Contact temporal network during motility induced phase separation

TL;DR

This study uses complex network analysis to explore particle interactions during motility-induced phase separation, revealing universal behaviors and phase-specific structures in active matter.

Contribution

It introduces a network-based approach to distinguish single-phase and phase-separated regimes in active matter, uncovering new topological features.

Findings

Degree distributions are Gaussian in the gas-like phase.

Distinct network structures emerge in dense and dilute phases.

Short simulations suffice to capture key network features.

Abstract

Motility-induced phase separation (MIPS) is a paradigmatic non-equilibrium transition in active matter, determined by the P\'eclet number and packing fraction. We investigate the single-phase and phase-separated regimes of MIPS using a complex network approach, where networks are constructed from particle interactions over finite time windows. In the single-phase (gas-like) regime, the degree distributions $P(k)$ exhibit Gaussian behavior and resemble those of random graphs. Plotting the location and height of the $P(k)$ peak reveals a universal curve across different P\'eclet numbers at fixed packing fraction. In the phase-separated regime, we analyze the dense and dilute phases independently. The $P(k)$ distributions unveil distinct collective dynamics, including caging in the dense phase and the emergence of active solid-like structures at longer times. Clustering coefficients and average path lengths in both phases stabilize rapidly, indicating that short simulations are sufficient to capture essential network features. Overall, our results show that network metrics expose both universal and phase-specific aspects of active matter dynamics. Notably, we identify distinct and previously unreported topological structures arising in the dense and dilute phases within the MIPS regime.