Active matter
Can frustrated self-propelled particles become hyperuniform?
Open access · cc by · source: Europe PMC
In simulations, self-propelled particles whose alignment rule is frustrated can settle into a disordered yet hyperuniform state, even though no single orientation group is hyperuniform on its own.
Study at a glance
- Design
- Computational / modelling — Euler-integrated simulations of a frustrated Vicsek-Kuramoto model in a 2D periodic box, scanning coupling strength, coupling radius and frustration and measuring structure factor and density-variance scaling.
- N
- Simulated particles, not a sample; a larger run with N = 20,000 particles checks finite-size effects.
- Population
- Simulated self-propelled particles with frustrated orientation coupling
- Outcome
- Structure factor S(q) and density-variance scaling exponents (hyperuniformity class), rotation-centre mean squared displacement, hysteresis
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Key findings
At high coupling and small interaction radius, so-called recessive lattice states showed strong (Class I) hyperuniformity: large-scale density fluctuations fell off much faster than for randomly placed points, a scaling usually seen in crystals and quasicrystals. The strength of hyperuniformity peaked at intermediate frustration and rose with coupling strength, with no hysteresis when parameters were swept up and down. Rotation centres kept drifting diffusively, so the state is dynamic rather than a frozen lattice, and each orientation bin on its own was not hyperuniform, which the authors call orientation-modulated hyperuniformity.
Methodology
The authors simulated particles moving at constant speed in two dimensions whose headings try to align with neighbours but with a built-in phase offset (frustration), a hybrid of the Vicsek flocking model and the Kuramoto-Sakaguchi oscillator model. They varied coupling strength, interaction radius and frustration, and measured how density fluctuations scale at large distances using the structure factor and the variance of particle counts in windows. They also tracked particles' rotation centres, tested for hysteresis, and split particles into orientation bins to see which subsets carry the order.
Limitations
This is a noiseless model studied only by simulation; the authors list noise, chirality, heterogeneity and three-dimensional systems as untested. No physical experiment was performed, so relevance to microfluidic rotors, vibrated granular matter or animal groups is suggested, not demonstrated, and the biological examples are explicitly called speculative. Hyperuniformity is inferred from finite-size scaling fits, checked at one larger system size only.
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