pith. sign in

arxiv: 2410.13705 · v3 · submitted 2024-10-17 · ❄️ cond-mat.soft

Collective dynamics of densely confined active polar disks with self- and mutual alignment

Weizhen Tang , Yating Zheng , Amir Shee , Guozheng Lin , Zhangang Han , Pawel Romanczuk , Cristi\'an Huepe This is my paper

Pith reviewed 2026-05-23 19:16 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords collective dynamicsactive polar disksself-alignmentmutual alignmentconfined arenamillingoscillationsactive matter
0
0 comments X

The pith

Self-alignment to contact forces combined with mutual alignment from off-center rotation produces collective states mixing high-frequency local oscillations and low-frequency milling in confined polar disks.

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

The paper examines a mechanical model of many self-propelled polar disks packed densely inside a circular arena. Each disk aligns its heading to the net contact force from the substrate and also aligns with neighbors because its rotation center lies a distance R behind its geometric center. These two alignment rules together generate motion patterns in which disks trace small fast circles while the group as a whole slowly mills around the arena center. The same hybrid states appear whether the disks move in fluid-like or solid-like arrangements. The patterns persist when the offset distance, damping properties, boundary smoothness, density, and total number of disks are varied.

Core claim

In this model each disk self-aligns toward the sum of contact forces from disk-substrate interactions and mutually aligns because its center of rotation sits a distance R behind its centroid so that central contacts produce torques. When many such disks are confined at high density in a circular arena the dual alignment yields collective states that combine high-frequency localized circular oscillations with low-frequency milling around the arena center; the states exist in both fluid and solid regimes and remain stable across changes in R, damping isotropy, boundary roughness, density, and system size.

What carries the argument

The dual alignment mechanism consisting of self-alignment to net contact forces together with mutual alignment generated by an offset rotation center a distance R behind each disk centroid.

If this is right

  • Collective states emerge that combine high-frequency localized circular oscillations with low-frequency milling around the arena center.
  • These states appear in both fluid-like and solid-like particle arrangements.
  • The hybrid states remain robust when the rotation offset R, damping anisotropy, boundary conditions, density, and system size are varied.

Where Pith is reading between the lines

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

  • The separation of fast local circling and slow global milling time scales could be exploited to design robotic swarms whose overall rotation rate is set independently of individual spin rates.
  • Similar dual alignment might stabilize milling in biological groups such as bacterial colonies or cell clusters even when explicit attraction rules are absent.
  • The robustness to boundary and density changes suggests the patterns could be reproduced in laboratory realizations with colloidal particles or micro-robots having adjustable drive offsets.

Load-bearing premise

Each disk orients toward the total force from substrate contacts and experiences torques from those contacts because its rotation center lies behind its centroid.

What would settle it

A simulation or physical experiment in which the disks exhibit either only uniform global milling without the high-frequency local oscillations or only disordered motion without milling would falsify the claimed emergence of the hybrid collective states.

Figures

Figures reproduced from arXiv: 2410.13705 by Amir Shee, Cristi\'an Huepe, Guozheng Lin, Pawel Romanczuk, Weizhen Tang, Yating Zheng, Zhangang Han.

