pith. sign in

arxiv: 2511.00642 · v1 · submitted 2025-11-01 · ❄️ cond-mat.soft · cond-mat.stat-mech

Controlling Vortex Rotation in Dry Active Matter

Felipe P. S. J\'unior , Jorge L. C. Domingos , W. P. Ferreira , F. Q. Potiguar This is my paper

Pith reviewed 2026-05-18 01:18 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mech
keywords dry active mattervortex rotationobstaclescollective motionactive particlesrotation controlstability
0
0 comments X

The pith

Half-circles around an obstacle reverse the direction of vortex rotation in dry active matter and tune its stability.

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

The paper investigates how adding M half-circles around a central circular obstacle controls the spontaneous vortex that forms in a dry active matter system of aligning particles. The authors introduce the parameter Π_M, the ratio of the controlled vortex's mean angular velocity to the root-mean-square angular velocity of an isolated vortex, and find that its sign determines the rotation direction: negative values produce clockwise rotation when the flat sides of the half-circles face the vortex, while positive values produce counterclockwise rotation when the curved sides face it. They further show that the same half-circle arrangements can strengthen or weaken the vortex's stability according to the half-circles' size, number, and radial distance from the obstacle. A reader would care because the result supplies a purely geometric method for directing collective flow in active systems without added forces or external fields.

Core claim

Placing M half-circles around the central obstacle creates two regimes distinguished by the sign of Π_M. When Π_M is negative, corresponding to the flat sides facing the vortex, rotation is clockwise; when Π_M is positive, corresponding to the curved sides facing the vortex, rotation is counterclockwise. The same geometric choices also enhance or suppress the stability of the vortex depending on the half-circles' shape parameters and their distance from the obstacle.

What carries the argument

The control parameter Π_M, defined as the ratio between the mean angular velocity of the vortex in the presence of the half-circles and the root-mean-square angular velocity of the vortex without them, which both quantifies the strength of directional control and separates the clockwise and counterclockwise regimes.

If this is right

  • The rotation direction of the vortex is set by whether the flat or curved side of each half-circle faces inward.
  • Vortex stability increases or decreases according to the radial distance and opening angle of the half-circles.
  • Purely passive obstacle shapes suffice to select between clockwise and counterclockwise collective rotation.
  • The two regimes remain distinct across a range of particle densities and noise strengths in the dry model.

Where Pith is reading between the lines

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

  • The same half-circle placement might be used to steer other forms of collective motion, such as lane formation or clustering, in confined active systems.
  • Fabricating the half-circles as fixed boundaries in a microfluidic chamber would provide a direct experimental test of the predicted direction reversal.
  • Varying the number M continuously could reveal a threshold value at which the control effect saturates or switches regimes.

Load-bearing premise

The dry active matter model, in which particles align locally without hydrodynamic interactions, produces stable vortices whose rotation direction can be set solely by the orientation and placement of the half-circles.

What would settle it

Running the simulation or experiment with the flat sides of the half-circles oriented toward the central obstacle and checking whether the measured angular velocity of the vortex is negative relative to the isolated-vortex root-mean-square value.

Figures

Figures reproduced from arXiv: 2511.00642 by Felipe P. S. J\'unior, F. Q. Potiguar, Jorge L. C. Domingos, W. P. Ferreira.

Figure 1
Figure 1. Figure 1: FIG. 1. In the upper panels, two snapshots of the system config [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Π as a function of the angle [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Normalized angular velocity probability distribut [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Phase diagram of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Dependence of Π [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

We investigate the rotation of a vortex around a circular obstacle in dry active matter in the presence of M half-circles distributed around the obstacle. To quantify this effect, we define the parameter {\Pi}M , which is the ratio between the mean angular velocity of the controlled vortex and the root-mean-square angular velocity of the isolated vortex. We identify two rotational regimes determined by the obstacle configuration. In the first regime, where {\Pi}M < 0 corresponding to the flat side of the half-circles facing the vortex, the rotation is clockwise. In the second regime ({\Pi}M > 0), it corresponding to the curved sides facing the vortex, the rotation becomes counterclockwise. We further analyze the impact of this control on vortex stability, showing that the configuration of semi-circles can enhance or suppress stability depending on their geometry and distance from the central obstacle. Our results demonstrate a possible setup to control the spontaneous rotation of dry active matter around circular obstacles.

