The collective dynamics of self-propelled particles interacting with obstacles is a central topic in active matter physics. However, how particle softness itself regulates such interactions remains largely unclear. In this work, we perform molecular dynamics simulations of self-propelled particles with continuously tunable softness, and investigate their accumulation and vortex behavior around a smooth circular obstacle in two dimensions.
Our results reveal a clear dynamical transition as particle stiffness increases: the system evolves from a random state characterized by disordered motion, through a transitional state, into a vortex state where particles persistently circulate around the obstacle. Notably, within the vortex state, both the vortex velocity and the mean tangential component of particle polarity exhibit a non-monotonic dependence on particle softness. Specifically, there exists an optimal softness at which these two quantities reach their maximum values simultaneously. This non-monotonic behavior mainly originates from the competition between a polarity-selective trapping mechanism and the ability of particles to deform and reorient. Near the obstacle surface, particles with polarity aligned with the vortex direction (pSPPs) are preferentially retained in the innermost layer, while those with opposite polarity (nSPPs) are more likely to be expelled. This selection bias strengthens as particles become stiffer.
Structural analysis reveals pronounced layering in the radial distribution of particles around the obstacle. In the region close to the obstacle surface, both the tangential velocity and polarity decay linearly with distance, reflecting the collective motion of the cluster; beyond this region, in the outer gas-like zone, the decay becomes exponential. As particle stiffness increases, the linear-decay region broadens and the decay slope becomes gentler, indicating enhanced interlayer cooperative motion. Meanwhile, analysis of the packing structure shows that the most efficient vortex flow arises from a balance between the polar ordering of the cluster and particle softness, which enables continuous particle rearrangement.
These results demonstrate that particle deformability serves as a key parameter governing collective dynamics in confined geometries. The non-monotonic behavior observed in the vortex state results from the interplay among polarity selection, orientational ordering, and jamming, offering new insight into the self-organization of deformable active particles. Our findings reveal a novel mechanism for the self-organization of deformable active matter in confined environments, and may inspire new design strategies for active materials in applications such as targeted drug delivery, microfluidic devices, and soft robotics.