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arxiv: 2607.02445 · v1 · pith:EIJ7LO64new · submitted 2026-07-02 · ❄️ cond-mat.soft

Curvature-induced host-mediated polarization of active particles

Giulia Janzen , D. A. Matoz-Fernandez This is my paper

Pith reviewed 2026-07-03 04:37 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords active Brownian particlespolar ordercurved confinementpassive mediumstress redistributioncollective motionspherescar formation
0
0 comments X

The pith

Non-aligning active Brownian particles on a sphere develop polar coherence through stress scars created in a dense passive host.

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

The paper establishes that polar collective motion can emerge without any alignment interactions between the active particles themselves. Instead, non-aligning active Brownian particles embedded in a dense passive medium on a compact curved surface such as a sphere redistribute stress in the host, forming passive-depleted regions. These regions merge into elongated scars once the stress-spreading length becomes comparable to the sphere radius. The scars then channel active motion and, through feedback with the active flux, drive the particles toward a shared direction. Removing the passive host eliminates the polarity even though clustering persists, showing that the effect depends on the coupling of activity, passive stress, and curvature.

Core claim

Persistent active motion redistributes stress through the host and creates passive-depleted regions. When the stress-spreading length becomes comparable to the sphere radius, these regions merge into elongated scars that channel active motion and, through feedback with the active flux, promote a common direction of motion. Removing the passive host suppresses polar coherence even though the active particles continue to cluster on the same sphere.

What carries the argument

Stress redistribution by active motion that forms passive-depleted scars on curved geometry, which then channel and polarize the active flux through feedback.

If this is right

  • Polar coherence arises without alignment interactions between the active particles.
  • The passive host is required; its removal suppresses polarity despite continued clustering.
  • Elongated scars form and channel motion specifically when the stress-spreading length matches the sphere radius.
  • Feedback between the scars and the active flux establishes the common direction of motion.

Where Pith is reading between the lines

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

  • The mechanism may generalize to other compact curved surfaces where curvature sets a length scale comparable to the stress-spreading length.
  • Varying activity level or host density in experiments could identify the threshold at which scars merge and polarity appears.
  • The direction of the resulting polarity might be controllable through initial conditions or boundary perturbations.

Load-bearing premise

The passive host must be dense enough that active motion redistributes its stress and creates depleted regions whose merging into scars depends on the stress-spreading length becoming comparable to the sphere radius.

What would settle it

A simulation or experiment that removes the passive host or tunes the sphere radius so the stress-spreading length no longer matches it should eliminate polar coherence while leaving clustering intact.

Figures

Figures reproduced from arXiv: 2607.02445 by D. A. Matoz-Fernandez, Giulia Janzen.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: a shows the contrast at ϕa = 0.40. In the presence of the passive host, active dopants form ex￾tended polar streams associated with passive-depleted scars. In the active-only case, the particles still aggre￾gate on the same curved surface, but the aggregates re￾main compact and weakly polarized. Consistently, the full correlation function of the active-only control lacks [PITH_FULL_IMAGE:figures/full_fig_… view at source ↗
read the original abstract

Polar collective motion commonly arises from alignment interactions, particle anisotropy, or an imposed directional bias. Here we identify a distinct route to polar order that does not rely on alignment interactions between the active particles. We show that non-aligning active Brownian particles embedded in a dense passive medium can develop polar coherence when confined to a compact curved surface. Persistent active motion redistributes stress through the host and creates passive-depleted regions. When the stress-spreading length becomes comparable to the sphere radius, these regions merge into elongated scars that channel active motion and, through feedback with the active flux, promote a common direction of motion. Removing the passive host suppresses polar coherence even though the active particles continue to cluster on the same sphere. Our results establish an environment-mediated route to collective polarity in which symmetry breaking emerges from the coupling between active motion, passive stress redistribution, and compact geometry.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that non-aligning active Brownian particles embedded in a dense passive medium develop polar coherence when confined to a compact curved surface such as a sphere. Persistent active motion redistributes stress in the host, creating depleted regions that merge into elongated scars when the stress-spreading length becomes comparable to the sphere radius; these scars then channel active flux into a common direction through feedback. Removing the passive host eliminates polar coherence even though clustering persists.

