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 $c_{\mathrm{th}}$. When the local concentration sensed by a particle, represented by an auxiliary variable $c_i(t)$ exceeds $c_{\mathrm{th}}$, 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 ($k\rightarrow\infty$), the tail of $S(k,t)$ consistently follows the Porod's law: $S(k,t)\sim k^{-3}$. Furthermore, the average domain size $L(t)$ exhibits a power-law growth, $L(t)\sim t^{1/3}$, independent of $λ$.