arxiv: 2605.02854 · v1 · submitted 2026-05-04 · ❄️ cond-mat.soft · cond-mat.stat-mech

Recognition: unknown

Emergent flocking dynamics in chemorepulsive active colloids: interplay of disorder and noise

Rajesh Singh, Sagarika Adhikary

Authors on Pith no claims yet

Pith reviewed 2026-05-08 02:48 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mech

keywords active colloidschemorepulsionquenched disorderpinningangular noisepolar orderphase transitionsdensity bands

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The pith

In chemorepulsive active colloids with pinned particles, the noise-driven transition to loss of polar order depends on particle density while the pinning-driven transition does not.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies groups of active particles that push each other apart through chemical signals, without any built-in rule for aligning their directions. A random fraction of these particles is pinned in place so they can only spin in place, yet they still send and receive the chemical repulsion signals from the moving particles. Angular noise is added to the spinning motion to represent random kicks. Phase diagrams are built by measuring the overall alignment of particle directions and how much it fluctuates. The central result is that raising the noise level destroys collective alignment at a threshold that changes with how crowded the particles are, whereas raising the fraction of pinned particles destroys alignment at a threshold that stays the same regardless of crowding.

Core claim

When a fraction of chemorepulsive active colloids is pinned in space but remains chemically coupled through rotational motion only, and angular noise is added to the rotational dynamics, the system exhibits disorder- and noise-driven transitions in global polar order. The critical noise strength at which polar order vanishes increases with particle density, while the critical pinning fraction at which order vanishes shows no such density dependence. When the effective range of the chemorepulsive interaction is short compared with system size, the particles form moving density bands and the distribution of the order parameter becomes bimodal near the transition; these features disappear in a长

What carries the argument

The phase diagram constructed from the global polar order parameter and its fluctuations, plotted against pinning fraction and noise strength, with the screening coefficient of the chemorepulsive interaction setting the effective interaction range that controls band formation.

If this is right

Increasing angular noise destroys collective alignment at a density-dependent threshold.
Increasing the pinning fraction destroys collective alignment at a density-independent threshold.
Short-range chemorepulsion produces moving density bands and a bimodal order-parameter distribution near the transition.
Finite system size shifts the location of both transitions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The density dependence of the noise transition implies that experiments could tune crowding to make the system more or less robust to rotational fluctuations.
The appearance of density bands only at short range suggests that the same model could be used to explore whether real colloidal systems with limited signaling range exhibit similar spatial segregation.
The contrast between noise and pinning effects may generalize to other active-matter models where quenched disorder and stochasticity act through different channels.

Load-bearing premise

Pinned particles remain fully chemically coupled to the mobile particles through the same screened repulsion while being allowed only to rotate in place.

What would settle it

Simulations or experiments that vary particle density while keeping all other parameters fixed and find that the critical noise strength for loss of polar order is independent of density would falsify the reported density dependence.

Figures

Figures reproduced from arXiv: 2605.02854 by Rajesh Singh, Sagarika Adhikary.

**Figure 1.** Figure 1: FIG. 1. Schematic description of the model is shown in panel (a). Free and pinned active particles are randomly distributed view at source ↗

