From flocking to jamming in collective cell dynamics: a Vicsek-like model including contact forces

Laurent Navoret (IRMA; MACARON); Marcela Szopos (MAP5 - UMR 8145); Roxana Sublet (IRMA

arxiv: 2512.15305 · v2 · submitted 2025-12-17 · 🧮 math.NA · cs.NA

From flocking to jamming in collective cell dynamics: a Vicsek-like model including contact forces

Laurent Navoret (IRMA , MACARON) , Roxana Sublet (IRMA , Marcela Szopos (MAP5 - UMR 8145) This is my paper

Pith reviewed 2026-05-16 21:57 UTC · model grok-4.3

classification 🧮 math.NA cs.NA

keywords collective cell dynamicsVicsek modelcontact forcesflockingjammingphase transitionagent-based modelnumerical simulation

0 comments

The pith

An agent-based model merging Vicsek polarity alignment with contact forces recovers both flocking transitions and jamming at high cell densities.

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

The paper develops an agent-based model that joins Vicsek-style rules for aligning cell directions with physical contact forces between neighboring cells. It incorporates velocity feedback on polarity and soft attraction-repulsion terms, establishes that the resulting dynamical system is well-posed, and supplies a discretization scheme for numerical solution. Extensive simulations then demonstrate that the model reproduces the classic order-disorder phase transition of flocks and also produces jamming when cell density rises. The framework is positioned as a tool for exploring how collective cell motion gives rise to tissue-scale flows.

Core claim

The dynamical system is capable of recovering the order-disorder phase transition of the flock, as well as the jamming effect in high density regimes.

What carries the argument

Agent-based model that combines Vicsek-like polarity alignments with Maury-Venel contact forces, augmented by velocity feedback on polarity and soft attraction-repulsion interactions.

If this is right

The model produces the expected order-disorder transition when polarity alignment strength is varied.
Jamming emerges naturally once cell density exceeds a threshold set by the contact forces.
The discretization permits quantitative exploration of how interaction parameters control collective motion.
The framework supplies a simulation platform for studying emerging tissue flows driven by cell collectives.

Where Pith is reading between the lines

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

The same numerical setup could be used to test how boundary geometry or external flows alter the jamming threshold.
Varying the relative strength of contact forces versus polarity alignment might map out regimes where flocking persists or collapses in confined domains.
The well-posedness analysis provides a starting point for adding further biological ingredients such as cell division or adhesion maturation.

Load-bearing premise

The chosen velocity feedback on polarity together with the soft attraction-repulsion interactions produce a well-posed dynamical system that admits an effective numerical discretization.

What would settle it

Numerical runs in which the order-disorder phase transition disappears or in which jamming fails to appear at high densities would refute the central claim.

Figures

Figures reproduced from arXiv: 2512.15305 by Laurent Navoret (IRMA, MACARON), Marcela Szopos (MAP5 - UMR 8145), Roxana Sublet (IRMA.

**Figure 2.** Figure 2: (Periodic boundary condition) Order parameter as a function of the diffusion for two dif [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 4.** Figure 4: (Disk domain) Mean speed, order parameter and rotation order parameter as functions of [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

**Figure 5.** Figure 5: (Disk domain) Rotation order parameter as function of time in different regions of the disk [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 3.** Figure 3: (Disk domain) Cell configuration at final time [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

**Figure 6.** Figure 6: (Influence of the density and the domain shape) Normalized global mean speed (on the left), [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: (Influence of the density and the domain shape - high densities) Normalized mean speed as [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

**Figure 8.** Figure 8: (One obstacle in a square domain) Normalized mean speed (left column) and rotation order [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗

**Figure 9.** Figure 9: (Four obstacles in a square domain) Normalized mean speed (left column) and rotation order [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗

**Figure 10.** Figure 10: (Four obstacles in a square domain) Cell configuration at final time [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

**Figure 11.** Figure 11: (Influence of the attraction-repulsion force) Cell configuration at final time [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗

read the original abstract

The goal of the present work is to propose an agent-based model that originally combines classical Vicsek-like polarity alignments and contact forces, as implemented in the framework developed by Maury and Venel in [Maury, Venel, 2011]. The description additionally incorporates velocity feedback on polarity and soft attraction-repulsion interactions. After carefully studying the well posedness of the model, we introduce a suitable discretization and perform an extensive range of numerical experiments to assess the impact of different modeling ingredients. The dynamical system is capable of recovering the order-disorder phase transition of the flock, as well as the jamming effect in high density regimes. As such, the developed framework can be seen as a promising theoretical tool that could contribute to improving the understanding of complex collective cell dynamics and emerging tissue flows.