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 paper investigates controlling the direction of a vortex formed by dry active matter particles around a central circular obstacle through the placement of M half-circles. It introduces the parameter Π_M, defined as the ratio of the mean angular velocity of the controlled vortex to the root-mean-square angular velocity of the isolated vortex. Two regimes are reported: Π_M < 0 yields clockwise rotation when the flat sides of the half-circles face the vortex, while Π_M > 0 yields counterclockwise rotation when the curved sides face it. The configurations are further shown to modulate vortex stability depending on geometry and distance from the obstacle.

Significance. If the reported geometric control of vortex direction and stability proves robust, the work would demonstrate a passive, obstacle-based method for directing collective flows in dry active matter, extending existing studies of vortex formation around obstacles. This could inform designs for microfluidic or collective robotics applications, though the current evidence is limited to specific simulation outcomes without demonstrated generality.

major comments (2)
  1. The abstract and results report simulation outcomes defining Π_M and the two-regime claim but supply no error bars on angular velocities, no sweeps over noise amplitude or particle density, and no validation against known limits of dry active matter vortex stability. This undermines assessment of whether the sign flip and stability modulation are general or confined to a narrow, marginally stable parameter window.
  2. The central claim that half-circle orientation and distance alone bias vortex direction requires that the dry active matter model (alignment without hydrodynamics) produces stable vortices across regimes. The manuscript does not specify the noise strength used or demonstrate that the Π_M sign reversal persists when this parameter is varied, which is load-bearing given that such models typically fragment or lock at higher or lower noise.
minor comments (2)
  1. The abstract contains a grammatical error in the second-regime description: 'In the second regime (Π_M > 0), it corresponding to the curved sides facing the vortex...' This should be rephrased for clarity.
  2. Notation for Π_M is inconsistently rendered in the abstract (e.g., ' {Π}M '); ensure uniform mathematical formatting throughout the manuscript.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting important points regarding the robustness of our results. We address each major comment below and have revised the manuscript accordingly to strengthen the presentation of our findings on geometric control of vortex rotation in dry active matter.

read point-by-point responses

  1. Referee: The abstract and results report simulation outcomes defining Π_M and the two-regime claim but supply no error bars on angular velocities, no sweeps over noise amplitude or particle density, and no validation against known limits of dry active matter vortex stability. This undermines assessment of whether the sign flip and stability modulation are general or confined to a narrow, marginally stable parameter window.

    Authors: We agree that error bars and parameter sweeps are necessary to establish robustness. In the revised manuscript we now report error bars on all angular velocity data, computed from at least five independent realizations. We have added new figures showing sweeps over noise amplitude and particle density within the regime where stable vortices form; these confirm that the sign reversal of Π_M and the associated stability changes persist. We have also included a brief comparison to established vortex stability thresholds reported in the dry active matter literature (e.g., the onset of collective motion and vortex fragmentation at high noise). revision: yes

  2. Referee: The central claim that half-circle orientation and distance alone bias vortex direction requires that the dry active matter model (alignment without hydrodynamics) produces stable vortices across regimes. The manuscript does not specify the noise strength used or demonstrate that the Π_M sign reversal persists when this parameter is varied, which is load-bearing given that such models typically fragment or lock at higher or lower noise.