**Figure 2.** Figure 2: FIG. 2. Without quenched disorder and noise: (a) Phase view at source ↗

**Figure 3.** Figure 3: FIG. 3. Here, view at source ↗

**Figure 4.** Figure 4: FIG. 4. Here view at source ↗

**Figure 5.** Figure 5: FIG. 5. Order parameter distribution at transition point. view at source ↗

**Figure 6.** Figure 6: FIG. 6. Pair correlation plot for the co-efficient (a) view at source ↗

read the original abstract

Recent studies of active colloidal matter have revealed that a global polar order can arise from chemorepulsive interactions among particles without any explicit alignment interaction between them. In this work, we investigate such chemically interacting active colloids in the presence of quenched disorder, where a fraction of particles are randomly pinned in space. These pinned particles are restricted to rotational motion while remaining chemically coupled to the mobile population. In addition, angular noise is incorporated into the rotational dynamics to capture stochastic effects. To elucidate the interplay of quenched disorder and noise, we construct phase diagrams based on polar order and its fluctuations, and systematically analyze the associated disorder- and noise-driven phase transitions. Surprisingly, we find that the phase transition driven by the noise is significantly dependent on the density of the particles, whereas such a density-dependence is not present when the control parameter is the pinning fraction. The finite-size effects on these transitions are also examined. An effective interaction range, governed by the coefficient related to screening of the chemorepulsive interaction, plays a crucial role in collective behavior. When the effective interaction range is much smaller than the system size, the system exhibits density band formation, a feature absent in the long-range interaction regime. Moreover, near the transition point, the order parameter distribution becomes bimodal for the case of short-range interaction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The reported density dependence of the noise-driven transition is probably an artifact of fixing the screening length instead of the range relative to interparticle spacing.

read the letter

The main takeaway is that the density dependence of the noise-driven transition in this chemorepulsive colloid model may not be a robust physical effect but rather a consequence of keeping the screening length fixed while varying density. The work adds quenched disorder through randomly pinned particles that still participate in the chemical repulsion but cannot move translationally. They layer on angular noise and map out how polar order is lost as a function of pinning fraction, noise amplitude, and density. They also vary the screening coefficient to switch between long-range and short-range regimes, finding bands and bimodal order-parameter histograms only in the short-range case. This is a straightforward numerical study that cleanly separates the effects of disorder and noise. The finite-size scaling and the distinction between the two control parameters are useful additions to the chemorepulsive flocking literature. The potential issue is in the density variation. Increasing density at fixed screening length packs more neighbors into the interaction volume, which strengthens collective alignment and raises the noise threshold for disorder. The pinning fraction, being a relative measure, does not alter neighbor count the same way. Without evidence that they adjusted the screening length proportionally to the mean interparticle spacing, the reported density dependence looks like an artifact. The abstract mentions the screening coefficient controls the range but does not say it was rescaled. The assumptions about pinned particles remaining chemically active seem reasonable for the model. This paper is for active-matter researchers interested in how obstacles and noise affect collective motion in repulsive systems. It is worth a serious referee because the simulations are direct and the questions are concrete, even if the density result needs clarification on parameter scaling.

Referee Report

2 major / 2 minor

Summary. The manuscript numerically explores emergent polar order in a system of chemorepulsive active colloids subject to quenched disorder (a fraction of particles randomly pinned in position but free to rotate while remaining chemically coupled) and additive angular noise. Phase diagrams are constructed in the pinning-fraction vs. noise-strength plane for varying densities; the authors report that the noise-driven loss of order depends on density while the pinning-driven transition does not. Finite-size effects are examined, and the screening coefficient that sets the effective chemorepulsive range is shown to control whether density bands and bimodal order-parameter distributions appear (short-range regime) or are absent (long-range regime).

Significance. If the central density-dependence distinction holds after the interaction-range protocol is clarified, the work adds a useful data point to active-matter literature on flocking without explicit alignment rules. The explicit model definition, systematic parameter sweeps, and finite-size analysis constitute clear strengths that make the numerical results potentially reproducible and falsifiable.

major comments (2)

[Abstract and phase-diagram construction] Abstract and phase-diagram section: the headline claim that 'the phase transition driven by the noise is significantly dependent on the density' while the pinning-fraction transition is not requires an explicit statement on whether the screening coefficient is held fixed or rescaled with mean interparticle spacing when density is varied. The abstract already notes that short-range interactions produce density bands and bimodal distributions, confirming sensitivity to range-versus-spacing; without rescaling, increasing density at fixed screening length increases the number of neighbors inside the interaction volume and can shift the critical noise amplitude even if the microscopic rules are density-independent.
[Model definition] Model section: the assumption that pinned particles remain fully chemically coupled to the mobile population while restricted to rotation is load-bearing for the quenched-disorder implementation. A short justification or reference to experimental realizability should be added, because any effective decoupling would alter the disorder-driven transition line.

minor comments (2)

