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REVIEW 4 major objections 6 minor 63 references

Contact Forces in Motility-Regulated Active Matter

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Repulsive forces change the fate of quorum-sensing active matter, either preventing collapse or densifying the liquid phase.

desk verdict Solid, genuinely new results on how contact forces reshape quorum-sensing phase behavior; the theory is semiquantitative and rests on closures deferred to a missing SM. read the letter →

arxiv 2507.08964 v1 pith:2PRX5PBE submitted 2025-07-11 cond-mat.soft cond-mat.stat-mech

Quan Manh Nguyen , Alberto Dinelli , Gianmarco Spera , Julien Tailleur This is my paper · ORCID
classification cond-mat.softcond-mat.stat-mech PACS 05.70.Fh64.70.pp87.18.Gh
keywords motilityregulationquorumsensingmotility-inducedphaseseparationcontactforcesactivematterabsorbingtransitionliquid-gascoexistenceIrving-Kirkwoodpressure
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that short-range repulsive forces, usually neglected in models of active particles with long-range motility regulation, play a decisive and two-sided role. When quorum sensing would drive all particles into an arrested, non-motile droplet, repulsion instead stabilizes a genuine liquid-gas coexistence, and the paper predicts the critical force range at which this switch occurs. When quorum sensing already produces a liquid-gas phase separation, repulsion can, counterintuitively, make the liquid phase about four times denser by triggering a secondary phase separation inside it. The authors support these claims with simulations and a local hydrodynamic theory that reproduces the phase diagrams semiquantitatively.

What carries the argument

The key object is the effective chemical potential µeff(ρ)=ρv*(ρ)/(2Dr)+∫^ρ ds ∂s pIK(s)/v(s), built from the mean-field gradient truncation of the density dynamics. Here v*(ρ)=⟨˙ri·ui⟩ is the mean particle speed reduced by both quorum sensing and collisions, and pIK is the Irving-Kirkwood pressure from pairwise forces. A homogeneous state is linearly unstable when the bracket in Eq. (4) is negative, and the same µeff defines a Lyapunov free-energy functional whose common-tangent construction predicts binodals, including metastable ones.

What would settle it

A direct test would be to measure the critical force range ¯rF in a 2D quorum-sensing system with vmin=0 and compare it to (√3ρt)^-1/2; a significant deviation beyond the 10% reported spread, or a coexistence that appears even for rF below that value, would falsify the kinetic arrest argument. The four-fold densification could be falsified by checking whether the liquid density at the merging point actually jumps by the predicted factor and whether the metastable region predicted by the common-tangent construction is absent in simulation.

Watch

Extended reading notes

Core claim

The central claim is that repulsive pairwise forces have opposite effects depending on whether motility regulation drives an absorbing condensation or a liquid-gas coexistence. For v(ρ→∞)=0, repulsion opposes condensation: beyond a critical force range ¯rF=(√3ρt)^-1/2, the absorbing arrested state gives way to an ergodic liquid-gas coexistence. For vmin>0, repulsion can induce a four-fold densification of the liquid phase of quorum-sensing MIPS, because the pairwise-force-driven instability (PF-MIPS) merges with the quorum-sensing instability and the dense PF-liquid becomes the coexisting phase. The paper shows that these behaviors can be captured by a coarse-grained hydrodynamic theory with an effective chemical potential that combines a density-dependent speed and the Irving-Kirkwood pressure, and that metastable coexistences appear in the crossover region.

Load-bearing premise

The theory treats the mean particle speed and the Irving-Kirkwood pressure as known local functions of density, but the paper does not give their closed forms; if these closures are inferred from the same simulations, the phase-diagram agreement is partly a self-consistency check rather than an independent prediction.

