Effect of Boundaries on Pattern Formation in a Monolayer of Interacting Dipoles

Self-organization can be defined as a process of arrangement of entities that start out in an irregular arrangement and evolve into a stable, regular pattern without the aid of an external agent. A system of magnetic particles that are constrained to move only in a plane is reported. The individual components in the system have dipole moments in an orientation perpendicular to the plane of motion and the interaction between components is purely repulsive. For such a system, it is attempted to understand the influence of the boundary of the monolayer on the patterns that emerge. A system with a small number of magnets is found where the range of the magnetic interactions is of the size of the boundary; the symmetry of the boundary imposed on the monolayer plays a crucial role in determining the pattern types, the number of different pattern types, and the frequency of appearance of a particular pattern type. The effect of scaling up the size of the system while maintaining the characteristics of individual components as well as the component areal density is also discussed. © 2024 Wiley-VCH GmbH.