[Paper Review] Long-ranged velocity correlations in dense systems of self-propelled particles

Grzegorz Szamel, Elijah Flenner|arXiv (Cornell University)|Jan 27, 2021

Micro and Nano Robotics37 references51 citations

TL;DR

This paper demonstrates that long-ranged velocity correlations—previously observed in dense, ordered systems of self-propelled particles—also emerge in dense, fluid-like systems of active particles. The authors show these correlations arise from the interplay between self-propulsion persistence and the virial bulk modulus from repulsive interactions, with correlation length scaling as √τ, and develop a simple theory that captures longitudinal correlations but not transverse ones.

ABSTRACT

Model systems of self-propelled particles reproduce many phenomena observed in laboratory active matter systems that defy our thermal equilibrium-based intuition. In particular, in stationary states of self-propelled systems, it is recognized that velocities of different particles exhibit non-trivial equal-time correlations. Such correlations are absent in equivalent equilibrium systems. Recently, researchers found that the range of the velocity correlations increases with increasing persistence time of the self-propulsion and can extend over many particle diameters. Here we review the initial studies of long-ranged velocity correlations in solid-like systems of self-propelled particles. Then, we demonstrate that the long-ranged velocity correlations are also present in dense fluid-like systems. We show that the range of velocity correlations in dense systems of self-propelled particles is determined by the combination of the self-propulsion and the virial bulk modulus that originates from repulsive interparticle interactions.

Motivation & Objective

• To investigate whether long-ranged velocity correlations, previously observed in solid-like active systems, also exist in dense fluid-like active matter.
• To identify the physical origin of these correlations in disordered, fluid-like systems of self-propelled particles.
• To develop a theoretical framework explaining the range of velocity correlations in active fluids based on self-propulsion and fluid elasticity.
• To distinguish the role of persistence time and interparticle interactions in determining correlation length.
• To clarify the limitations of existing theories in describing transverse velocity correlations in active fluids.

Proposed method

• Conduct extensive equilibrium and non-equilibrium molecular dynamics simulations of overdamped active Brownian particles with polydispersity to prevent crystallization.
• Use the velocity correlation function C(r) = ⟨v(r)·v(0)⟩/⟨v²⟩ to quantify equal-time velocity correlations.
• Apply a normal mode analysis based on inherent structures (local energy minima) to model short-time dynamics in amorphous systems.
• Develop a continuum elasticity theory expressing velocity correlations in terms of bulk and shear moduli and persistence time.
• Calculate the virial bulk modulus Bv = ρ∂ρPv from simulation data to quantify the fluid’s resistance to compression.
• Compare theoretical predictions with simulation results for varying persistence time τ, fixed v₀, and fixed Ta (activity parameter).

Experimental results

Research questions

• RQ1 Do long-ranged velocity correlations persist in dense, disordered, fluid-like systems of self-propelled particles?
• RQ2 What physical mechanisms govern the range of velocity correlations in active fluids, distinct from ordered solids?
• RQ3 How does the correlation length depend on persistence time τ and system parameters like activity and density?
• RQ4 Can a simple theory based on virial bulk modulus and self-propulsion explain the observed longitudinal velocity correlations?
• RQ5 Why do existing theories fail to describe transverse velocity correlations in active fluids?

Key findings

• Long-ranged velocity correlations exist in dense, fluid-like systems of self-propelled particles, even in the absence of structural order.
• The longitudinal velocity correlation length ξ∥ increases approximately as √τ for fixed activity (v₀ or Ta), consistent with experimental and simulation trends.
• The correlation length is well described by a simple theory combining self-propulsion and the virial bulk modulus Bv, with ξ∥ = √(τBv/(γρ)).
• The virial bulk modulus Bv remains approximately constant over a wide range of persistence times (from 136 to 148), indicating that the increase in correlation length is primarily due to τ.
• The theoretical model accurately predicts the longitudinal correlation length but fails to capture transverse velocity correlations.
• The system remains single-phase and liquid-like across all parameter ranges, with no signs of phase separation, crystallization, or structural arrest, as confirmed by pair correlation functions and mean-square displacement.