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REVIEW 4 major objections 5 minor 63 references

Attractive active Brownian particles in a static activity gradient spontaneously form droplets that migrate up the gradient, dissolve, and reassemble in a sustained cycle — all without biochemical feedback.

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2026-08-04 09:19 UTC pith:QB5MI2NO

load-bearing objection Solid simulation study of attractive ABPs in activity gradients; the up-gradient migration is a real, well-argued result, but the headline 'cyclic positioning' is asserted rather than demonstrated, and the binary-mixture section contains contradictions that need fixing. the 4 major comments →

arxiv 2510.15771 v3 pith:QB5MI2NO submitted 2025-10-17 cond-mat.soft

Self-organization and cyclic positioning of active condensates

Hossein Vahid , Jens-Uwe Sommer , Abhinav Sharma This is my paper
classification cond-mat.soft
keywords active Brownian particlescondensatesactivity gradientphase separationliving clustersself-organizationinterfacial polarizationdroplet migration
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that a suspension of attractive active Brownian particles in a spatially varying activity field can self-organize into condensates that migrate toward regions of higher activity and, at intermediate attraction strengths, undergo continuous cycles of nucleation, migration, evaporation, and reassembly. The cycles emerge without any biochemical feedback loops, purely from the interplay of interparticle cohesion, self-propulsion, and the activity gradient. The authors identify the driving mechanism as the outward polarization of particles at the droplet interface, which generates a net force toward the high-activity side; they support this by showing that passive droplets in thermal gradients and motility-induced phase-separated clusters, which lack this polarization, move in the opposite direction. If correct, this establishes a minimal physical route for spatial control and turnover of condensates, with potential applications to biological positioning and synthetic active materials.

Core claim

Using Brownian dynamics simulations, the authors show that attractive active Brownian particles (ABPs) in a box with a spatially varying activity field phase-separate into a dense liquid-like condensate coexisting with a dilute vapor. When the activity increases along one axis, the condensate migrates toward the highest-activity region. The motion is attributed to interfacial polarization: ABPs at the droplet boundary align outward from the dense phase, and because particles on the high-activity side push more strongly, the oriented interfacial layer produces a net force up the gradient. At intermediate attraction strengths, the condensate becomes a 'living cluster' that continuously exchang

What carries the argument

The central mechanism is interfacial polarization of active Brownian particles at the liquid–vapor interface. Particles at the droplet surface preferentially point outward, away from the dense phase; when the propulsion force varies spatially, the outward-oriented particles on the high-activity side exert a stronger force, creating a net push that drives the entire droplet up the activity gradient. This orientation ordering, rather than bulk pressure differences, is presented as the dominant driving force, based on control simulations of a passive droplet in a thermal gradient and a MIPS cluster in an activity gradient, both of which migrate in the opposite direction.

Load-bearing premise

The load-bearing premise is that the outward interfacial polarization of the active particles, not bulk pressure differences or other effects, provides the dominant force driving the droplet’s up-gradient migration; this attribution rests on only two control comparisons rather than direct force measurements or a perturbation that eliminates the alignment.

What would settle it

A clean falsifying observation would be a condensate whose surface particles are prevented from aligning outward (for instance by a temporary torque) yet still moves up the activity gradient. That would show the interfacial polarization is not essential. Alternatively, a direct measurement of the local force balance at the interface (e.g., via optical trapping or microfluidic gradients) could determine whether the outward-oriented layer is indeed the main driver.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Activity gradients alone can position and recycle condensates without chemical feedback, offering a generic physical principle for subcellular organization such as nucleolus or P-body dynamics.
  • The cyclic assembly–dissolution behavior provides a minimal route to synthetic 'living' materials that autonomously oscillate between condensed and dispersed states.
  • The opposite migration direction compared to MIPS clusters indicates that a new theoretical framework beyond MIPS is required for attractive ABPs in inhomogeneous environments.
  • In binary mixtures, differential cohesion yields a physical sorting principle equivalent to differential adhesion in cell aggregates, which could guide engineering of multicomponent condensates with programmable internal architecture.
  • Experimental realizations with enzyme-powered nanomotors or light-activated Janus particles could test the predicted migration and cycling directly.