Significance. If the central mechanism holds, the work identifies a distinct, environment-mediated route to polar order that does not rely on alignment interactions, particle anisotropy, or external bias, with potential relevance to biological active matter on curved geometries. The explicit comparison showing that polarity vanishes without the host while clustering remains is a clear strength of the evidence presented.

major comments (2)
  1. [Abstract, final paragraph] Abstract, final paragraph: the claim that scars merge and promote polarity specifically when the stress-spreading length becomes comparable to the sphere radius is not shown to be necessary or causal. The description does not establish that this length is the controlling variable (as opposed to density or activity strength) nor demonstrate that the merging produces directed channeling rather than isotropic depletion.
  2. [Results on scar formation] Results section describing scar formation: the feedback loop between scars and active flux is presented as promoting a common direction, but no quantitative measure (e.g., correlation between scar orientation and velocity field) is provided to confirm that the scars are the cause rather than a correlated byproduct of the curvature and confinement.
minor comments (2)
  1. [Methods] Notation for the stress-spreading length is introduced without an explicit definition or formula in the main text; a clear equation or parameter table would improve reproducibility.
  2. [Figures] Figure captions for the sphere visualizations should explicitly state the value of the stress-spreading length relative to the radius in each panel.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the two major comments point by point below and will incorporate revisions to strengthen the supporting evidence for the proposed mechanism.

read point-by-point responses

  1. Referee: [Abstract, final paragraph] Abstract, final paragraph: the claim that scars merge and promote polarity specifically when the stress-spreading length becomes comparable to the sphere radius is not shown to be necessary or causal. The description does not establish that this length is the controlling variable (as opposed to density or activity strength) nor demonstrate that the merging produces directed channeling rather than isotropic depletion.

    Authors: We acknowledge that the manuscript presents this length-scale condition primarily through parameter choices in the presented simulations rather than through explicit variation. In the revised version we will add a set of simulations in which the stress-spreading length is varied independently (via host viscosity and interaction range) while holding density and activity fixed. These runs will show the transition from isotropic depletion to elongated scars and directed flux only when the length becomes comparable to the sphere radius, thereby establishing the length as the controlling variable. revision: yes

  2. Referee: [Results on scar formation] Results section describing scar formation: the feedback loop between scars and active flux is presented as promoting a common direction, but no quantitative measure (e.g., correlation between scar orientation and velocity field) is provided to confirm that the scars are the cause rather than a correlated byproduct of the curvature and confinement.

    Authors: The current text relies on qualitative visualization of scar evolution and particle trajectories. To address the request for quantitative support, we will compute and report the spatial correlation between the local orientation of passive-depleted scars (obtained from coarse-grained density fields) and the time-averaged active velocity field within those regions. The resulting correlation function and its statistical significance will be added to the results section or a supplementary figure. revision: yes

Circularity Check

0 steps flagged

No circularity; mechanism emerges from physical coupling without definitional reduction

full rationale

The abstract and described claims present polar coherence as arising from the coupling of persistent active motion, passive stress redistribution into depleted regions, and compact curvature when a stress-spreading length becomes comparable to the sphere radius. This length-scale condition is a stated physical parameter governing scar formation and feedback, not a fitted input renamed as a prediction or a self-referential definition. No equations, self-citations, or ansatzes are quoted that reduce the central result to its own inputs by construction. The derivation chain is therefore self-contained against external physical modeling and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on standard active-matter dynamics plus the domain assumption of a dense passive host whose stress response couples to curvature; no free parameters or invented entities are identifiable from the abstract.

axioms (2)
  • standard math Active Brownian particles follow persistent random-walk dynamics without alignment interactions.
    Stated directly in the abstract as the starting condition.
  • domain assumption The passive medium is dense and redistributes stress created by active motion.
    Central premise required for depleted-region and scar formation.

pith-pipeline@v0.9.1-grok · 5673 in / 1223 out tokens · 27733 ms · 2026-07-03T04:37:42.343055+00:00 · methodology

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