Figure 1
Figure 1. Figure 1: Active polar disks with linear elastic repulsion model and arena. a Schematic diagram of two interacting self-propelled disks, i and j, oriented along nˆi and nˆj , respectively. Each disk has diameter l0 and its center of rotation is labeled by a red point, located a distance R behind its geometrical center. Linear repulsive forces, proportional to |⃗l i j| − l0 , act on each centroid, resulting in forces… view at source ↗
Figure 2
Figure 2. Figure 2: Emerging collective states for different disk dynamics and bound￾ary conditions. Snapshots of collective states that emerge under different condi￾tions, for the same Dθ = 0.001 noise level. Each arrow, colored by angle, rep￾resents the location and orientation of a self-propelled disk. Black arrows signal high local vorticity. The top row panels (a-d) present cases with isotropic mobil￾ity, where agents ca… view at source ↗
Figure 3
Figure 3. Figure 3: Orientation autocorrelation functions for different collective states. The same cases presented in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Orientation autocorrelation in Fourier space for different collective states. The same cases presented in Figs. 2 and 3 are displayed, for smooth or rough arena boundaries and isotropic or anisotropic active disk mobility. The blue dashed curves represent large off-centered rotation distance R = 0.3; the red solid curves correspond to small R = 0.03. Low frequency milling can be found to different de￾grees… view at source ↗
Figure 5
Figure 5. Figure 5: Trajectory and dynamics of orbiting vortex. The position of the orbiting vortex that appears in small N = 400 systems with a smooth boundary and small off￾centered rotation distance R = 0.03 is displayed over time. a The trajectory of the vortex is traced in the arena by labeling its position every ∆t = 100 computational time units as successive blue dots connected by red arrows. b Fitting of the cosine fu… view at source ↗
Figure 6
Figure 6. Figure 6: Probability density functions of vortex radial positions. We display the PDF of the distance from the center of the arena ⃗rc to each identified vortex ⃗rv in simulations with smooth (S) or rough (R) arena boundaries, isotropic (I) or anisotropic (A) active disk mobility, different values of R = 0, 0.03, 0.3, and different number of disks N = 400, 1600, 6400. Each column is labeled by its corresponding com… view at source ↗
Figure 7
Figure 7. Figure 7: Emerging collective states and mean squared displacement for dif￾ferent densities and R values, in a smooth boundary confinement. The packing fraction φ is controlled by the disk diameter l0 in a system of N = 400 disks, set￾ting l0 = 0.8, φ = 0.580 in panels a, e; l0 = 1.0, φ = 0.907 in b, f; and l0 = 1.2, φ = 1.306 in c, g. The corresponding polar (P) and milling (M) order parameters are given by: P = 0.… view at source ↗
Figure 8
Figure 8. Figure 8: Emerging collective states and mean squared displacement for differ￾ent densities and R values, in a rough boundary confinement. As in [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: State Diagrams in the Dθ –R plane. Polarization P and milling order parameter M as a function of Dθ and R, showing the different collective states that can emerge in systems with isotropic or anisotropic agent-substrate damping and with a rough or smooth boundary. Regions with low P and high M correspond to milling states, high P and low M corresponds to localized rotation states, and high P and M correspo… view at source ↗
Figure 10
Figure 10. Figure 10: Polarization and milling as a function of control parameter R. Polar￾ization P and milling order parameter M as a function of R in systems with isotropic or anisotropic agent-substrate damping and with a rough or smooth boundary. Here, l0 = 1.0, v0 = 0.002, and each point is averaged over 20 realizations. 𝑦 𝑥 𝑟 ⃗ ! 𝑟 ⃗ " 𝑑 𝜃! Ω! [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Tracking of vortex dynamics. Starting from the orientation of all disks, regions of high vorticity are detected (labeled by black arrows), and the vortex po￾sition ⃗rv is defined as the mean position of all the agents within this region. This position is then expressed in polar coordinates with respect to the center of the arena ⃗rc , in terms of the radial position |⃗rv − ⃗rc | ≤ d and angle θv . 20 [PI… view at source ↗
Figure 12
Figure 12. Figure 12: presents the orientation autocorrelation functions for the same parameter combinations presented in [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Fourier transforms of orientation autocorrelation functions. The dis￾played plots are equivalent to those presented in [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Frequencies and amplitudes of orientation autocorrelation peaks for N = 400. The low-frequency (LF) and high-frequency (HF) oscillation peaks are identified in the Fourier transform of the orientation autocorrelation function, and their frequency and amplitude is displayed as a function of the off-centered rotation distance R. The frequency and amplitude plots are displayed for four different cases of iso… view at source ↗
Figure 15
Figure 15. Figure 15: Frequencies and amplitudes of orientation autocorrelation peaks for N = 1600. The low-frequency (LF) and high-frequency (HF) oscillation peaks are identified in the Fourier transform of the orientation autocorrelation function, and their frequency and amplitude is displayed as a function of the off-centered rotation distance R. The frequency and amplitude plots are displayed for four different cases of is… view at source ↗
Figure 16
Figure 16. Figure 16: Vortex positions for isotropic mobility and a smooth boundary. The red points indicate the vortex positions identified during a run for different off￾centered rotation distances and system sizes, keeping the density constant. The num￾ber in each panel displays the mean number of vortices per snapshot. Here, agent￾substrate interactions are isotropic and the confining boundary is smooth. Other simulation p… view at source ↗
Figure 17
Figure 17. Figure 17: Vortex positions for isotropic mobility and a rough boundary. The red points indicate the vortex positions identified during a run for different off-centered rotation distances and system sizes, keeping the density constant. The number in each panel displays the mean number of vortices per snapshot. Here, agent-substrate interactions are isotropic and the confining boundary is rough. Other simulation para… view at source ↗
Figure 18
Figure 18. Figure 18: Vortex positions for anisotropic mobility and a smooth boundary. The red points indicate the vortex positions identified during a run for different off￾centered rotation distances and system sizes, keeping the density constant. The num￾ber in each panel displays the mean number of vortices per snapshot. Here, agent￾substrate interactions are anisotropic and the confining boundary is smooth. Other simulati… view at source ↗
Figure 19
Figure 19. Figure 19: Vortex positions for anisotropic mobility and a rough boundary. The red points indicate the vortex positions identified during a run for different off￾centered rotation distances and system sizes, keeping the density constant. The number in each panel displays the mean number of vortices per snapshot. Here, agent-substrate interactions are anisotropic and the confining boundary is rough. Other simulation … view at source ↗
read the original abstract

