Trapping aligning self-propelled particles into static clusters

The far-from-equilibrium nature of active particles forms clusters with excessive dynamics, which can be suppressed by external physical fields in various applications. These application scenarios often require clusters with specific scales and numbers. To discover how to regulate these properties, we investigate the characteristics of clusters formed by aligning self-propelled particles in a Gaussian potential. This potential traps particles into static clusters (SCs) around the equivalent potential trough. During the process of formation, we use the order parameters defined on the connection graph to distinguish both the stability of these clusters and the number of static ones. We find that both increasing self-propulsion velocity and local density of the active particles lead to their partial or complete escape. This finding inspires a regulation strategy of both the scale and number of SCs by adjusting the potential parameters. The resulting SCs are endowed with diverse spanning scales, from giant clusters to wreath-like slender structures. Our results open new perspectives on controlling motility-induced phase separation and multitask manipulation for active particle systems.