Editorial extensions

If this is right

  • If repulsive forces stabilize liquid-gas coexistence against absorbing collapse, then many chemotactic or quorum-sensing aggregation models that neglect excluded volume will overpredict the formation of fully arrested clusters.
  • The predicted critical force range ¯rF=(√3ρt)^-1/2 gives a concrete, testable scale: when the force range exceeds this value, absorption into an arrested droplet should not occur.
  • The secondary PF-MIPS instability implies that dense liquid phases in quorum-sensing active matter can be further densified by tuning the short-range force range, which could be exploited in designing synthetic active materials.
  • The theory's phase diagrams, including metastable regions with multiple common tangents, predict that density fluctuations and nucleation dynamics near the merging point will involve long-lived transient coexisting phases.
  • The results extend beyond quorum sensing to chemotactic systems with similar large-scale descriptions, so contact forces should similarly alter collapse and phase-separation scenarios there.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the local closure for v*(ρ) and pIK(ρ) is extracted from the same simulations used to build the phase diagrams, the agreement between theory and simulation is partly a consistency check; a true test would use closures from an independent calculation or from a different system.
  • The predicted densification (four-fold) applies to the specific parameter region studied; in other regimes, the same mechanism could produce a densification of a different magnitude or a different metastable pathway, which could be tested by systematically varying vmin and the force-range scale.
  • The common-tangent construction relies on a free-energy functional that is a Lyapunov function only for the local dynamics; it remains unclear whether the same phase equilibria survive in the presence of strong fluctuations or in three dimensions, which would be a natural extension.
  • The idea that contact forces can either oppose or enhance phase separation depending on the nature of the motility-regulation transition suggests a general design rule for active matter: short-range forces act as a switch between absorbing and ergodic coexistence, and as an amplifier of density contrast in liquid-gas coexistence.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. This Letter studies active Brownian particles with quorum-sensing motility regulation (density-dependent speed) plus short-range repulsive forces. It reports two main effects: when quorum sensing leads to an absorbing condensation transition (v(ρ)=0 at high density), repulsive forces oppose arrest and stabilize a liquid-gas coexistence; when quorum sensing induces MIPS with finite v_min, repulsive forces can densify the liquid phase several-fold by triggering a secondary PF-MIPS instability. The authors propose a local hydrodynamic theory in which an effective speed v*(ρ) and Irving-Kirkwood pressure pIK(ρ) enter an effective chemical potential, yielding spinodals and binodals via a generalized free energy. They compare theory with particle simulations and report semiquantitative agreement.

Significance. If correct, the central claim is significant: short-range contact forces, usually neglected in models of biologically motivated taxis/QS active matter, cannot be ignored once dense phases form, and they can yield qualitatively different phase behavior (arrest stabilization vs. densification). The simulations provide clear evidence for both effects, and the closed-form prediction for the critical force range, Eq. (2), matches the simulated threshold without adjustable parameters. The local theory captures the topology of the phase diagrams and the metastable coexistence region. However, the theory's quantitative predictive power is not fully established because the constitutive inputs v*(ρ) and pIK(ρ) are not specified in the main text and the Supplemental Material is referenced with a placeholder.