We study the emerging collective states in a simple mechanical model of a dense group of self-propelled polar disks with off-centered rotation, confined within a circular arena. Each disk presents self-alignment towards the sum of contact forces acting on it, resulting from disk-substrate interactions, while also displaying mutual alignment with neighbors due to having its center of rotation located a distance R behind its centroid so that central contact forces can also introduce torques. The effect of both alignment mechanisms produces a variety of collective states that combine high-frequency localized circular oscillations with low-frequency milling around the center of the arena, in fluid or solid regimes. We consider cases with small/large R values, isotropic/anisotropic disk-substrate damping, smooth/rough arena boundaries, different densities, and multiple systems sizes, showing that the emergent collective states that we identify are robust, generic, and potentially observable in real-world natural or artificial systems.

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

1 major / 2 minor

Summary. The manuscript presents a minimal mechanical model of densely confined self-propelled polar disks that incorporates both self-alignment to the sum of substrate contact forces and mutual alignment arising from an off-center rotation point at distance R. Direct numerical simulations across variations in R, damping anisotropy, boundary roughness, density, and system size demonstrate the emergence of collective states that combine high-frequency localized circular oscillations with low-frequency milling around the arena center, occurring in both fluid-like and solid-like regimes.

Significance. If the reported states are robust, the work supplies a concrete, parameter-explored example of how two elementary mechanical alignment rules can generate superimposed fast and slow collective motions in confinement. The explicit demonstration of persistence under changes in R, damping, boundaries, density, and size is a strength that supports the claim of genericity and potential observability in natural or engineered systems.

major comments (1)
  1. [Numerical implementation and analysis] The manuscript provides no dedicated methods section or supplementary material detailing the numerical integration scheme (e.g., integrator type, time step, convergence checks), quantitative diagnostics used to extract oscillation frequencies and milling periods, or statistical measures of state robustness. These details are load-bearing for the central simulation-based claim that the combined alignment mechanisms produce the reported states across parameter variations.
minor comments (2)
  1. [Figures] Figure captions and axis labels should explicitly state the values of R, damping anisotropy, and density used in each panel to allow direct comparison with the parameter sweeps described in the text.
  2. [Results] The distinction between fluid and solid regimes is invoked repeatedly but is not accompanied by a quantitative order parameter or threshold (e.g., mean-squared displacement or velocity correlation length); adding this would clarify the regime classification.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive comments and positive assessment of the work's significance. We address the single major comment below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: The manuscript provides no dedicated methods section or supplementary material detailing the numerical integration scheme (e.g., integrator type, time step, convergence checks), quantitative diagnostics used to extract oscillation frequencies and milling periods, or statistical measures of state robustness. These details are load-bearing for the central simulation-based claim that the combined alignment mechanisms produce the reported states across parameter variations.