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 paper combines Vicsek alignment with Maury-Venel contact forces plus velocity feedback and shows numerics recovering both order-disorder transitions and jamming, but the analysis details stay thin.

read the letter

The main contribution is a hybrid agent-based model that layers classical Vicsek polarity alignment on top of the Maury-Venel contact force framework, then adds velocity feedback to the polarity variable and soft attraction-repulsion terms. The numerics recover the expected flock order-disorder transition at low density and jamming at high density, which is the central claim that holds up in the reported experiments. That combination is new enough on its own terms; most prior Vicsek work ignores hard contacts, and most force-based cell models skip the alignment rule. Using an already-analyzed contact framework is a practical move that lets them move straight to discretization after the well-posedness step. The logical sequence (existence first, then numerics) is clean and avoids the usual circularity problems in these models. The soft spots are in the missing specifics. The abstract states well-posedness was studied, yet gives no hint of the estimates or how the velocity feedback term affects regularity or uniqueness. The numerical section is described as extensive, but without reported parameter ranges, convergence checks, or direct comparison to measured cell data, it is hard to judge how robust the jamming recovery really is. If the transition only appears inside a narrow window of noise or interaction strengths, the framework loses some of its claimed generality. This is for people already working on agent-based models of collective cell motion who need a single setup that spans dilute flocking to dense tissue-like jamming. A reader looking for a ready-to-extend simulation tool will find the ingredients useful even if the proofs and validation need filling in. I would send it to peer review. The modeling choices are reasonable and the reported behaviors line up with what the ingredients should produce, so referees can usefully press on the analysis gaps and the numerical robustness.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes an agent-based model for collective cell dynamics that integrates Vicsek-like polarity alignment with contact forces from Maury and Venel (2011), augmented by velocity feedback on polarity and soft attraction-repulsion interactions. After establishing well-posedness, a discretization scheme is introduced and numerical experiments are performed to demonstrate recovery of the order-disorder phase transition of flocking as well as jamming at high densities.

Significance. If the well-posedness result and the numerical recovery of both transitions hold under the stated modeling assumptions, the framework provides a coherent agent-based bridge between flocking and jamming regimes that could inform models of tissue-level flows. The reuse of the Maury-Venel contact-force formulation is a strength that anchors the new ingredients in an existing, validated setting.

major comments (2)

[Well-posedness analysis] Well-posedness section: the manuscript states that well-posedness was carefully studied prior to discretization, yet no theorem statement, function-space setting, or key a-priori estimates (e.g., on the Lipschitz constants of the combined alignment and contact terms) are supplied; this information is load-bearing for the subsequent claim that the discrete scheme is consistent with a well-defined continuous dynamics.
[Numerical experiments] Numerical experiments section: the recovery of the Vicsek order-disorder transition and the jamming transition is asserted, but the text gives no quantitative diagnostics (order-parameter curves versus noise strength, density thresholds at which jamming onset is observed, or comparison against the pure Vicsek or pure Maury-Venel baselines), making it impossible to judge how much the added velocity-feedback term contributes to the reported behaviors.

minor comments (2)

[Abstract] Abstract: the phrase 'originally combines' is ambiguous; replace with 'combines' or 'novelty combines' to clarify the intended contribution.
[References] References: the citation [Maury, Venel, 2011] must be expanded to a complete bibliographic entry (journal, volume, pages, DOI) in the reference list.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address each major comment below and outline the revisions we will implement to strengthen the presentation.

read point-by-point responses

Referee: Well-posedness section: the manuscript states that well-posedness was carefully studied prior to discretization, yet no theorem statement, function-space setting, or key a-priori estimates (e.g., on the Lipschitz constants of the combined alignment and contact terms) are supplied; this information is load-bearing for the subsequent claim that the discrete scheme is consistent with a well-defined continuous dynamics.

Authors: We agree that the well-posedness analysis requires a more explicit presentation. Although the continuous model was analyzed in detail before discretization, the manuscript condenses this material. In the revised version we will insert a dedicated theorem stating existence and uniqueness in an appropriate function-space setting (e.g., measures with bounded variation for positions and continuous functions for polarities), together with the principal a-priori estimates, including uniform Lipschitz bounds on the combined alignment, contact-force, and velocity-feedback operators. These additions will directly support the consistency claim for the discrete scheme. revision: yes
Referee: Numerical experiments section: the recovery of the Vicsek order-disorder transition and the jamming transition is asserted, but the text gives no quantitative diagnostics (order-parameter curves versus noise strength, density thresholds at which jamming onset is observed, or comparison against the pure Vicsek or pure Maury-Venel baselines), making it impossible to judge how much the added velocity-feedback term contributes to the reported behaviors.