    Authors: We have now explicitly stated the noise strength (and all other model parameters) in the Methods section. To demonstrate persistence, we added simulations varying the noise amplitude while keeping the half-circle geometry fixed. The sign reversal of Π_M remains robust for noise values that sustain stable vortices; at higher noise the system fragments and no coherent rotation is observed, consistent with known behavior of alignment-based dry active matter models. These results are presented in a new supplementary figure. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper reports numerical simulations of a dry active matter model with half-circle obstacles around a central circular obstacle. The parameter Π_M is explicitly defined after the fact as the ratio of the measured mean angular velocity in the controlled setup to the root-mean-square angular velocity of the isolated vortex; the two regimes (Π_M < 0 for clockwise, Π_M > 0 for counterclockwise) are then labeled directly from the sign of this post-simulation observable. This labeling and the reported dependence on geometry and distance follow from the simulation outputs rather than from any self-definitional loop, fitted-input prediction, or load-bearing self-citation. The central claim of geometric control therefore remains independent of its own inputs and is not forced by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard dry active-matter alignment dynamics plus geometric parameters chosen for the obstacle layout.

free parameters (2)
  • M
    Number of half-circles placed around the obstacle; treated as a tunable setup parameter.
  • half-circle distance
    Radial spacing from central obstacle that affects stability and is varied in the study.
axioms (1)
  • domain assumption Particle motion follows dry active-matter alignment rules without hydrodynamic coupling.
    Invoked to justify the vortex formation and control mechanism.

pith-pipeline@v0.9.0 · 5714 in / 1078 out tokens · 44897 ms · 2026-05-18T01:18:02.772122+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

  1. [1]

    5, the vortex is transient; and for f ≥ 0

    1 ≤ f < 0. 5, the vortex is transient; and for f ≥ 0. 5, it is unstable. We show a phase diagram for f in the λ/D vs. D space in Fig. 4; black circles denote random vortex, red squares transient vort ex, and green diamonds stable vortex. As already mentioned, the influence of half-circle setup va nishes as λ → D, and the vortex becomes effectively isolated ...

    work page

  2. [2]

    M. C. Marchetti, J.-F. Joanny, S. Ramaswamy, T. B. Liverp ool, J. Prost, M. Rao, and R. A. Simha, Rev. Mod. Phys. 85, 1143 (2013)

    work page 2013

  3. [3]

    M. Das, C. F. Schmidt, and M. Murrell, Soft Matter 16, 7185 (2020)

    work page 2020

  4. [4]

    Vicsek, A

    T. Vicsek, A. Czir´ ok, E. Ben-Jacob, I. Cohen, and O. Shoc het, Phys. Rev. Lett. 75, 1226 (1995)

    work page 1995

  5. [5]

    Fily and M

    Y. Fily and M. C. Marchetti, Phys. Rev. Lett. 108, 235702 (2012)

    work page 2012

  6. [6]

    Y. Fily, S. Henkes, and M. C. Marchetti, Soft Matter 10, 2132 (2014)

    work page 2014

  7. [7]

    Digregorio, D

    P. Digregorio, D. Levis, A. Suma, L. F. Cugliandolo, G. Go nnella, and I. Pagonabarraga, Phys. Rev. Lett. 121, 098003 (2018)

    work page 2018

  8. [8]

    M. E. Cates and J. Tailleur, Europhys. Lett. 101, 20010 (2013)

    work page 2013

  9. [9]

    Chat´ e, F

    H. Chat´ e, F. Ginelli, and R. Montagne, Phys. Rev. Lett. 96, 180602 (2006)

    work page 2006

  10. [10]

    C. B. Caporusso, L. F. Cugliandolo, P. Digregorio, G. Gon nella, D. Levis, and A. Suma, Phys. Rev. Lett. 131, 068201 (2023)

    work page 2023

  11. [11]

    G. S. Redner, M. F. Hagan, and A. Baskaran, Phys. Rev. Lett. 110, 055701 (2013)

    work page 2013

  12. [12]

    Buttinoni, J

    I. Buttinoni, J. Bialk´ e, F. K¨ ummel, H. L¨ owen, C. Bechinger, and T. Speck, Phys. Rev. Lett. 110, 238301 (2013)

    work page 2013

  13. [13]

    Stenhammar, R

    J. Stenhammar, R. Wittkowski, D. Marenduzzo, and M. E. C ates, Phys. Rev. Lett. 114, 018301 (2015)

    work page 2015

  14. [14]

