Particles that push each other away with extreme force can actually end up sticking together in tight clusters.
Logic suggests that increasing repulsion would force objects further apart, but self-propelled particles follow different rules. In this minimal model, a higher push force creates a feedback loop that results in effective attraction. The particles end up trapped in clusters because they are trying so hard to move away from each other. This counterintuitive behavior shows that collective motion can lead to results that are the exact opposite of individual intent. It provides a new framework for understanding how swarms of robots or bacteria behave.
Effective attraction by repulsion
arXiv · 2605.01421
Repulsive self-propelled particles tend to cluster, leading to Motility-Induced Phase Separation (MIPS). By analogy with equilibrium phase separation, the onset of MIPS has been associated with a transition to effective attraction between particles. Using an exact microscopic theory, we quantify the emergence of effective attraction in a minimal model: two soft run-and-tumble particles in a periodic domain. We show that, as repulsion increases, the leading-order behaviour is that of effective re