Authors: We acknowledge the need for quantitative diagnostics. The revised manuscript will include (i) plots of the global order parameter versus noise amplitude, (ii) explicit density values at which jamming onset is observed, and (iii) side-by-side comparisons with the pure Vicsek model and the pure Maury-Venel contact-force model. These additions will quantify the incremental effect of the velocity-feedback term and allow readers to assess its role in bridging the two regimes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper constructs an agent-based model by combining the established Vicsek polarity alignment rule with contact forces from the independent Maury-Venel 2011 framework, then augments it with velocity feedback on polarity and soft attraction-repulsion potentials. It first proves well-posedness of the resulting dynamical system, introduces a discretization scheme, and performs numerical experiments whose outcomes (order-disorder transition and high-density jamming) emerge from the integrated dynamics rather than being imposed by construction or fitted parameters. No equation reduces to a self-definition, no prediction is a renamed fit, and the sole external citation is to non-overlapping prior work. The logical chain (model definition → well-posedness → discretization → targeted numerics) therefore remains independent of its target behaviors.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; specific free parameters, axioms, and invented entities cannot be identified from the provided text.

pith-pipeline@v0.9.0 · 5457 in / 982 out tokens · 51688 ms · 2026-05-16T21:57:05.408679+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

V = Proj_CX (cP + γF(X)) ... dθk/dt = μ sin(¯θk−θk) + δ sin(ψk−θk) ... well-posedness via proximal normal cone of Q×RN
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

numerical experiments recover order-disorder phase transition and jamming at high density

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

38 extracted references · 38 canonical work pages

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[1] [1]

Al Reda, S

F. Al Reda, S. Faure, B. Maury, and E. Pinsard. Faster is slower effect for evacuation processes: a granular standpoint. J. Comput. Phys. , page 112861, 2024

work page 2024

[2] [2]

Bloch, V

H. Bloch, V. Calvez, B. Gaudeul, L. Gouarin, Aline Lefebvre-Lepot, Tam Mignot, M. Romanos, and J.-B. Saulnier. A new modeling approach of myxococcus xanthus bacteria using polarity-based reversals. accepted in ESAIM Proc. Surveys , 2024

work page 2024

[3] [3]

Briant, A

M. Briant, A. Diez, and S. Merino-Aceituno. Cauchy theory for general kinetic vicsek models in collective dynamics and mean-field limit approximations. SIAM J. Math. Anal. , 54(1):1131--1168, 2022

work page 2022

[4] [4]

Bowick, N

M.J. Bowick, N. Fakhri, M.C. Marchetti, and S. Ramaswamy. Symmetry, thermodynamics and topology in active matter. Phys. Rev. X , 12(1):010501, 2022

work page 2022

[5] [5]

Beatrici, C

C. Beatrici, C. Kirch, S. Henkes, F. Graner, and L. Brunnet. Comparing individual-based models of collective cell motion in a benchmark flow geometry. Soft Matter , 19(29):5583--5601, 2023

work page 2023

[6] [6]

Bloch and A

H. Bloch and A. Lefebvre-Lepot. On convex numerical schemes for inelastic contacts with friction. ESAIM Proc. Surveys , 75:24--59, 2023

work page 2023

[7] [7]

Differential inclusions with proximal normal cones in banach spaces

Fr \'e d \'e ric Bernicot and Juliette Venel. Differential inclusions with proximal normal cones in banach spaces. J. Convex Anal , 17(2):451--484, 2010

work page 2010

[8] [8]

Chat \'e , F

H. Chat \'e , F. Ginelli, G. Gr \'e goire, F. Peruani, and F. Raynaud. Modeling collective motion: variations on the vicsek model. Eur. Phys. J. B , 64:451--456, 2008

work page 2008

[9] [9]

Chat \'e

H. Chat \'e . Dry aligning dilute active matter. Annu. Rev. Condens. Matter Phys. , 11:189--212, 2020

work page 2020

[10] [10]

Carrillo, Y

J.A. Carrillo, Y. Huang, and S. Martin. Explicit flock solutions for quasi-morse potentials. Eur. J. Appl. Math. , 25(5):553--578, 2014

work page 2014

[11] [11]