Where Pith is reading between the lines

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

  • If interfacial polarization is truly the dominant driver, then manipulating the orientation of surface particles (e.g., through a coating that favors inward alignment) should reverse or suppress the migration direction, providing a direct design knob for active condensates.
  • The cycle frequency likely scales with the local activity-gradient steepness and the difference between attraction strength and a critical value; a systematic sweep of these parameters would reveal a phase boundary between stationary condensation (strong cohesion) and cyclic living clusters, a testable prediction.
  • The discrepancy between the main text (passive β particles) and the Supplementary Material (active β particles) for the binary-mixture setup means the robustness of the core-shell stabilization claim depends on which variant is physically intended; resolving this would clarify whether the stabilizing effect requires passivity or just weaker cohesion.
  • One could imagine extending the model to feedback between condensate size and local activity (e.g., activity that increases with local density), which might convert the transient cycles into sustained oscillations or traveling waves, a behavior that could be explored in follow-up simulations.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper uses Brownian dynamics simulations of attractive active Brownian particles (ABPs) in spatially varying activity fields to argue that cohesive active droplets migrate up activity gradients, that at intermediate attraction they form 'living clusters' engaged in repeated nucleation, migration, evaporation, and reassembly cycles, and that adding passive or weakly active particles stabilizes these clusters. The authors also present phase diagrams for attractive ABPs, measure interfacial orientation and velocity streamlines, and compare attractive active droplets, passive droplets in thermal gradients, and MIPS clusters to attribute the direction of migration to interfacial polarization. The central claim is that a purely physical system can exhibit cyclic condensation and dissolution without biochemical feedback.

Significance. If the cyclic positioning claim holds, the paper would identify a minimal physical mechanism for spatiotemporal control of condensates, relevant to biomolecular condensates and synthetic active matter. The paper includes standard direct-coexistence protocols, detailed phase diagrams, and clear visualizations, which are strengths. However, the headline claim of cyclic positioning is not quantified or demonstrated by the presented data; the evidence for the stated cycle is limited to cluster-size transition matrices, which show persistence rather than cyclic motion. The mechanism attribution to interfacial polarization is based on indirect comparisons rather than direct force or perturbation measurements. These issues currently prevent the paper from establishing its central claims, but they are addressable with additional analysis and simulations.