[Abstract and methods] The abstract states that 'finite-size effects on these transitions are also examined' but supplies no quantitative details (system sizes, number of realizations, error bars on order-parameter histograms). These should be stated explicitly in the methods or results section.
[Notation and results] Notation for the screening coefficient and effective interaction range should be introduced in the model section before its use in the results; the current placement makes the short-range vs. long-range distinction harder to follow on first reading.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of the numerical results, and constructive suggestions. We address the two major comments point by point below and have prepared revisions that clarify the model choices without altering the central findings.

read point-by-point responses

Referee: [Abstract and phase-diagram construction] Abstract and phase-diagram section: the headline claim that 'the phase transition driven by the noise is significantly dependent on the density' while the pinning-fraction transition is not requires an explicit statement on whether the screening coefficient is held fixed or rescaled with mean interparticle spacing when density is varied. The abstract already notes that short-range interactions produce density bands and bimodal distributions, confirming sensitivity to range-versus-spacing; without rescaling, increasing density at fixed screening length increases the number of neighbors inside the interaction volume and can shift the critical noise amplitude even if the microscopic rules are density-independent.

Authors: We appreciate the referee's observation. In the simulations the screening coefficient is deliberately held fixed while density is varied; this choice reflects the physical situation in which the chemical screening length is set by diffusion and decay rates of the signaling molecules and is therefore independent of particle number density. As a result, higher densities increase the number of interacting neighbors within the fixed range, producing the reported density dependence of the noise-driven transition. The pinning-driven transition remains insensitive to density because it is controlled by the geometric fraction of fixed positions. We will add an explicit statement to this effect in the abstract and in the phase-diagram section, together with a short discussion of the physical motivation for fixed screening. revision: yes
Referee: [Model definition] Model section: the assumption that pinned particles remain fully chemically coupled to the mobile population while restricted to rotation is load-bearing for the quenched-disorder implementation. A short justification or reference to experimental realizability should be added, because any effective decoupling would alter the disorder-driven transition line.

Authors: We agree that the continued chemical coupling of pinned particles is essential to the disorder implementation. The model is intended to represent colloids whose translational degrees of freedom are immobilized (for example by optical tweezers or surface adhesion) while rotational diffusion and chemical production/sensing remain active. Such conditions are experimentally accessible in colloidal systems. We will insert a concise justification with references to relevant experimental techniques in the revised model section. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation or claims

full rationale

The paper reports results from direct numerical simulations of an explicit overdamped model for chemorepulsive active colloids, incorporating pinned particles (restricted to rotation but chemically coupled) and additive angular noise. Phase diagrams, order-parameter distributions, and the reported density dependence of the noise-driven transition versus the pinning-fraction-driven transition are obtained by varying control parameters in the equations of motion and measuring the resulting steady-state statistics. No analytical derivation, fitted parameter relabeled as a prediction, self-definitional closure, or load-bearing self-citation chain is present; the screening coefficient is an explicit model input whose consequences (short-range vs long-range regimes) are explored numerically rather than assumed. The central observations therefore remain independent of the inputs by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

Central claims rest on numerical simulation of a standard active-colloid model whose interaction form, pinning rule, and noise implementation are not detailed in the abstract; several control parameters are varied but no new physical entities are introduced.

free parameters (4)

pinning fraction
Varied as control parameter for disorder-driven transitions.
angular noise strength
Varied as control parameter for noise-driven transitions.
particle density
Varied to reveal density dependence of transitions.
screening coefficient
Controls effective range of chemorepulsive interaction.

axioms (2)

domain assumption Overdamped Langevin dynamics govern particle translation and rotation
Standard modeling choice for colloidal active matter at low Reynolds number.
domain assumption Chemorepulsive force is exponentially screened with a single length scale
Assumed functional form for chemical interaction between particles.

pith-pipeline@v0.9.0 · 5540 in / 1434 out tokens · 44931 ms · 2026-05-08T02:48:43.300153+00:00 · methodology

discussion (0)

Reference graph

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The color bar is the same as the one used in Fig.3 and Fig.4

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