor of metastable state energies, regardless of the exact interfacial energy functionals. The landscape of equivalent foam energies is in turn described accurately by theoretical predictions based either on geometric measures or on statistical measures. Here, we show that this theoretical framework can be extended to systems with particle-based interactions. While the energy of particle-based systems depends on constituent particle positions rather than interfacial structure, the equivalent foam energy of a 2D tessellation generated from particle positions not only yields a strong correlation with the actual energy level but also generates an identical energy landscape. Geometric measures and statistical measures can be obtained from visual information only so this framework can serve as a diagnostic tool for identifying mechanical energy states in a variety of domain systems, including foams, emulsions, granular systems, and confluent tissues.