Introduction

This repository contains representative data and exemplary data-analysis codes supplementing the manuscript

Goh et al., Alignment-induced self-organization of autonomously steering microswimmers: Turbulence, clusters, vortices, and jets, Phys. Rev. Research 7, 013142 (2025),

which investigates the collective motion of autonomously aligning microswimmers by large-scale multiparticle collision dynamics (MPC) simulations.

Data 1. Pusher

Parameters

Péclet number ${\rm Pe} = 128$, maneuverability $\Omega=512$, system size $(L/a)^3=512^3$ collision cells, and number of squirmers $N_{\rm sq}=110,592$

Squirmer data

• File name: pusher.squirmer.dat
• 301 snapshots with a print interval of 2500 MPC steps
• Data structure
  • Each row: a snapshot of the squirmers at a given MPC step
  • Column: $N_{\rm sq}$ state vectors (space-separated)
    • State vectors (12 components, space-separated): position (3D), velocity (3D), orientation (3D), angular velocity (3D)

Fluid data

• File name: pusher.fluid.dat
• A snapshot of fluid data at $300 \times 2500$ MPC step, $512 \times 512 \times 512$ cells
• The velocity of each cell is averaged over 2500 MPC steps
• Data structure
  • Column: cell position (3D), velocity (3D)

Data 2. Puller

Parameters

Péclet number ${\rm Pe} = 128$, maneuverability $\Omega=2048$, system size $(L/a)^3 = 768^3$ collision cells, and number of squirmers $N_{\rm sq}=373,248$

Squirmer data

• File name: puller.squirmer.dat
• 301 snapshots with a print interval of 2500 MPC steps
• Data structure
  • Each row: a snapshot of the squirmers at a given MPC step
  • Column: $N_{\rm sq}$ state vectors (space-separated)
    • State vectors (12 components, space-separated): position (3D), velocity (3D), orientation (3D), angular velocity (3D)

Fluid data

• File name: puller.fluid.dat
• A snapshot of fluid data at $300 \times 2500$ MPC step, rescaled to $512 \times 512 \times 512$ cells
• The velocity of each cell is averaged over 2500 MPC steps
• Data structure
  • Column: cell position (3D), velocity (3D)

Exemplary script

Squirmer MSD

C code computing $(\Delta r)^2$ with an initial time of $200 \times 2500$ MPC step from the squirmer data files

• File name: squirmer_MSD.c
• Compile

gcc -o squirmer_MSD squirmer_MSD.c

• Usage

./squirmer_MSD pusher.squirmer.dat 512 110592

• Output

pusher.squirmer.dat.MSD

Fluid energy spectrum

Python script computing $E(k)$ from the fluid data files

• File name: fluid_energy_spectrum.py
• Usage (prerequisite: NumPy)

python fluid_energy_spectrum.py pusher.fluid.dat pusher.fluid.espec

Appendix. Meta-data

Units

• Time: in units of $a\sqrt{m/(k_{\rm B}T)}$
• Length: in units of the side length of a collision cell $a$
• Energy: in units of $k_BT$

MPC fluid

• Viscosity $\eta = 42.6\sqrt{mk_BT}/a^2$

Squirmer

• Rotational diffusion coefficient $D_R = 0.000041\sqrt{k_BT/m}/a$