major comments (4)
  1. [Fig. 3 and SM Sec. SIII] The central claim of 'cyclic positioning through repeated nucleation, migration, evaporation, and reassembly' (abstract) is not supported by the data shown. The transition matrices P(N1|N0, dt) in Figs. 3(c-g) and S4 are diagonal-dominated, indicating that most clusters persist and change size gradually; the text itself says 'most clusters persist and maintain a relatively stable size.' These matrices contain no information about cluster positions, spatial locations of nucleation or dissolution, or time ordering of a cycle. They cannot distinguish a cyclic regime from a microphase-separated steady state in which clusters fluctuate in size at fixed positions. To substantiate the headline claim, the authors should provide time-resolved cluster center-of-mass trajectories, event statistics (nucleation, migration, evaporation, re-nucleation), and a measure of cycle periodicity or recurrence.
  2. [Fig. 4 and Conclusions] The causal claim that outward interfacial polarization of ABPs is the dominant driving force for up-gradient migration is asserted but not directly tested. The authors compare an attractive active condensate with a passive droplet in a thermal gradient and a MIPS cluster in an activity gradient (Fig. 4). These comparisons are correlational and do not isolate interfacial polarization from other contributions such as interior pressure imbalances or finite-size wall effects. A direct test would be a local force measurement, a perturbation that suppresses or reverses interfacial alignment, or a control matched in bulk equation of state. Without such a test, 'Our results confirm this to be the case' (Conclusions) is an overstatement.
  3. [Fig. 5 vs. SM Sec. SV] There is a direct inconsistency in the binary-mixture model. The main text (Fig. 5 caption) states type-beta particles are passive with epsilon_beta_beta=2. Supplemental Section SV states type-beta particles are ABPs (active) with epsilon_beta_beta=2. The stabilization argument differs substantially between passive and active components. The authors must clarify which model was simulated, and if both were used, present and interpret results separately. If the SM version was simulated, the word 'passive' in the abstract and main text is incorrect.
  4. [Simulation protocol, SM Sec. SIII and Fig. 3(a)] The simulated box is non-periodic along z, with repulsive harmonic walls at z=+-25 and activity fa(z)=20(z+25)/50, vanishing at the lower wall and peaking at the upper wall. The claimed cycle involves nucleation in low-activity regions and evaporation at high activity, with particles 'redistribut[ing] through the simulation box.' In this closed geometry, particles evaporated at high activity are trapped by the lower wall and accumulate at low activity, which could produce the observed density peak without a genuine cyclic reassembly mechanism. The authors do not provide a system-size dependence study or a control with a periodic activity profile that avoids wall accumulation. The cyclic claim would be considerably strengthened by demonstrating cycling in a larger or periodic domain, or by showing that nucleation location is not simply the wall-adjacent low-activity region.
minor comments (5)
  1. [Abstract and main text] The abstract's wording about evaporated ABPs reassembling and migrating again is stronger than the evidence presented; the wording should be tempered until the cycle is directly demonstrated.
  2. [Fig. 1(d-f)] The velocity streamlines are described as 'turbulence-like' and 'analogous to turbulent flows.' This strong visual analogy would benefit from quantitative measures such as correlation length or vorticity.
  3. [SM Eq. S2] The exponent lambda in Eq. S2 is varied between 0.2 and 0.3 'to achieve the best fit.' This should be reported as a fitting parameter with uncertainty, and the authors should state whether the conclusions depend on this range.
  4. [Throughout] There are typographical errors, e.g., 'APBs' instead of 'ABPs' in the paragraph on directed motion. A careful proofread is needed.
  5. [SM Sec. SIV] The thermal-gradient simulation uses energy injection/removal at a fixed rate, while the activity-gradient simulations use step changes in Pe with different magnitudes (Pe=5 for attractive, Pe=120 for MIPS). The comparison would be more compelling if the effective activity scale were matched.

Circularity Check

0 steps flagged

No significant circularity: the migration/cycling results are direct simulation outputs with fixed parameters; the only fits (critical ρ*, ε*) normalize the phase diagrams without generating the headline behavior, and the sole self-citation (ref 38) is a non-load-bearing analogy.

full rationale

The derivation chain — phase separation, up-gradient droplet migration, cyclic nucleation/migration/evaporation/reassembly — is produced directly by Brownian dynamics with fixed model parameters (Pe, ε, fa*); no parameter is fitted to a target behavior and then repackaged as a prediction. The only fitted quantities are the critical density ρ* and attraction strength ε* from coexistence-density fits (Eqs. S1–S2, Table SI), used only to normalize ε/ε* and classify regimes; they do not enter the gradient-migration or transition-matrix results. The dominant-mechanism claim (interfacial polarization) is argued from three independent control simulations (passive droplet in a thermal gradient, attractive active droplet, MIPS cluster, Fig. 4) plus externally verified orientation results (refs 25–27, 44–45); those controls are not implied by construction, so the mechanism inference is correlational evidence, not a circular reduction. The only self-citation, ref [38] (Vuijk/Sommer/Sharma), is explicitly a qualitative analogy ('Qualitatively, it is analogous to active colloidal dimers with opposite orientations') and is qualified by the paper itself as insufficient ('orientation ordering is a necessary but not sufficient condition'); it is not load-bearing. Two non-circular flaws are flagged as correctness risk only: (i) 'This process creates a continuous cycle' is under-supported, since the presented transition matrices P(N1|N0, Δt) quantify cluster-size persistence ('the high probability concentrated along the diagonal... indicates that most clusters persist'), not the spatial nucleation–migration–evaporation–reassembly loop; and (ii) the main text (Fig. 5: 'type-β particles are passive with εββ=2... shifts monotonically toward the higher activity region') contradicts SM S5 ('Type-β particles are ABPs with εββ=2... shifts monotonically toward the lower activity region'). Neither makes a result definitionally equal to its input. The paper is self-consistent against external anchors (Pe=0 critical point matches known passive values; MIPS clusters migrate to low activity as in refs 44–45), so the honest circularity finding is low.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