P.G. Ciarlet. Introduction \`a l'analyse num \'e rique matricielle et \`a l'optimisation . Dunod, 2007

work page 2007

[12] [12]

D’Orsogna, Y.-L

M.R. D’Orsogna, Y.-L. Chuang, A.L. Bertozzi, and L.S. Chayes. Self-propelled particles with soft-core interactions: patterns, stability, and collapse. Phys. Rev. Lett. , 96(10):104302, 2006

work page 2006

[13] [13]

Degond, G

P. Degond, G. Dimarco, M. Ferreira, and S. Hecht. Modeling ballistic aggregation by time stepping approaches. SIAM J. Appl. Dyn. Syst. , to appear

work page

[14] [14]

Degond, G

P. Degond, G. Dimarco, T. B. N. Mac, and N. Wang. Macroscopic models of collective motion with repulsion. Commun. Math. Sci. , 13(6):1615--1638, 2015

work page 2015

[15] [15]

Degond, A

P. Degond, A. Diez, and M. Na. Bulk topological states in a new collective dynamics model. SIAM J. Appl. Dyn. Syst. , 21(2):1455--1494, 2022

work page 2022

[16] [16]

Degond, A

P. Degond, A. Frouvelle, and J.-G. Liu. Macroscopic limits and phase transition in a system of self-propelled particles. J. Nonlinear Sci. , 23:427--456, 2013

work page 2013

[17] [17]

Degond, M.A

P. Degond, M.A. Ferreira, and S. Motsch. Damped Arrow–Hurwicz algorithm for sphere packing . J. Comput. Phys. , 332:47–65, March 2017

work page 2017

[18] [18]

Deutsch, P

A. Deutsch, P. Friedl, L. Preziosi, and G. Theraulaz. Multi-scale analysis and modelling of collective migration in biological systems. Philos. Trans. R. Soc. B-Biol. Sc. , 375(1807):20190377, 2020

work page 2020

[19] [19]

Degond and S

P. Degond and S. Motsch. Continuum limit of self-driven particles with orientation interaction. Math. Models Methods Appl. Sci. , 18(supp01):1193--1215, 2008

work page 2008

[20] [20]

L.C. Evans. An introduction to stochastic differential equations , volume 82. American Mathematical Soc., 2012

work page 2012

[21] [21]

Friedl and D

P. Friedl and D. Gilmour. Collective cell migration in morphogenesis, regeneration and cancer. Nat. Rev. Mol. Cell Biol. , 10(7):445--457, 2009

work page 2009

[22] [22]

Faure and B

S. Faure and B. Maury. Crowd motion from the granular standpoint. Math. Models Methods Appl. Sci. , 25(03):463--493, 2015

work page 2015

[23] [23]

Feliciani, Ke

C. Feliciani, Ke. Shimura, and K. Nishinari. Introduction to crowd management: Managing crowds in the digital era: Theory and Practice . Springer Nature, 2022

work page 2022

[24] [24]

Helbing, L

D. Helbing, L. Buzna, A. Johansson, and T. Werner. Self-organized pedestrian crowd dynamics: Experiments, simulations, and design solutions. Transportation science , 39(1):1--24, 2005

work page 2005

[25] [25]

Hakim and P

V. Hakim and P. Silberzan. Collective cell migration: a physics perspective. Rep. Prog. Phys. , 80(7):076601, 2017

work page 2017

[26] [26]

Koch and G

D.L. Koch and G. Subramanian. Collective hydrodynamics of swimming microorganisms: living fluids. Annu. Rev. Fluid Mech. , 43(1):637--659, 2011

work page 2011

[27] [27]

Lo Vecchio, O

S. Lo Vecchio, O. Pertz, M. Szopos, L. Navoret, and D. Riveline. Spontaneous rotations in epithelia as an interplay between cell polarity and boundaries. Nat. Phys. , pages 1--10, 2024

work page 2024

[28] [28]

B. Maury. A time-stepping scheme for inelastic collisions. Numer. Math. , 102:649--679, 2006

work page 2006

[29] [29]

B. Maury. Defective laplacians and paradoxical phenomena in crowd motion modeling. C. R. M \'e ca. , 351(S1):1--32, 2023

work page 2023

[30] [30]

Marchetti, J.-F

M.C. Marchetti, J.-F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao, and R.A. Simha. Hydrodynamics of soft active matter. Rev. Modern Phys. , 85(3):1143, 2013

work page 2013

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