Kinetics and steady state of polar flock with birth and death

TL;DR

This study investigates how birth and death processes influence the dynamics and steady state of a polar flock on a 2D substrate, revealing effects on density fluctuations and sound wave propagation.

Contribution

It introduces a hydrodynamic model for polar flocks with birth and death, analyzing their impact on ordering kinetics and steady state properties.

Findings

Density fluctuations are suppressed with higher birth and death rates.

Velocity ordering remains unaffected by birth and death.

Density growth crosses over from 5/6 to 1/3 exponent with increasing birth/death rate.

Abstract

We study a collection of polar self-propelled particles or polar flock on a two dimensional substrate with birth and death. Most of the previous studies of polar flock with birth and death have assumed the compressible flock, such that the local density of flock is completely ignored. Effect of birth and death of particles on the flock with moderate density is focus of our study. System is modeled using coarse-grained hydrodynamic equations of motion for local density and velocity of the flock and solved using numerical integration of the nonlinear coupled partial differential equations of motion and linearised hydrodynamics about the broken symmetry state. We studied the ordering kinetics as well as the steady state properties of the immortal flock and flock with finite birth and death rate. The ordering kinetics of the velocity field remains unaffected whereas the density field shows a crossover from asymptotic growth exponent $5/6$ for the immortal flock to diffusive limit $1/3$ for large birth and death rates. In the steady state, the presence of birth and death rate leads to the suppression of speed of sound wave and density fluctuations in the system.