Origin of Similar Decay Exponents in Vortex and Bulk Cluster Distributions

Determine the origin of the observed similarity between the decay exponents of the bulk cluster-size distribution at intermediate cluster sizes and the vortex cluster-size distribution at small cluster sizes in dry active matter around circular obstacles, and establish whether the similarity is coincidental.

Background

The paper analyzes cluster-size distributions separately for the obstacle-attached vortex and the bulk. It reports that the vortex distribution has an approximately power-law decay for small cluster sizes, while the bulk distribution exhibits a similar power-law decay at intermediate cluster sizes. Although the numerical similarity is observed across obstacle sizes, densities, and sufficiently large system-size ratios, the mechanism producing it is not resolved. Clarifying whether the matching exponents reflect a common physical process or an accidental numerical coincidence would improve understanding of cluster formation in obstacle-induced condensation and its relationship to bulk motility-induced phase separation.

References

Although the origin of this similarity remains unclear and it may be coincidental, we observe that the decay exponents of $P_{\mathrm{bulk}(S)$ at intermediate sizes and $P_{\mathrm{vor}(S)$ at small sizes are very similar for all $D$, $\varphi$ and large $L/D$.

— Scaling and Condensation of Dry Active Matter Around Circular Obstacles  (2609.20743 - Júnior et al., 17 Sep 2026) in Section 3, subsection “Cluster-size distributions”