The simulations produced phase-separated states—low- and high-energy regions separating into different parts of the system—with passive particles forming holes, stripes and labyrinthine structures while active particles formed a gas. The states appeared under sufficiently high critical-density, quorum-size and activity conditions.
The question was what states emerged as the quorum length scale—the size of the local area used to read crowding—changed for hard particles whose motility was enhanced by local density. It was a modeling study of simulated steady states. The author presented density-enhanced motility as a simple physical mechanism associated with criticality and multiple spatial morphologies, rather than as a specific biological prediction.
A crowding rule
Using Langevin dynamics, the simulation assigned particles to passive or active states according to local density. Density was measured from neighbours inside a disk whose diameter was σs = 2Rs; particles were passive below a critical local density and active above it, with the global and critical densities set equal.
The simulated system was a two-dimensional periodic square box with side length 100σ containing N particles. Interactions were represented by a short-range repulsive Weeks–Chandler–Andersen potential.
The same rule, different shapes
At a global density of 0.4, combinations of sensing range and activity were associated with different shapes: low sensing radius and low activity with hole-like patterns; sufficiently large sensing radius and activity with stripe-like patterns; and shorter sensing ranges combined with high activity with labyrinthine patterns.
One comparison fixed global density at 0.4 and activity at b = 10. Larger quorum sizes were associated with increasingly extended passive domains and with stripe-like structures coexisting with an active-particle gas. The reported comparison therefore applies to that fixed density and activity setting.
At b = 40, increasing sensing range was accompanied by more compact passive domains, smoother interfaces and stronger local hexatic order—a measure of how orderly nearby particles were.
The simulations remained comparatively homogeneous below an unspecified activity threshold, while patterned states were reported at finite activity. The study did not report the threshold value.
What density changed
In a separate density comparison, activity was fixed at b = 10 and sensing radius at Rs = 20σ. As density rose from 0.3 to 0.6, average passive-particle hexatic order increased monotonically, while interfaces became sharper and smoother.
Different starting configurations, including one that was already phase-separated, converged to qualitatively similar steady states. The report did not state the number of independent realizations or provide quantitative reproducibility measures.
Where the evidence stops
These are results from a two-dimensional particle model with an approximate hard-core potential. Whether the reported pattern behaviour generalizes across dimensions or interaction laws remains uncertain. The morphology comparisons were qualitative, and exact boundaries between regimes were not reported.
The author frames density-enhanced motility as a physical mechanism associated with criticality and multiple spatial morphologies, not as a specific biological prediction. The document is an arXiv preprint, version 1, dated 26 Aug 2026, and the author reports that the work was self-funded.
Paper data and sources
Original title: Multiple pattern formation in quorum sensing of density enhanced motility
Authors: Itay Azizi
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text