Extended Data Fig. 8: Dynamics and statistics of two-particle interaction events.
From: Active phase separation by turning towards regions of higher density
a,b, Two examples of interaction events between two particles, which we define by the condition r12 < 3R, with R the particle radius. We also require the minimal interparticle distance to be min r12 < 2.2R. We analyzed 2061 of such interaction events. In a, both particles turn clockwise. Therefore, the interaction torque has the same sign on both particles, showing that torques are non-reciprocal (Γ12 ≠-Γ21). This type of interaction with particles initially pointing in opposite directions, defined by the condition ∣θ1(t = 0) + θ2(t = 0)∣ < 0.2 rad, occurred in ~33% of the analyzed events. In b, particle 1 changes its orientation very little compared to particle 2, showing another example of non-reciprocal torques. The particles end up aligned in a chain. This type of interaction, defined by the condition \(\min ({\theta }_{1}({\rm{t}})-{\theta }_{2}({\rm{t}}))<0.5\) rad during the interaction event, occurred in ~2.8% of the analyzed events. c,d, Evolution of the interparticle distance, r12, and the change in angle of each particle, Δθ1,2, for the interaction events in a and b, respectively. e,f, Joint probability distribution functions of the angle changes of each particle in an interacting pair. The pre-collision (e) and post-collision (f) phases respectively correspond to the times before and after the particles reach their minimal distance. These histograms show that, statistically, both particles in the interacting pair tend to turn in the same direction, showing that interaction torques are non-reciprocal. Reciprocal torques would lead to particles rotating in opposite directions and by the same magnitude, as indicated by the dashed lines.