major comments (4)
  1. [Local hydrodynamic theory, Eq. (3)] The central theoretical predictions in Figs. 3-4 (spinodals, binodals, metastable coexistence) follow from the effective chemical potential µ_eff in Eq. (3), which depends on the effective speed v*(ρ) and the Irving-Kirkwood pressure pIK(ρ). Neither function is given in closed form or via a measurement protocol in the main text; the text defers to the Supplemental Material, which is referenced only as a placeholder with 'Refs. XXX' (ref. [48]). As a result, the reader cannot determine whether these inputs are computed a priori from the model parameters or measured from simulations. Please provide the explicit definitions or expressions and state the source of these functions.
  2. [Fig. 3 caption and text after Eq. (4)] The binodal predictions are described as 'without free parameters,' but if v*(ρ) and pIK(ρ) are extracted from the same phase-separated simulations whose binodals are then compared, the agreement is partly a consistency check rather than an independent test. Please clarify the provenance of these constitutive inputs and, if they are simulation-measured, qualify the 'without free parameters' claim.
  3. [Overall manuscript completeness] The Supplemental Material is essential for the paper's claims (refined gradient theory, numerical details, and Fig. S3), but the citation in ref. [48] contains placeholder 'url' and 'Refs. XXX'. Without a complete SM, the quantitative claims cannot be verified. This must be fixed before publication.
  4. [Figs. 3 and 4] The simulated binodals in Figs. 3 and 4 are plotted without error bars. Given that the theory is semiquantitative, error bars are needed to judge whether the observed discrepancies are significant and to support the claimed merging of QS and PF binodals at rF≈0.06.
minor comments (6)
  1. [Abstract] In the abstract, 'repulsive forces opposes' should be 'repulsive forces oppose'.
  2. [Section 2, paragraph after Eq. (2)] The word 'prediciton' should be 'prediction'.
  3. [Section 'Local hydrodynamic theory' and Fig. 4 caption] The phrase 'some of which lay strictly inside the convex hull of g' should refer to the convex hull of f; the function g is undefined.
  4. [Section 'Pairwise forces densify the saturated liquid'] The main text describes the agreement with theory as 'remarkable,' while the Fig. 3 caption says theory and simulations 'agree qualitatively but not quantitatively'; please reconcile these statements.
  5. [End Matter, Eq. (6)] With the stated parameters, v1(ρ→0)=v0(e^λ−1)≈8.59 for v0=5, so the low-density speed is not v0; please state whether v0 is intended as a scale or the actual maximum speed.
  6. [Fig. 4e] The metastability evidence in Fig. 4e is a single trajectory; additional independent runs or a distribution of nucleation times would strengthen the claim that the dense phase nucleates within the QS liquid.

Circularity Check

1 steps flagged · score 3.0 of 10

Partial circularity risk: binodal 'predictions' from Eq. (3) depend on v*(ρ) and pIK(ρ), whose provenance is deferred to a placeholder Supplemental Material; the central simulation-based claim remains independent.

  1. fitted input called prediction [Sec. 'Local hydrodynamic theory', Eq. (3); Fig. 3 caption; reference [48]]
    "Here we have introduced the effective speed v∗(ρ) ≡ ⟨˙ri · ui⟩, which accounts for self-propulsion reduction due to both QS and collisions. ... Note that pairwise forces also enter the effective chemical potential µeff through the direct pressure, defined as pIK ≡ −Tr(σIK αβ)/2, where σIK αβ is the Irving-Kirkwood stress tensor. ... See Supplemental Material [url], which includes theoretical and numerical details, as well as Refs. XXX."

    The common-tangent binodals in Figs. 3–4 are obtained from f′(ρ)=µeff(ρ), where µeff is constructed from v*(ρ) and pIK(ρ). Neither input is given a closed form in the main text; v* is defined as the simulated mean speed and pIK as the Irving–Kirkwood stress. If these functions are evaluated from the same Eq. (1) coexistence simulations whose binodal densities are then compared with the tangent construction, the 'no-free-parameter' prediction is a consistency check: the coexisting densities are the ones used to build µeff. The paper defers the measurement protocol to a placeholder SM ('Refs. XXX'), so the input source is not auditable from the manuscript.

full rationale

The central physical claim—that repulsive forces play a versatile role, opposing condensation when vmin=0 and densifying the liquid when vmin>0—is established by direct simulation of Eq. (1) and does not depend on the hydrodynamic theory. The closed-form predictions that are given (Eq. (2) for r̄F, the ρd≈2ρt droplet-density estimate, and the rF^PF≈0.24 merging estimate) are derived from model parameters and standard MIPS results, not fitted to the phase diagrams. The only circularity-adjacent element is Eq. (3): µeff is expressed in terms of v*(ρ) and pIK(ρ), which are introduced as measured microscopic quantities rather than as closed-form functions of the model parameters. The main text states that theory and simulations agree 'qualitatively' but 'not quantitatively,' and the SM containing the closures is a placeholder. Thus the quantitative binodal comparison in Figs. 3–4 cannot be independently verified; if the same coexistence runs supply v* and pIK, the comparison reduces to a consistency check. Because the central claim is simulation-based and the theory is not load-bearing for it, the overall circularity score is 3 rather than 6.

