Active Matter: Motility-Induced Phase Separation (2D)

Conditions

Packing fraction φ 0.55

Self-propulsion speed v₀ 2.4

Orientational noise Dr 0.30

Presets

Uniform, gas-like state — raise v₀ and φ together to trigger phase separation.

Live Readout

Largest cluster

Mean free path

—

Péclet-like ratio

0.0

Particles

How it works

Each disk is an active Brownian particle: it self-propels at constant speed v₀ along its own heading θ, and θ itself performs a slow random walk set by the rotational-noise strength D_r. Particles never align with their neighbours — the only interaction is a short-range, purely repulsive contact force that pushes overlapping disks apart. There is no attraction anywhere in this model.

The MIPS mechanism: when a particle gets crowded, the repulsive pushes from its neighbours cancel out its own forward push more of the time, so its effective speed drops — the model applies this directly as a local-density-dependent motility factor, exactly as in the reduced "quorum-sensing" active Brownian particle models used in the active-matter literature. Slower particles linger longer near other particles, which makes the local region even denser, which slows it down further — a positive feedback loop with no energy-minimising force behind it at all.

Above a critical combination of packing fraction φ and propulsion speed v₀ (roughly, when self-propulsion outruns diffusive spreading — a Péclet-like ratio v₀/(D_r·d) exceeding a few), this feedback runs away and the population spontaneously splits into dense, slow, jammed clusters surrounded by a dilute, fast-moving gas — even though every pairwise force in the system is repulsive. This is the same statistical-physics phenomenon shown in the paired 3D simulation, viewed here as a flat top-down 2D canvas instead of a rendered 3D box.