No new entities are postulated. The free parameters are confined to the phenomenological phase-diagram fits, which are used for regime classification rather than as inputs to the migration/cycling claims. The main load-bearing modeling choices are the ABP dynamics, the Wang–Frenkel potential, and the assumption that an equilibrium-like binodal exists for the active system; all are domain assumptions standard in this literature. The migration mechanism's causality is assumed after comparison to controls, not measured directly.

free parameters (4)
  • Critical attraction strength ε* = 0.96 (Pe=0), 1.13 (Pe=3), 1.37 (Pe=5), 2.17 (Pe=10), 3.27 (Pe=15), 4.14 (Pe=20)
    Fitted from binodal curves in Fig. 1(b)/Table SI using Eq. (S2); used to normalize ε/ε* and to delimit intermediate vs strong attraction regimes in the gradient simulations.
  • Critical density ρ* = 0.31 (Pe=0) to 0.42 (Pe=20)
    Fitted from the average-density branch of the coexistence curves; used to classify phase behavior.
  • Binodal fit amplitude A and density-difference amplitude Δρ0 = not listed in the paper
    Empirical constants in Eq. (S2) that set the shape of the liquid and vapor branches.
  • Coexistence exponent λ = varied between 0.2 and 0.3
    Ad hoc choice to fit the density-difference branch; affects the extracted ε* values and hence the regime labels.
axioms (4)
  • domain assumption Active Brownian particle model with translational and rotational Langevin dynamics (Eqs for γt ṙi and ėi) is an adequate description of cohesive active matter.
    Standard model adopted in Model section; the biology relevance rests on this mapping.
  • domain assumption Wang–Frenkel potential UWF(r) captures the essential physics of short-range cohesion in active condensates.
    Chosen in Model for a continuous force cutoff and LJ-like behavior; no comparison to other potentials is provided.
  • domain assumption Direct coexistence simulations yield well-defined coexisting liquid/vapor densities for a driven active system.
    Used to build phase diagrams (Fig. 1b); assumes a binodal exists despite the non-equilibrium active driving.
  • domain assumption Interfacial polarization is the dominant mechanism for droplet migration in activity gradients.
    Inferred from two control simulations (passive thermal gradient and MIPS cluster), not from direct force balance; location: 'Is interfacial polarization the dominant mechanism...?'.

pith-pipeline@v1.3.0-alltime-deepseek · 14385 in / 15647 out tokens · 125082 ms · 2026-08-04T09:19:04.738542+00:00 · methodology

0 comments
read the original abstract

Cohesive active assemblies are often regulated by spatially heterogeneous nonequilibrium driving, such as gradients in motility, biochemical turnover, or mechanical activity. Such heterogeneous driving can influence where condensates or cell collectives accumulate, how stable they are, and how they exchange material with their surroundings. However, the minimal physical mechanisms by which activity gradients control the positioning and turnover of cohesive active matter remain unclear. Here, we address this question using a model of attractive active Brownian particles (ABPs) in a spatially varying activity field. Using Brownian dynamics simulations, we show that these particles undergo liquid-gas phase separation, and spatially varying activity fields induce striking emergent dynamics. Attractive active droplets migrate up activity gradients, and at sufficiently high activity, they can fragment or evaporate into a dilute phase. For finite clusters, evaporated ABPs can redistribute through the simulation box, reassemble into new clusters in lower-activity regions, and migrate again toward higher activity, giving rise to cyclic positioning through repeated nucleation, migration, evaporation, and reassembly.

Figures

Figures reproduced from arXiv: 2510.15771 by Abhinav Sharma, Hossein Vahid, Jens-Uwe Sommer.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) A snapshot of the simulation box for [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Steady-state density profile of ABPs along the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Steady-state density profiles ( [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

discussion (0)

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Works this paper leans on

63 extracted references · 5 canonical work pages · 1 internal anchor

  1. [1]

    A. A. Hyman, C. A. Weber, and F. Jülicher, Annu. Rev. Cell Dev. Biol.30, 39 (2014)

    2014

  2. [2]

    C. A. Weber, D. Zwicker, F. Jülicher, and C. F. Lee, Rep. Prog. Phys.82, 064601 (2019)

    2019

  3. [3]