Assumptions & free parameters 2 free parameters · 5 assumptions · 1 invented entities

The central claims rest on standard coarse-graining of active Brownian particles plus several explicit modeling choices: local truncation of the QS speed, a local chemical potential with pair forces entering only through the Irving-Kirkwood pressure, and a Lyapunov free energy for a nonequilibrium system. The simulation parameters (ρt=25, v0=5, Dr=1, ε=100) are model inputs in the End Matter, not fit parameters. The main unresolved inputs are the closure functions v*(ρ) and pIK(ρ), needed to evaluate Eq. (3), which are not specified in the main text.

free parameters (2)
  • Effective speed closure v*(ρ) = Not specified in main text; input function accounting for QS and collision slowdown
    Appears in Eqs. (3) and (4); its microscopic expression is deferred to the Supplemental Material. If taken from simulation, the theory is not fully self-contained, and the binodal agreement is partly a consistency check.
  • Irving-Kirkwood pressure closure pIK(ρ) = Not specified in main text; stress-tensor closure
    Direct pressure enters the effective chemical potential in Eq. (3); no explicit density dependence is provided in the main text, so the phase-diagram predictions cannot be evaluated from the Letter alone.
assumptions (5)
  • domain assumption v(ρ̃) ≈ v(ρ) + O(∇²), i.e. the self-propulsion speed is local
    Used to derive the local hydrodynamic current Eq. (3); the authors state this neglects gradient terms known to affect MIPS phase equilibria.
  • domain assumption The current takes the form −v∇µ_eff with µ_eff a local function of ρ, with pair forces entering only through pIK(ρ)
    This is the central closure of the generalized thermodynamics; the closure functions are not given in the main text, and deviations are acknowledged as quantitative discrepancies.
  • domain assumption F[ρ] with f'(ρ)=µ_eff is a Lyapunov functional, so common-tangent construction predicts binodals in this nonequilibrium system
    The Letter states the Lyapunov property and applies equilibrium-style coexistence rules to a nonequilibrium system, following refs. [25,57,58].
  • ad hoc to paper Incoming particles arrest when the local density at the cluster interface reaches ρt, giving droplet density ρd ≈ 2ρt
    Heuristic kinetic argument leading to Eq. (2); supported by simulations within 10% for rF < rF bar, but not derived from first principles.
  • domain assumption The large-scale physics of chemotactic and QS active particles are similar enough that conclusions extend to chemotaxis
    Statement in the introduction and conclusions based on refs. [32,45]; not directly simulated in this work.
invented entities (1)
  • Generalized free energy functional F[ρ]
    purpose: To predict stable and metastable binodals via common-tangent construction from the local theory Eq. (3)
    A mathematical object whose Lyapunov property is asserted. It is not independently measured or derived from first principles in the main text, though it follows established generalized-thermodynamics practice for MIPS.

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Cite this review

Pith. "Pith review of Contact Forces in Motility-Regulated Active Matter." pith.science (2026). https://pith.science/paper/2PRX5PBE

@misc{pith2026250708964,
  author       = {Pith},
  title        = {Pith review of: Contact Forces in Motility-Regulated Active Matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2PRX5PBE}},
  note         = {Machine review of arXiv:2507.08964}
}
read the original abstract

Long-range interactions are ubiquitous in nature, where they are mediated by diffusive fields at the cellular scale or by visual cues for groups of animals. Short-range forces, which are paradigmatic in physics, can thus often be neglected when modeling the collective behaviors of biological systems induced by mediated interactions. However, when self-organization leads to the emergence of dense phases, we show that excluded-volume interactions play an important and versatile role. We consider assemblies of active particles that undergo either condensation or phase-separation due to motility regulation and show that short-range repulsive forces can induce opposite effects. When motility regulation triggers an absorbing phase transition, such as a chemotactic collapse, repulsive forces opposes the formation of condensates and stabilize the coexistence between finite-density phases. In contrast, when motility regulation induces liquid-gas coexistence, repulsive forces can, counterintuitively, lead to a significant increase in the liquid density.