    Authors: We agree that the absence of a dedicated methods section limits the reproducibility and strength of the simulation claims. In the revised manuscript we will add a Methods section (or expanded supplementary material) that specifies the numerical integration scheme, including integrator type, chosen time step, and convergence checks; the quantitative diagnostics for extracting high-frequency oscillation periods and low-frequency milling periods (e.g., Fourier analysis or peak-detection algorithms applied to center-of-mass trajectories); and statistical measures of robustness such as variability across independent runs and parameter sweeps. These additions will directly support the reported genericity across R, damping anisotropy, boundary conditions, density, and system size. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper defines an explicit mechanical model of active polar disks incorporating self-alignment to contact forces and mutual alignment via off-center rotation at distance R. Collective states are obtained by direct numerical integration of the resulting ODEs under varied parameters (R, damping anisotropy, boundaries, density, system size). No parameters are fitted to target outputs, no predictions reduce to the inputs by construction, and no self-citations or uniqueness theorems are invoked to justify the central claims. The reported states emerge from the defined dynamics rather than from any self-referential step.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on a mechanical model with several domain assumptions about force-based alignment and confinement; no free parameters are explicitly fitted to data in the abstract, but R, damping anisotropy, and density are varied as inputs.

free parameters (2)
  • R (off-center distance)
    Controls strength of mutual alignment; varied as small/large values.
  • disk-substrate damping anisotropy
    Varied as isotropic/anisotropic.
axioms (2)
  • domain assumption Disks are self-propelled polar particles whose rotation center is offset behind the centroid.
    Core modeling choice enabling mutual alignment from central contact forces.
  • domain assumption Self-alignment occurs toward the vector sum of contact forces from substrate interactions.
    Defines the self-alignment rule in the model.

pith-pipeline@v0.9.0 · 5708 in / 1388 out tokens · 23121 ms · 2026-05-23T19:16:30.759011+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages

  1. [1]

    Ramaswamy , The Mechanics and Statistics of Active Matter , Annual Review of Con- densed Matter Physics 1(1), 323 (2010), doi:10.1146 /annurev-conmatphys-070909- 104101

    S. Ramaswamy , The Mechanics and Statistics of Active Matter , Annual Review of Con- densed Matter Physics 1(1), 323 (2010), doi:10.1146 /annurev-conmatphys-070909- 104101

    work page 2010

  2. [2]

    Romanczuk, M

    P . Romanczuk, M. Bär, W . Ebeling, B. Lindner and L. Schimansky-Geier, Active Brow- nian particles , The European Physical Journal Special Topics 202(1), 1 (2012), doi:10.1140/epjst/e2012-01529-y

    work page doi:10.1140/epjst/e2012-01529-y 2012

  3. [3]

    M. C. Marchetti, J. F . Joanny , S. Ramaswamy , T . B. Liverpool, J. Prost, M. Rao and R. A. Simha, Hydrodynamics of soft active matter , Reviews of Modern Physics 85(3), 1143 (2013), doi:10.1103 /RevModPhys.85.1143

    work page 2013

  4. [4]

    Baconnier, O

    P . Baconnier, O. Dauchot, V . Démery , G. Düring, S. Henkes, C. Huepe and A. Shee,Self- Aligning Polar Active Matter (2024)

    work page 2024

  5. [5]

    J. L. Deneubourg and S. Goss, Collective patterns and decision-making, Ethology Ecology & Evolution 1(4), 295 (1989), doi:10.1080 /08927014.1989.9525500

    work page arXiv 1989

  6. [6]

    Czirok , author E

    T . Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel Type of Phase Tran- sition in a System of Self-Driven Particles , Physical Review Letters 75(6), 1226 (1995), doi:10.1103/PhysRevLett.75.1226

    work page doi:10.1103/physrevlett.75.1226 1995

  7. [7]