    A. J. Ewald, A. Brenot, M. Duong, B. S. Chan, and Z. Werb, Dev. Cell.14, 570 (2008)

    2008

  4. [4]

    Scarpa and R

    E. Scarpa and R. Mayor, J. Cell Biol.212, 143 (2016)

    2016

  5. [5]

    Riahi, Y

    R. Riahi, Y. Yang, D. D. Zhang, and P. K. Wong, J. Lab. Autom.17, 59 (2012)

    2012

  6. [6]

    L. Li, Y. He, M. Zhao, and J. Jiang, Burns Trauma1, 2321 (2013)

    2013

  7. [7]

    W. T. Snead and A. S. Gladfelter, Mol. Cell.76, 295 (2019)

    2019

  8. [8]

    Linsenmeier, M

    M. Linsenmeier, M. Hondele, F. Grigolato, E. Secchi, K. Weis, and P. Arosio, Nat. Commun.13, 3030 (2022)

    2022

  9. [9]

    C. P. Brangwynne, T. J. Mitchison, and A. A. Hyman, Proc. Natl. Acad. Sci.108, 4334 (2011)

    2011

  10. [10]

    Feric, N

    M. Feric, N. Vaidya, T. S. Harmon, D. M. Mitrea, L. Zhu, T. M. Richardson, R. W. Kriwacki, R. V. Pappu, and C. P. Brangwynne, Cell165, 1686 (2016)

    2016

  11. [11]

    S. Jain, J. R. Wheeler, R. W. Walters, A. Agrawal, A. Barsic, and R. Parker, Cell164, 487 (2016)

    2016

  12. [12]

    Guilhas, J.-C

    B. Guilhas, J.-C. Walter, J. Rech, G. David, N. O. Wal- liser, J. Palmeri, C. Mathieu-Demaziere, A. Parmeggiani, J.-Y. Bouet, A. Le Gall,et al., Mol. Cell.79, 293 (2020)

    2020

  13. [13]

    Jambon-Puillet, A

    E. Jambon-Puillet, A. Testa, C. Lorenz, R. W. Style, A. A. Rebane, and E. R. Dufresne, Nat. Commun.15, 3919 (2024)

    2024

  14. [14]

    S. Saha, C. A. Weber, M. Nousch, O. Adame-Arana, C. Hoege, M. Y. Hein, E. Osborne-Nishimura, J. Ma- hamid, M. Jahnel, L. Jawerth,et al., Cell166, 1572 (2016)

    2016

  15. [15]

    S. F. Banani, H. O. Lee, A. A. Hyman, and M. K. Rosen, Nat. Rev. Mol. Cell Biol.18, 285 (2017)

    2017

  16. [16]

    Carmona-Fontaine, H

    C. Carmona-Fontaine, H. K. Matthews, S. Kuriyama, M. Moreno, G. A. Dunn, M. Parsons, C. D. Stern, and R. Mayor, Nature456, 957 (2008)

    2008

  17. [17]

    Mayor and C

    R. Mayor and C. Carmona-Fontaine, Trends Cell Biol. 20, 319 (2010)

    2010

  18. [18]

    B. Lin, T. Yin, Y. I. Wu, T. Inoue, and A. Levchenko, Nat. Commun.6, 6619 (2015)

    2015

  19. [19]

    Miskolci, L

    V. Miskolci, L. C. Klemm, and A. Huttenlocher, Trends Cell Biol.31, 86 (2021)

    2021

  20. [20]

    Y. Li, F. M. Vieceli, W. G. Gonzalez, A. Li, W. Tang, C. Lois, and M. E. Bronner, Cell Rep.26, 1489 (2019)

    2019

  21. [21]

    Theveneau, L

    E. Theveneau, L. Marchant, S. Kuriyama, M. Gull, B. Moepps, M. Parsons, and R. Mayor, Dev. Cell19, 39 (2010)

    2010

  22. [22]

    X. Wang, S. Ramírez-Hinestrosa, J. Dobnikar, and D. Frenkel, Phys. Chem. Chem. Phys.22, 10624 (2020)

    2020

  23. [23]