Figures

Figures reproduced from arXiv: 2507.08964 by the authors.

Figure 1
Figure 1. FIG. 1. Impact of repulsive forces of range [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Large-scale behavior when QS induces an absorbing phase [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. we report the spinodal lines for both QS- and PF-MIPS predicted from Eq. (4), which shows the merging of the two phase transitions. The densification of the QS liquid phase can [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Metastable coexistence: comparison between theory and simulations. (a) Zoom on the phase diagram of Fig. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Schematic plots of [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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Works this paper leans on

63 extracted references · 60 canonical work pages

  1. [48]

    See Supplemental Material [url], which includes theoretical and numerical details, as well as Refs. XXX

    work page

  2. [1]

    C. Liu, X. Fu, L. Liu, X. Ren, C. K. Chau, S. Li, L. Xiang, H. Zeng, G. Chen, L.-H. Tang, et al., Sequential establishment of stripe patterns in an expanding cell population, Science 334, 238 (2011)

    work page 2011

  3. [2]

    Curatolo, N

    A. Curatolo, N. Zhou, Y . Zhao, C. Liu, A. Daerr, J. Tailleur, and J. Huang, Cooperative pattern formation in multi-component bacterial systems through reciprocal motility regulation, Nature Physics 16, 1152 (2020)

    work page 2020

  4. [3]

    Helbing and P

    D. Helbing and P. Molnar, Social force model for pedestrian dynamics, Physical review E 51, 4282 (1995)

    work page 1995

  5. [4]

    Ballerini, N

    M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V . Lecomte, A. Orlandi, G. Parisi, A. Procaccini, et al., Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, Proceedings of the national academy of sciences 105, 1232 (2008). 6

    work page 2008

  6. [5]

    F. A. Lavergne, H. Wendehenne, T. B¨auerle, and C. Bechinger, Group formation and cohesion of active particles with visual perception–dependent motility, Science 364, 70 (2019)

    work page 2019

  7. [6]

    M. A. Fernandez-Rodriguez, F. Grillo, L. Alvarez, M. Rathlef, I. Buttinoni, G. V olpe, and L. Isa, Feedback-controlled active brownian colloids with space-dependent rotational dynamics, Nature communications 11, 4223 (2020)

    work page 2020

  8. [7]

    Mui ˜nos-Landin, A

    S. Mui ˜nos-Landin, A. Fischer, V . Holubec, and F. Cichos, Re- inforcement learning with artificial microswimmers, Science Robotics 6, eabd9285 (2021)

    work page 2021

Show all 63 references
  1. [8]

    M. Y . Ben Zion, J. Fersula, N. Bredeche, and O. Dauchot, Mor- phological computation and decentralized learning in a swarm of sterically interacting robots, Science Robotics 8, eabo6140 (2023)

    2023

  2. [9]

    Geyer, D

    D. Geyer, D. Martin, J. Tailleur, and D. Bartolo, Freezing a flock: Motility-induced phase separation in polar active liquids, Phys. Rev. X 9, 031043 (2019)

    2019

  3. [10]

    Lefranc, A

    T. Lefranc, A. Dinelli, C. Fern ´andez-Rico, R. Dullens, J. Tailleur, and D. Bartolo, Quorum sensing and absorbing phase transitions in colloidal active matter, arXiv preprint arXiv:2502.13919; in Press at Phys. Rev. X (2025)

    2025

  4. [11]