    C. W . Reynolds,Flocks, herds and schools: A distributed behavioral model, ACM SIGGRAPH Computer Graphics 21(4), 25 (1987), doi:10.1145 /37402.37406

    work page arXiv 1987

  8. [8]

    G. M. Whitesides and B. Grzybowski, Self-Assembly at All Scales , Science 295(5564), 2418 (2002), doi:10.1126 /science.1070821

    work page 2002

  9. [9]

    I. D. Couzin and J. Krause, Self-Organization and Collective Behavior in Vertebrates, Ad- vances in the Study of Behavior 32, 1 (2003), doi:10.1016 /S0065-3454(03)01001-5

    work page 2003

  10. [10]

    Toner, Y

    J. Toner, Y. Tu and S. Ramaswamy ,Hydrodynamics and phases of flocks, Annals of Physics 318(1), 170 (2005), doi:https: //doi.org/10.1016/j.aop.2005.04.011

    work page doi:10.1016/j.aop.2005.04.011 2005

  11. [11]

    Chat \' e , author F

    H. Chaté, F . Ginelli, G. Grégoire, F . Peruani and F . Raynaud,Modeling collective motion: variations on the Vicsek model , The European Physical Journal B 64(3-4), 451 (2008), doi:10.1140/epjb/e2008-00275-9

    work page doi:10.1140/epjb/e2008-00275-9 2008

  12. [12]

    Collective Motion

    T . Vicsek and A. Zafeiris, Collective motion , Physics Reports 517(3-4), 71 (2012), doi:10.1016/j.physrep.2012.03.004

    work page doi:10.1016/j.physrep.2012.03.004 2012

  13. [13]

    Ferrante, A

    E. Ferrante, A. E. Turgut, C. Huepe, A. Stranieri, C. Pinciroli and M. Dorigo,Self-organized flocking with a mobile robot swarm: a novel motion control method , Adaptive Behavior 20(6), 460 (2012), doi:10.1177 /1059712312462248

    work page 2012

  14. [14]

    Ballerini, N

    M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V . Zdravkovic, Empirical investigation of starling flocks: a benchmark study in collective animal behaviour , Animal Behaviour 76(1), 201 (2008), doi:10.1016 /j.anbehav.2008.02.004

    work page 2008

  15. [15]

    Bialek , author A

    W . Bialek, A. Cavagna, I. Giardina, T . Mora, E. Silvestri, M. Viale and A. M. Wal- czak, Statistical mechanics for natural flocks of birds , Proceedings of the Na- tional Academy of Sciences of the United States of America 109(13), 4786 (2012), doi:10.1073/pnas.1118633109. 29 SciPost Physics Submission

    work page doi:10.1073/pnas.1118633109 2012

  16. [16]

    Y. Katz, K. Tunstrøm, C. C. Ioannou, C. Huepe and I. D. Couzin, Inferring the structure and dynamics of interactions in schooling fish , Proceedings of the Na- tional Academy of Sciences of the United States of America 108(46), 18720 (2011), doi:10.1073/pnas.1107583108

    work page doi:10.1073/pnas.1107583108 2011

  17. [17]

    J. E. Herbert-Read, A. Perna, R. P . Mann, T . M. Schaerf, D. J. Sumpter and A. J. Ward, Inferring the rules of interaction of shoaling fish , Proceedings of the Na- tional Academy of Sciences of the United States of America 108(46), 18726 (2011), doi:10.1073/pnas.1109355108

    work page doi:10.1073/pnas.1109355108 2011

  18. [18]

    Gómez-Nava, R

    L. Gómez-Nava, R. Bon and F . Peruani, Intermittent collective motion in sheep results from alternating the role of leader and follower , Nature Physics 18(12), 1494 (2022), doi:10.1038/s41567-022-01769-8

    work page doi:10.1038/s41567-022-01769-8 2022

  19. [19]

    Huepe, Sheep lead the way , Nature Physics 2022 18:12 18(12), 1402 (2022), doi:10.1038/s41567-022-01744-3

    C. Huepe, Sheep lead the way , Nature Physics 2022 18:12 18(12), 1402 (2022), doi:10.1038/s41567-022-01744-3

    work page doi:10.1038/s41567-022-01744-3 2022

  20. [20]