    A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolin- tineanu, W. M. Brown, P. S. Crozier, P. J. in ’t Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimp- ton, Comp. Phys. Comm.271, 108171 (2022)

    2022

  24. [24]

    Stukowski, Model

    A. Stukowski, Model. Simul. Mater. Sci. Eng.18, 015012 (2009)

    2009

  25. [25]

    Prymidis, S

    V. Prymidis, S. Paliwal, M. Dijkstra, and L. Filion, J. Chem. Phys.145, 10.1063/1.4963191 (2016)

    work page doi:10.1063/1.4963191 2016

  26. [26]

    Paliwal, V

    S. Paliwal, V. Prymidis, L. Filion, and M. Dijkstra, J. Chem. Phys.147, 10.1063/1.4989764 (2017)

    work page doi:10.1063/1.4989764 2017

  27. [27]

    A. K. Omar, Z.-G. Wang, and J. F. Brady, Phys. Rev. E 101, 012604 (2020)

    2020

  28. [28]

    Omori and Y

    T. Omori and Y. Yamaguchi, J. Chem. Phys.161, 10.1063/5.0235858 (2024)

    work page doi:10.1063/5.0235858 2024

  29. [29]

    Schwarz-Linek, A

    J. Schwarz-Linek, A. Winkler, L. G. Wilson, N. T. Pham, T. Schilling, and W. C. Poon, Soft Matter6, 4540 (2010)

    2010

  30. [30]

    Schwarz-Linek, C

    J. Schwarz-Linek, C. Valeriani, A. Cacciuto, M. Cates, D. Marenduzzo, A. Morozov, and W. Poon, Proc. Natl. Acad. Sci.109, 4052 (2012)

    2012

  31. [31]

    Y.-E. Keta, J. U. Klamser, R. L. Jack, and L. Berthier, Phys. Rev. Lett.132, 218301 (2024)

    2024

  32. [32]

    Ginot, I

    F. Ginot, I. Theurkauff, F. Detcheverry, C. Ybert, and C. Cottin-Bizonne, Nat. Commun.9, 696 (2018)

    2018

  33. [33]

    B. M. Mognetti, A. Šarić, S. Angioletti-Uberti, A. Cacci- uto, C. Valeriani, and D. Frenkel, Phys. Rev. Lett.111, 245702 (2013)

    2013

  34. [34]

    Caprini, D

    L. Caprini, D. Breoni, A. Ldov, C. Scholz, and H. Löwen, Commun. Phys.7, 343 (2024)

    2024

  35. [35]

    Palacci, S

    J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Science339, 936 (2013)

    2013

  36. [36]

    Bechinger, R

    C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Rev. Mod. Phys.88, 045006 (2016)

    2016

  37. [37]

    Alert and X

    R. Alert and X. Trepat, Annu. Rev. Condens. Matter Phys.11, 77 (2020)

    2020

  38. [38]

    H. D. Vuijk, S. Klempahn, H. Merlitz, J.-U. Sommer, and A. Sharma, Phys. Rev. E106, 014617 (2022)

    2022

  39. [39]

    S. C. Takatori and J. F. Brady, Soft Matter11, 7920 (2015)

    2015

  40. [40]

    Ginot, I

    F. Ginot, I. Theurkauff, D. Levis, C. Ybert, L. Boc- quet, L. Berthier, and C. Cottin-Bizonne, Phys. Rev. X 5, 011004 (2015)

    2015

  41. [41]

    Speck, Europhys

    T. Speck, Europhys. Lett.114, 30006 (2016). 6

    2016

  42. [42]

    Q. Dai, Z. Chong, W. Huang, and X. Wang, Langmuir 36, 6268 (2020)

    2020

  43. [43]

    V. H. Cunha, C. A. Dorao, and M. Fernandino, Phys. Fluids36, 10.1063/5.0239562 (2024)

    work page doi:10.1063/5.0239562 2024

  44. [44]

    A. K. Omar, H. Row, S. A. Mallory, and J. F. Brady, Proc. Natl. Acad. Sci.120, e2219900120 (2023)

    2023

  45. [45]

    L. Li, Z. Sun, and M. Yang, Proc. Natl. Acad. Sci.122, e2505010122 (2025)

    2025

  46. [46]

