Fig. 2.

Aggregation–fragmentation process in active clusters. a Sketch of the events considered without and with the monomer approximation (left and right respectively). b–f Experimental data for activity v₀ = 8.6 μm s⁻¹ and area fraction Φ = 9%. b Cluster size distribution in semilog scale evidencing the exponential decay at large size. Symbols: experimental data and solid line: theoretical fit (see main text). The dashed lines show the effect of the 2% relative uncertainty on κ, obtained upon assuming a 10% relative uncertainty on all data points for CSD and rates. Inset: same data in loglog scale to emphasize the power law regime at small size. c Transition matrix showing the probability $P\left(N_1\mid N_0,\mathrm{\Delta }t\right)$ for a cluster of size N₀ to have a size N₁ after a time lag Δt = τ_s = 0.05 s. d Aggregation and fragmentation rates for monomeric events. Symbols: experimental data and solid line: theoretical fit (see main text). e Probability $P\left(N_0\mid N_0,\mathrm{\Delta }t\right)$ that a cluster of size N₀ has the same size after a time Δt = 1, 2, 3, 5, 10, 20 and 40τ_s, from top to bottom. f Transition probability $P\left(N_1\mid N_0,\mathrm{\Delta }t\right)$ for N₀ = 10 and 20, Δt = 5τ_s = 0.25 s and 40τ_s = 2 s. Blue circle: experimental data and black losange: prediction of Eq. (7)