2025/05/15 by Charles R. Packard, Packard, Charles R., Daniel M. Sussman +1
Computer Science · Physics and Astronomy · #Distributed Control Multi-Agent Systems #FOS: Physical sciences #Micro and Nano Robotics #Opinion Dynamics and Social Influence #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.2505.10657
openalex publication_date 2025/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a Vicsek-like flocking model with a minimal form of time-delayed orientational interactions, in which the delays occur on a time scale that is well-separated from other time scales in the model. We achieve this by implementing an ``index-ordered'' update rule, mimicking a scenario in which agents have a distribution of times with which they react to information. This model retains the usual disorder-to-order transition common in flocking models, but we show that it also possesses a second transition, deep in the polar flocking phase, to a state with spatially patterned transverse velocities. We characterize this transition and its sensitivity to finite-size effects using the Binder cumulant, and demonstrate -- via direct measurements and by measuring a susceptibility of the phase to particle index permutations -- that the stability of this phase is directly tied to a subtle spatial organization of a slow-relaxing index-order field. These results highlight the potential for even seemingly insignificant temporal asymmetries to fundamentally alter the collective behavior of active matter.