Self-Propelled Voronoi Model

Bi, Yang, Marchetti, Manning  ·  Phys. Rev. X 6, 021011 (2016)
-- fps
⟨q⟩ — D_eff — ⟨|v|⟩ — steps 0
Equilibrating
About this model

A confluent 2D tissue, where each cell is a Voronoi region around a self-propelled particle. The energy E = Σ [Kₐ(A−A₀)² + Kₚ(P−P₀)²] penalizes deviations in cell area and perimeter from target values.

The dimensionless target shape index p₀ = P₀/√A₀ controls rigidity: below p₀* ≈ 3.813 the tissue is a jammed solid; above, a fluid that flows via T1 rearrangements. Self-propulsion v₀ and rotational noise Dᵣ add active dynamics.

Model Parameters
p₀target shape index
P₀ / √A₀ — jamming transition at p₀* ≈ 3.813
3.80
v₀self-propulsion speed
Magnitude of active motility force per cell
0.05
Dᵣrotational noise
Polarity diffusion — persistence time τ = 1/Dᵣ
1.00
Phase Presets
Passive solid
Passive fluid
Near jamming
Active fluid
Persistent (low Dᵣ)
Noisy (high Dᵣ)
Simulation
N cells
Steps / frame: 4
Visualization
Voronoi edges
Cell centres
Polarity arrows
Displacement trails
Color cells by
shape index q
speed
polarity
neighbours
Shape-Index Distribution
p₀* = 3.813
3.4q = P/√A4.6
MSD(t) — log-log
Record & plot MSD
References

Bi, D., Yang, X., Marchetti, M. C., Manning, M. L. Motility-Driven Glass and Jamming Transitions in Biological Tissues. Phys. Rev. X 6, 021011 (2016).

Sussman, D. M. cellGPU: Massively parallel simulations of dynamic vertex models. Computer Physics Communications 219, 400–406 (2017).  [GitHub]

Disclaimer
This demo was developed with assistance from AI coding tools. Scientific accuracy is not guaranteed — treat results as illustrative, not authoritative, and consult the cited references (and cellGPU) for production simulations.