    M. P. Brenner, L. S. Levitov, and E. O. Budrene, Physical mech- anisms for chemotactic pattern formation by bacteria, Biophys- ical journal 74, 1677 (1998)

    1998

  5. [12]

    M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015)

    2015

  6. [13]

    E. O. Budrene and H. C. Berg, Complex patterns formed by motile cells of escherichia coli, Nature 349, 630 (1991)

    1991

  7. [14]

    D. E. Woodward, R. Tyson, M. Myerscough, J. Murray, E. Bu- drene, and H. Berg, Spatio-temporal patterns generated by salmonella typhimurium, Biophysical journal 68, 2181 (1995)

    1995

  8. [15]

    H. C. Berg, E. coli in Motion (Springer, 2004)

    2004

  9. [16]

    G. Liu, A. Patch, F. Bahar, D. Yllanes, R. D. Welch, M. C. Marchetti, S. Thutupalli, and J. W. Shaevitz, Self-driven phase transitions drive myxococcus xanthus fruiting body formation, Physical review letters 122, 248102 (2019)

    2019

  10. [17]

    Theurkauff, C

    I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, and L. Bocquet, Dynamic clustering in active colloidal suspensions with chemical signaling, Physical review letters 108, 268303 (2012)

    2012

  11. [18]

    Palacci, S

    J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Living crystals of light-activated colloidal surfers, Sci- ence 339, 936 (2013)

    2013

  12. [19]

    Soto and R

    R. Soto and R. Golestanian, Run-and-tumble dynamics in a crowded environment: Persistent exclusion process for swim- mers, Physical Review E 89, 012706 (2014)

    2014

  13. [20]

    Pohl and H

    O. Pohl and H. Stark, Dynamic clustering and chemotactic col- lapse of self-phoretic active particles, Physical review letters 112, 238303 (2014)

    2014

  14. [21]

    B ¨auerle, A

    T. B ¨auerle, A. Fischer, T. Speck, and C. Bechinger, Self- organization of active particles by quorum sensing rules, Nature communications 9, 3232 (2018)

    2018

  15. [22]

    Zhang, R

    J. Zhang, R. Alert, J. Yan, N. S. Wingreen, and S. Granick, Active phase separation by turning towards regions of higher density, Nature Physics 17, 961 (2021)

    2021

  16. [23]

    Tailleur and M

    J. Tailleur and M. E. Cates, Statistical mechanics of interacting run-and-tumble bacteria, Physical review letters 100, 218103 (2008)

    2008

  17. [24]

    S. Saha, R. Golestanian, and S. Ramaswamy, Clusters, asters, and collective oscillations in chemotactic colloids, Physical Re- view E 89, 062316 (2014)

    2014

  18. [25]

    A. P. Solon, J. Stenhammar, M. E. Cates, Y . Kafri, and J. Tailleur, Generalized thermodynamics of motility-induced phase separation: phase equilibria, laplace pressure, and change of ensembles, New Journal of Physics 20, 075001 (2018)

    2018

  19. [26]

    Gnan and C

    N. Gnan and C. Maggi, Critical behavior of quorum-sensing active particles, Soft Matter 18, 7654 (2022)

    2022

  20. [27]

    W. J. Ridgway, M. P. Dalwadi, P. Pearce, and S. J. Chapman, Motility-induced phase separation mediated by bacterial quo- rum sensing, Physical Review Letters 131, 228302 (2023)

    2023

  21. [28]

    Dinelli, J

    A. Dinelli, J. O’Byrne, A. Curatolo, Y . Zhao, P. Sollich, and J. Tailleur, Non-reciprocity across scales in active mixtures, Na- ture Communications 14, 7035 (2023)

    2023

  22. [29]

    Y . Duan, J. Agudo-Canalejo, R. Golestanian, and B. Mahault, Dynamical pattern formation without self-attraction in quorum- sensing active matter: the interplay between nonreciprocity and motility, Physical Review Letters 131, 148301 (2023)

    2023

  23. [30]