    J. Buhl, D. J. Sumpter, I. D. Couzin, J. J. Hale, E. Despland, E. R. Miller and S. J. Simp- son, From disorder to order in marching locusts , Science 312(5778), 1402 (2006), doi:10.1126/science.1125142

    work page doi:10.1126/science.1125142 2006

  21. [21]

    Zhang, A

    H.-P . Zhang, A. Be’er, E.-L. Florin and H. L. Swinney ,Collective motion and density fluctu- ations in bacterial colonies, Proceedings of the National Academy of Sciences 107(31), 13626 (2010), doi:10.1073 /pnas.1001651107

    work page 2010

  22. [22]

    Peruani, J

    F . Peruani, J. Starruß, V . Jakovljevic, L. Søgaard-Andersen, A. Deutsch and M. Bär,Collec- tive Motion and Nonequilibrium Cluster Formation in Colonies of Gliding Bacteria, Physical Review Letters 108(9), 098102 (2012), doi:10.1103 /PhysRevLett.108.098102

    work page 2012

  23. [23]

    Beppu, Z

    K. Beppu, Z. Izri, J. Gohya, K. Eto, M. Ichikawa and Y. T . Maeda, Geometry- driven collective ordering of bacterial vortices , Soft Matter 13(29), 5038 (2017), doi:10.1039/c7sm00999b

    work page doi:10.1039/c7sm00999b 2017

  24. [24]

    Deseigne, O

    J. Deseigne, O. Dauchot and H. Chaté, Collective Motion of Vibrated Polar Disks, Physical Review Letters 105(9), 098001 (2010), doi:10.1103 /PhysRevLett.105.098001

    work page 2010

  25. [25]

    Deseigne, S

    J. Deseigne, S. Léonard, O. Dauchot and H. Chaté, Vibrated polar disks: spontaneous motion, binary collisions, and collective dynamics , Soft Matter 8(20), 5629 (2012), doi:10.1039/c2sm25186h

    work page doi:10.1039/c2sm25186h 2012

  26. [26]

    Snezhko, Complex collective dynamics of active torque-driven colloids at in- terfaces, Current Opinion in Colloid & Interface Science 21, 65 (2016), doi:10.1016/j.cocis.2015.11.010

    A. Snezhko, Complex collective dynamics of active torque-driven colloids at in- terfaces, Current Opinion in Colloid & Interface Science 21, 65 (2016), doi:10.1016/j.cocis.2015.11.010

    work page doi:10.1016/j.cocis.2015.11.010 2016

  27. [27]

    S. Das, M. Ciarchi, Z. Zhou, J. Yan, J. Zhang and R. Alert,Flocking by turning away, Phys. Rev. X14, 031008 (2024), doi:10.1103 /PhysRevX.14.031008

    work page 2024

  28. [28]

    Hamann, Swarm Robotics: A Formal Approach , Springer International Publishing, Cham, ISBN 978-3-319-74526-8, doi:10.1007 /978-3-319-74528-2 (2018)

    H. Hamann, Swarm Robotics: A Formal Approach , Springer International Publishing, Cham, ISBN 978-3-319-74526-8, doi:10.1007 /978-3-319-74528-2 (2018)

    work page 2018

  29. [29]

    M. Y. Ben Zion, J. Fersula, N. Bredeche and O. Dauchot, Morphological computation and decentralized learning in a swarm of sterically interacting robots, Science Robotics 8(75), eabo6140 (2023), doi:10.1126 /scirobotics.abo6140. 30 SciPost Physics Submission

    work page 2023

  30. [30]

    I. D. Couzin, J. Krause, N. R. Franks and S. A. Levin, Effective leadership and decision-making in animal groups on the move , Nature 433(7025), 513 (2005), doi:10.1038/nature03236

    work page doi:10.1038/nature03236 2005

  31. [31]

    Peruani, A

    F . Peruani, A. Deutsch and M. Bär,Nonequilibrium clustering of self-propelled rods, Physical Review E 74(3), 030904 (2006), doi:10.1103 /PhysRevE.74.030904

    work page 2006

  32. [32]

