Pattern phase transitions in 3D minimal Vicsek model

A large part of biological collective behaviors involves motional formation patterns like migration, vortex, aggregation, etc., in three-dimensional space, but the phase transition principles among these patterns still remain a dilemma. In this letter, by tweaking the vision range of the particles in a minimal collective motion model, phase transitions are observed among gas-like, crystal-like, and liquid-sphere–like patterns. Significantly, the increase of noise magnitudes will destroy the moving direction synchronization of gas-like and crystal-like phases, but not the liquid-sphere–like phase. By contrast, three sub-phases of migration liquid-sphere, vortex liquid-sphere and aggregation liquid-sphere emerge by slightly increasing noise magnitudes. This study sheds some light onto the forming mechanisms of 3D motional patterns of abundant biological groups. These insights could be expected to enable tuning the collective motional formations of multi-unmanned systems or robots by simply tweaking a few dynamical parameters as well.