    M. R. Evans and T. Hanney, Nonequilibrium statistical mechan- ics of the zero-range process and related models, Journal of Physics A: Mathematical and General 38, R195 (2005)

    2005

  24. [31]

    Golestanian, Bose-einstein-like condensation in scalar active matter with diffusivity edge, Physical Review E 100, 010601 (2019)

    R. Golestanian, Bose-einstein-like condensation in scalar active matter with diffusivity edge, Physical Review E 100, 010601 (2019)

    2019

  25. [32]

    O’Byrne and J

    J. O’Byrne and J. Tailleur, Lamellar to micellar phases and be- yond: When tactic active systems admit free energy functionals, Physical Review Letters 125, 208003 (2020)

    2020

  26. [33]

    Mahault and R

    B. Mahault and R. Golestanian, Bose–einstein-like condensa- tion due to diffusivity edge under periodic confinement, New Journal of Physics 22, 063045 (2020)

    2020

  27. [34]

    Mayor and C

    R. Mayor and C. Carmona-Fontaine, Keeping in touch with contact inhibition of locomotion, Trends in cell biology20, 319 (2010)

    2010

  28. [35]

    Peruani and G

    F. Peruani and G. J. Sibona, Dynamics and steady states in excitable mobile agent systems, Physical review letters 100, 168103 (2008)

    2008

  29. [36]

    Soto and R

    R. Soto and R. Golestanian, Self-assembly of catalytically active colloidal molecules: tailoring activity through surface chemistry, Physical review letters 112, 068301 (2014)

    2014

  30. [37]

    Paoluzzi, M

    M. Paoluzzi, M. Leoni, and M. C. Marchetti, Fractal aggrega- tion of active particles, Physical Review E 98, 052603 (2018)

    2018

  31. [38]

    Abaurrea Velasco, M

    C. Abaurrea Velasco, M. Abkenar, G. Gompper, and T. Auth, Collective behavior of self-propelled rods with quorum sensing, Physical Review E 98, 022605 (2018)

    2018

  32. [39]

    Paoluzzi, M

    M. Paoluzzi, M. Leoni, and M. C. Marchetti, Information and motility exchange in collectives of active particles, Soft Matter 16, 6317 (2020)

    2020

  33. [40]

    Saintillan and M

    D. Saintillan and M. J. Shelley, Instabilities and pattern forma- tion in active particle suspensions: Kinetic theory and contin- uum simulations, Physical Review Letters 100, 178103 (2008)

    2008

  34. [41]

    Baskaran and M

    A. Baskaran and M. C. Marchetti, Statistical mechanics and hy- drodynamics of bacterial suspensions, Proceedings of the Na- tional Academy of Sciences 106, 15567 (2009)

    2009

  35. [42]

    M. C. Marchetti, J.-F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft ac- tive matter, Reviews of modern physics 85, 1143 (2013)

    2013

  36. [43]

    Tlili, E

    S. Tlili, E. Gauquelin, B. Li, O. Cardoso, B. Ladoux, H. De- lano¨e-Ayari, and F. Graner, Collective cell migration without proliferation: density determines cell velocity and wave veloc- ity, Royal Society open science 5, 172421 (2018)

    2018

  37. [44]

    Alert and X

    R. Alert and X. Trepat, Physical models of collective cell mi- gration, Annual Review of Condensed Matter Physics 11, 77 (2020)

    2020

  38. [45]

    Dinelli, J

    A. Dinelli, J. O’Byrne, and J. Tailleur, Fluctuating hydrody- namics of active particles interacting via taxis and quorum sens- ing: static and dynamics, Journal of Physics A: Mathematical and Theoretical 57, 395002 (2024)

    2024

  39. [46]

    M. E. Cates and J. Tailleur, When are active brownian parti- cles and run-and-tumble particles equivalent? consequences for 7 motility-induced phase separation, EPL (Europhysics Letters) 101, 20010 (2013)

    2013

  40. [47]