    Heisenberg and Y

    C.-P. Heisenberg and Y. Bellaïche, Cell153, 948 (2013)

    2013

  47. [47]

    Ladoux and R.-M

    B. Ladoux and R.-M. Mège, Nat. Rev. Mol. Cell Biol. 18, 743 (2017)

    2017

  48. [48]

    Dance, Nature589, 186 (2021)

    A. Dance, Nature589, 186 (2021)

    2021

  49. [49]

    R. A. Foty and M. S. Steinberg, Dev. Biol.278, 255 (2005)

    2005

  50. [50]

    Chanson, D

    L. Chanson, D. Brownfield, J. C. Garbe, I. Kuhn, M. R. Stampfer, M. J. Bissell, and M. A. LaBarge, Proc. Natl. Acad. Sci.108, 3264 (2011)

    2011

  51. [51]

    A. E. Cerchiari, J. C. Garbe, N. Y. Jee, M. E. Todhunter, K. E. Broaders, D. M. Peehl, T. A. Desai, M. A. LaBarge, M. Thomson, and Z. J. Gartner, Proc. Natl. Acad. Sci. 112, 2287 (2015)

    2015

  52. [52]

    S. Toda, L. R. Blauch, S. K. Tang, L. Morsut, and W. A. Lim, Science361, 156 (2018)

    2018

  53. [53]

    S. Wang, K. Matsumoto, S. R. Lish, A. X. Cartagena- Rivera, and K. M. Yamada, Cell184, 3702 (2021)

    2021

  54. [54]

    V. G. Santos, A. G. Pires, R. J. Alitappeh, P. A. Rezeck, L. C. Pimenta, D. G. Macharet, and L. Chaimowicz, Swarm Intell.14, 259 (2020)

    2020

  55. [55]

    Ceron, G

    S. Ceron, G. Gardi, K. Petersen, and M. Sitti, Proc. Natl. Acad. Sci.120, e2221913120 (2023)

    2023

  56. [57]

    Ellison, A

    D. Ellison, A. Mugler, M. D. Brennan, S. H. Lee, R. J. Huebner, E. R. Shamir, L. A. Woo, J. Kim, P. Amar, I. Nemenman,et al., Proc. Natl. Acad. Sci.113, E679 (2016)

    2016

  57. [58]

    Giampieri, C

    S. Giampieri, C. Manning, S. Hooper, L. Jones, C. S. Hill, and E. Sahai, Nat. Cell Biol.11, 1287 (2009)

    2009

  58. [59]

    Malet-Engra, W

    G. Malet-Engra, W. Yu, A. Oldani, J. Rey-Barroso, N. S. Gov, G. Scita, and L. Dupré, Curr. Biol.25, 242 (2015)

    2015

  59. [60]

    Bussmann and E

    J. Bussmann and E. Raz, EMBO J.34, 1309 (2015)

    2015

  60. [61]

    Caprini and H

    L. Caprini and H. Löwen, Phys. Rev. Lett.130, 148202 (2023)

    2023

  61. [62]

    Comment on "Flocking without Alignment Interactions in Attractive Active Brownian Particles [arXiv:2303.07746]"

    B. Mahault, arXiv preprint arXiv:2309.00015 10.48550/arXiv.2309.00015 (2023)

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2309.00015 2023

  62. [63]

    S. Song, A. F. Mason, R. A. Post, M. De Corato, R. Mestre, N. A. Yewdall, S. Cao, R. W. van der Hofstad, S.Sanchez, L.K.Abdelmohsen,et al.,Nat.Commun.12, 6897 (2021)

    2021

  63. [64]

    A. F. Mason, B. C. Buddingh’, D. S. Williams, and J. C. Van Hest, J. Am. Chem. Soc.139, 17309 (2017). Supplemental Material for Self-Organization and Cyclic Positioning of Active Condensates Hossein Vahid,1 Jens-Uwe Sommer,1, 2,∗ and Abhinav Sharma3, 1,† 1Leibniz-Institut für Polymerforschung Dresden, Bereich Theorie der Polymere, 01069 Dresden, Germany 2...

    arXiv 2017