Classification of emerging patterns in self-assembled two-dimensional magnetic lattices

Self-assembled granular materials can be utilized in many applications such as shock absorption and energy harvesting. Such materials are inherently discrete with an easy path to tunability through external applied forces such as stress or by adding more elements to the system. However, the self-assembly process is statistical in nature with no guarantee for repeatability, stability, or order of emergent final assemblies. Here we study both numerically and experimentally the two-dimensional self-assembly of free-floating disks with repulsive magnetic potentials confined to a boundary with embedded permanent magnets. Six different types of disks and seven boundary shapes are considered. An agent-based model is developed to predict the self-assembled patterns for any given disk type, boundary, and number of disks. The validity of the model is experimentally verified. While the model converges to a physical solution, these solutions are not always unique and depend on the initial position of the disks. The emerging patterns are classified into monostable patterns (i.e., stable patterns that emerge regardless of the initial conditions) and multistable patterns. We also characterize the emergent order and crystallinity of the emerging patterns. The developed model along with the self-assembly nature of the can be in re materials with nonlinear