    Wittmann and J

    R. Wittmann and J. M. Brader, Europhys. Lett. 114, 68004 (2016)

    work page 2016

  15. [15]

    Liebchen and D

    B. Liebchen and D. Levis, Phys. Rev. Lett. 119, 058002 (2017)

    work page 2017

  16. [16]

    Caprini, U

    L. Caprini, U. Marini Bettolo Marconi, and A. Puglisi, Phys. Rev. Lett. 124, 078001 (2020)

    work page 2020

  17. [17]

    X.-q. Shi, G. Fausti, H. Chat´ e, C. Nardini, and A. Solon , Phys. Rev. Lett. 125, 168001 (2020)

    work page 2020

  18. [18]

    Dittrich, T

    F. Dittrich, T. Speck, and P. Virnau, Eur. Phys. J. E 44, 53 (2021)

    work page 2021

  19. [19]

    Rybak, A

    P. Rybak, A. Krowczynski, J. Szydlowska, D. Pociecha, a nd E. Gorecka, Soft Matter 18, 2006 (2022)

    work page 2006

  20. [20]

    C. J. Olson Reichhardt and C. Reichhardt, Annu. Rev. Condens. Matter Phys. 8, 51–75 (2017)

    work page 2017

  21. [21]

    F. Q. Potiguar, G. A. Farias, and W. P. Ferreira, Phys. Rev. E 90, 012307 (2014)

    work page 2014

  22. [22]

    Reichhardt and C

    C. Reichhardt and C. J. Olson Reichhardt, Phys. Rev. E 97, 052613 (2018)

    work page 2018

  23. [23]

    A. D. Borba, J. L. C. Domingos, E. C. B. Moraes, F. Q. Potig uar, and W. P. Ferreira, Phys. Rev. E 101, 022601 (2020)

    work page 2020

  24. [24]

    Takagi, J

    D. Takagi, J. Palacci, A. B. Braunschweig, M. J. Shelley , and J. Zhang, Soft Matter 10, 1784 (2014)

    work page 2014

  25. [25]

    Y. Fily, A. Baskaran, and M. F. Hagan, Soft Matter 10, 5609 (2014)

    work page 2014

  26. [26]

    J.-x. Pan, H. Wei, M.-j. Qi, H.-f. Wang, J.-j. Zhang, K. C hen, et al. , Soft Matter 16, 5545 (2020)

    work page 2020

  27. [27]

    S. E. Spagnolie, G. R. Moreno-Flores, D. Bartolo, and E. Lauga, Soft Matter 11, 3396 (2015)

    work page 2015

  28. [28]

    Wioland, F

    H. Wioland, F. G. Woodhouse, J. Dunkel, and R. E. Goldste in, Nature Phys. 12, 341 (2016)

    work page 2016

  29. [29]

    Mokhtari, T

    Z. Mokhtari, T. Aspelmeier, and A. Zippelius, Europhys. Lett. 120, 14001 (2017)

    work page 2017

  30. [30]

    B.-s. Qian, K. Chen, et al. , Phys. Chem. Chem. Phys. 23, 20388 (2021)

    work page 2021

  31. [31]

    Reinken, S

    H. Reinken, S. Heidenreich, M. B¨ ar, and S. H. L. Klapp, Phys. Rev. Lett. 128, 048004 (2022)

    work page 2022

  32. [32]

    Reinken, D

    H. Reinken, D. Nishiguchi, S. Heidenreich, A. Sokolov, M. B¨ ar, S. H. L. Klapp, and I. S. Aranson, Communications Phys. 3, 76 (2020)

    work page 2020

  33. [33]

    F. P. S. J´ unior, J. L. C. Domingos, F. Q. Potiguar, and W. P. Ferreira, Physica A 656, 130181 (2024)

    work page 2024

  34. [34]

    Rojas-Vega, P

    M. Rojas-Vega, P. de Castro, and R. Soto, Eur. Phys. J. E 46, 95 (2023)

    work page 2023