Kinetics of Self-Organization in One-Component Active Matter Systems

Abstract We study an inherently nonequilibrium system consisting of self-propelled particles using molecular dynamics simulation in d = 2. The system self-organizes through quorum-sensing interactions characterized by an interaction range λ and a parameter cth. When the local concentration sensed by a particle, represented by an auxiliary variable ci(t) exceeds cth, its self-propulsion velocity abruptly drops to zero, leading to the emergence of particle rich domains. For small λ, we observe a droplet-like morphology of clusters, which crosses over to a bicontinuous structure as λ increases. We confirm this transition by computing the eccentricity of the domains. Next, we characterize the evolving domain morphologies using equal-time correlation function C(r, t) and structure factor S(k, t) of the density field. For a fixed λ, the scaled C(r, t)’s at different times are indistinguishable from each other, indicating dynamical scaling. However, at a fixed time t, the scaling functions differ for different values of λ, confirming a λ-dependent morphological transition. In the large-wavevector limit (k → ∞), the tail of S(k, t) consistently follows the Porod’s law: S(k, t) ∼ k–3. Furthermore, the average domain size L(t) exhibits a power-law growth, L(t) ∼ t1/3, independent of λ.