Collective aggregation pattern dynamics control via attractive/repulsive function

In the coordinated collective behaviors of biological swarms and flocks, the attractive/repulsive (A/R) functional link between each pair of particles plays an important role. By changing the slope of the A/R function, a dramatic transition between different aggregation patterns surfaces. With a high value of the slope, the particle aggregation shows a liquid-like pattern in which the outer particles are sparsely distributed while the inner ones densely. In addition, the particle density is reduced from the outside to the inside of each cluster. By comparison, when the slope decreases to a sufficiently low value, the particle aggregation exhibits a crystal-like pattern as the distance between each pair of neighboring particles remains constant. Remarkably, there is an obvious spinodal in the curve of particle-particle distance variance versus the slope, indicating a transition between liquid-like and crystal-like aggregation patterns. Significantly, this work may reveal some common mechanism behind the aggregation of physical particles and swarming of organisms in nature, and may find its potential engineering applications, for example, UAVs and multi-robot systems.