    Ballerini, N

    M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V . Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V . Zdravkovic,Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proceedings of the National Academy of Sciences of the United States of Am...

    work page 2008

  33. [33]

    Conradt and T

    L. Conradt and T . J. Roper,Consensus decision making in animals , Trends in Ecology & Evolution 20(8), 449 (2005), doi:10.1016 /j.tree.2005.05.008

    work page 2005

  34. [34]

    E. R. Kande John D Koester and M. A. Steven, PRINCIPLES OF NEURAL SCIENCE Sixth Edition Me Graw Hill L (2021)

    work page 2021

  35. [35]

    A. J. King and G. Cowlishaw, When to use social information: the advantage of large group size in individual decision making , Biology Letters 3(2), 137 (2007), doi:10.1098/RSBL.2007.0017

    work page doi:10.1098/rsbl.2007.0017 2007

  36. [36]

    P . K. McGregor,Animal Communication Networks, Animal Communication Networks pp. 1–657 (2005), doi:10.1017/CBO9780511610363

    work page doi:10.1017/cbo9780511610363 2005

  37. [37]

    Romanczuk, I

    P . Romanczuk, I. D. Couzin and L. Schimansky-Geier, Collective motion due to individual escape and pursuit response , Phys. Rev. Lett. 102, 010602 (2009), doi:10.1103/PhysRevLett.102.010602

    work page doi:10.1103/physrevlett.102.010602 2009

  38. [38]

    J. R. Dyer, A. Johansson, D. Helbing, I. D. Couzin and J. Krause,Leadership, consensus de- cision making and collective behaviour in humans, Philosophical Transactions of the Royal Society B: Biological Sciences 364(1518), 781 (2009), doi:10.1098 /rstb.2008.0233

    work page arXiv 2009

  39. [39]

    Szabó, G

    B. Szabó, G. J. Szöllösi, B. Gönci, Z. Jurányi, D. Selmeczi and T . Vicsek, Phase transition in the collective migration of tissue cells: Experiment and model , Physi- cal Review E - Statistical, Nonlinear, and Soft Matter Physics 74(6), 061908 (2006), doi:10.1103/PhysRevE.74.061908

    work page doi:10.1103/physreve.74.061908 2006

  40. [40]

    Henkes, Y

    S. Henkes, Y. Fily and M. C. Marchetti, Active jamming: Self-propelled soft particles at high density, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 84(4), 040301 (2011), doi:10.1103 /PhysRevE.84.040301

    work page 2011

  41. [41]

    Ferrante, A

    E. Ferrante, A. E. Turgut, M. Dorigo and C. Huepe, Collective motion dynamics of active solids and active crystals , New Journal of Physics 15(9), 095011 (2013), doi:10.1088/1367-2630/15/9/095011

    work page doi:10.1088/1367-2630/15/9/095011 2013

  42. [42]

    Ferrante, A

    E. Ferrante, A. E. Turgut, M. Dorigo and C. Huepe, Elasticity-Based Mechanism for the Collective Motion of Self-Propelled Particles with Springlike Interactions: A Model System for Natural and Artificial Swarms , Physical Review Letters 111(26), 268302 (2013), doi:10.1103/PhysRevLett.111.268302

    work page doi:10.1103/physrevlett.111.268302 2013

  43. [43]

    Zheng, C

    Y. Zheng, C. Huepe and Z. Han, Experimental capabilities and limitations of a position- based control algorithm for swarm robotics , Adaptive Behavior 30(1), 19 (2022), doi:10.1177/1059712320930418. 31 SciPost Physics Submission

    work page doi:10.1177/1059712320930418 2022

  44. [44]

    Baconnier, D

    P . Baconnier, D. Shohat, C. H. López, C. Coulais, V . Démery , G. Düring and O. Dauchot, Selective and collective actuation in active solids, Nature Physics 2022 18:1018(10), 1234 (2022), doi:10.1038 /s41567-022-01704-x

    work page 2022

  45. [45]