    A. K. Omar, H. Row, S. A. Mallory, and J. F. Brady, Mechanical theory of nonequilibrium coexistence and motility-induced phase separation, Proceedings of the Na- tional Academy of Sciences 120, e2219900120 (2023), https://www.pnas.org/doi/pdf/10.1073/pnas.2219900120

    2023 doi

  41. [49]

    Speck, Coexistence of active brownian disks: van der waals theory and analytical results, Phys

    T. Speck, Coexistence of active brownian disks: van der waals theory and analytical results, Phys. Rev. E 103, 012607 (2021)

    2021

  42. [50]

    Fily and M

    Y . Fily and M. C. Marchetti, Athermal phase separation of self- propelled particles with no alignment, Phys. Rev. Lett. 108, 235702 (2012)

    2012

  43. [51]

    G. S. Redner, M. F. Hagan, and A. Baskaran, Structure and dy- namics of a phase-separating active colloidal fluid, Phys. Rev. Lett. 110, 055701 (2013)

    2013

  44. [52]

    Stenhammar, D

    J. Stenhammar, D. Marenduzzo, R. J. Allen, and M. E. Cates, Phase behaviour of active brownian particles: the role of di- mensionality, Soft matter 10, 1489 (2014)

    2014

  45. [53]

    Wysocki, R

    A. Wysocki, R. G. Winkler, and G. Gompper, Cooperative mo- tion of active brownian spheres in three-dimensional dense sus- pensions, Europhysics Letters 105, 48004 (2014)

    2014

  46. [54]

    C. B. Caporusso, P. Digregorio, D. Levis, L. F. Cugliandolo, and G. Gonnella, Motility-induced microphase and macrophase separation in a two-dimensional active brownian particle sys- tem, Physical Review Letters 125, 178004 (2020)

    2020

  47. [55]

    A. P. Solon, J. Stenhammar, R. Wittkowski, M. Kardar, Y . Kafri, M. E. Cates, and J. Tailleur, Pressure and phase equilibria in in- teracting active brownian spheres, Phys. Rev. Lett.114, 198301 (2015)

    2015

  48. [56]

    Irving and J

    J. Irving and J. G. Kirkwood, The statistical mechanical theory of transport processes. iv. the equations of hydrodynamics, The Journal of chemical physics 18, 817 (1950)

    1950

  49. [57]

    J. M. Yeomans, Statistical mechanics of phase transitions (Clarendon Press, 1992)

    1992

  50. [58]

    O’Byrne, A

    J. O’Byrne, A. Solon, J. Tailleur, and Y . Zhao, An introduction to motility-induced phase separation (2023)

    2023

  51. [59]

    Wittkowski, A

    R. Wittkowski, A. Tiribocchi, J. Stenhammar, R. J. Allen, D. Marenduzzo, and M. E. Cates, Scalar φ 4 field theory for active-particle phase separation, Nature communications 5, 4351 (2014)

    2014

  52. [60]

    D. R. Zusman, A. E. Scott, Z. Yang, and J. R. Kirby, Chemosen- sory pathways, motility and development in myxococcus xan- thus, Nature Reviews Microbiology 5, 862 (2007)

    2007

  53. [61]

    Bricard, J.-B

    A. Bricard, J.-B. Caussin, N. Desreumaux, O. Dauchot, and D. Bartolo, Emergence of macroscopic directed motion in pop- ulations of motile colloids, Nature 503, 95 (2013)

    2013

  54. [62]

    Nishiguchi and M

    D. Nishiguchi and M. Sano, Mesoscopic turbulence and local order in janus particles self-propelling under an ac electric field, Physical Review E 92, 052309 (2015)

    2015

  55. [63]

    Bechinger, R

    C. Bechinger, R. Di Leonardo, H. L ¨owen, C. Reichhardt, G. V olpe, and G. V olpe, Active particles in complex and crowded environments, Reviews of modern physics88, 045006 (2016)

    2016

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