    H. Xu, Y. Huang, R. Zhang and Y. Wu, Autonomous waves and global motion modes in living active solids, Nature Physics 2022 19:1 19(1), 46 (2022), doi:10.1038 /s41567- 022-01836-0

    work page 2022

  46. [46]

    Baconnier, D

    P . Baconnier, D. Shohat and O. Dauchot, Discontinuous Tension-Controlled Transition between Collective Actuations in Active Solids , Physical Review Letters 130(2), 028201 (2023), doi:10.1103 /PhysRevLett.130.028201

    work page 2023

  47. [47]

    M. R. Davidescu, P . Romanczuk, T . Gregor and I. D. Couzin,Growth produces coordina- tion trade-offs in Trichoplax adhaerens, an animal lacking a central nervous system , Pro- ceedings of the National Academy of Sciences of the United States of America 120(11), e2206163120 (2023), doi:https: //www.pnas.org/doi/abs/10.1073/pnas.2206163120

    work page doi:10.1073/pnas.2206163120 2023

  48. [48]

    T . A. Karagüzel, A. E. Turgut, A. Eiben and E. Ferrante,Collective gradient perception with a flying robot swarm , Swarm Intelligence 17(1-2), 117 (2023), doi:10.1007 /s11721- 022-00220-1

    work page 2023

  49. [49]

    Martín-Gómez, D

    A. Martín-Gómez, D. Levis, A. Díaz-Guilera and I. Pagonabarraga, Collective motion of active Brownian particles with polar alignment , Soft Matter 14(14), 2610 (2018), doi:10.1039/C8SM00020D

    work page doi:10.1039/c8sm00020d 2018

  50. [50]

    Y. Zhao, T . Ihle, Z. Han, C. Huepe and P . Romanczuk,Phases and homogeneous ordered states in alignment-based self-propelled particle models, Phys. Rev. E104, 044605 (2021), doi:10.1103/PhysRevE.104.044605

    work page doi:10.1103/physreve.104.044605 2021

  51. [51]

    N. D. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic heisenberg models , Phys. Rev. Lett. 17, 1133 (1966), doi:10.1103/PhysRevLett.17.1133

    work page doi:10.1103/physrevlett.17.1133 1966

  52. [52]

    Aldana and C

    M. Aldana and C. Huepe, Phase Transitions in Self-Driven Many-Particle Systems and Re- lated Non-Equilibrium Models: A Network Approach, Journal of Statistical Physics 112(1- 2), 135 (2003), doi:https: //doi.org/10.1023/A:1023675519930

    work page doi:10.1023/a:1023675519930 2003

  53. [53]

    Arbel, N

    E. Arbel, N. Oppenheimer, Y. Lahini and M. Y. B. Zion,A mechanical origin of cooperative transport (2024)

    work page 2024

  54. [54]

    G. Lin, Z. Han and C. Huepe, Order-disorder transitions in a minimal model of active elasticity, New Journal of Physics 23(2) (2021), doi:10.1088 /1367-2630/abe0da

    work page 2021

  55. [55]

    G. Lin, Z. Han, A. Shee and C. Huepe, Noise-induced quenched disorder in dense active systems , Physical Review Letters 131(16), 168301 (2023), doi:10.1103/PhysRevLett.131.168301

    work page doi:10.1103/physrevlett.131.168301 2023

  56. [56]

    N. A. M. Araújo, L. M. C. Janssen, T . Barois, G. Boffetta, I. Cohen, A. Corbetta, O. Dauchot, M. Dijkstra, W . M. Durham, A. Dussutour, S. Garnier, H. Gelderblom et al., Steering self-organisation through confinement, Soft Matter 19(9), 1695 (2023), doi:10.1039/D2SM01562E

    work page doi:10.1039/d2sm01562e 2023

  57. [57]

    Canavello, R

    D. Canavello, R. H. Damascena, L. R. E. Cabral and C. C. de Souza Silva, Polar order, shear banding, and clustering in confined active matter, Soft Matter 20(10), 2310 (2024), doi:10.1039/D3SM01721D. 32

    work page doi:10.1039/d3sm01721d 2024