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  • Letter
  • Open Access

Active jamming at criticality

Shalabh K. Anand1,2, Chiu Fan Lee1,*, and Thibault Bertrand2,†

  • 1Department of Bioengineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
  • 2Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

  • *c.lee@imperial.ac.uk
  • †t.bertrand@imperial.ac.uk
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Phys. Rev. Research 6, L022018 – Published 22 April, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022018

Abstract

Jamming is ubiquitous in disordered systems, but the critical behavior of jammed solids subjected to active forces or thermal fluctuations remains elusive. In particular, while passive athermal jamming remains mean-field-like in two and three dimensions, diverse active matter systems exhibit anomalous scaling behavior in all physical dimensions. It is therefore natural to ask whether activity leads to anomalous scaling in jammed systems. Here, we use numerical and analytical methods to study systems of active, soft, frictionless spheres in two dimensions, and elucidate the universal scaling behavior that relates the excess coordination, active forces or temperature, and pressure close to the athermal jammed point. We show that active forces and thermal effects around the critical jammed state can again be captured by a mean-field picture, thus highlighting the distinct and crucial role of amorphous structure in active matter systems.

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References (105)

  1. M. E. Cates, J. P. Wittmer, J.-P. Bouchaud, and P. Claudin, Jamming, force chains, and fragile matter, Phys. Rev. Lett. 81, 1841 (1998).
  2. A. J. Liu and S. R. Nagel, Jamming is not just cool any more, Nature (London) 396, 21 (1998).
  3. L. P. Kadanoff, Built upon sand: Theoretical ideas inspired by granular flows, Rev. Mod. Phys. 71, 435 (1999).
  4. A. J. Liu and S. R. Nagel, The jamming transition and the marginally jammed solid, Annu. Rev. Condens. Matter Phys. 1, 347 (2010).
  5. C. S. O'Hern, S. A. Langer, A. J. Liu, and S. R. Nagel, Random packings of frictionless particles, Phys. Rev. Lett. 88, 075507 (2002).
  6. C. S. O'Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel, Jamming at zero temperature and zero applied stress: The epitome of disorder, Phys. Rev. E 68, 011306 (2003).
  7. L. E. Silbert, A. J. Liu, and S. R. Nagel, Vibrations and diverging length scales near the unjamming transition, Phys. Rev. Lett. 95, 098301 (2005).
  8. N. Xu, J. Blawzdziewicz, and C. S. O'Hern, Random close packing revisited: Ways to pack frictionless disks, Phys. Rev. E 71, 061306 (2005).
  9. T. S. Majmudar, M. Sperl, S. Luding, and R. P. Behringer, Jamming transition in granular systems, Phys. Rev. Lett. 98, 058001 (2007).
  10. C. Heussinger and J.-L. Barrat, Jamming transition as probed by quasistatic shear flow, Phys. Rev. Lett. 102, 218303 (2009).
  11. P. Chaudhuri, L. Berthier, and S. Sastry, Jamming transitions in amorphous packings of frictionless spheres occur over a continuous range of volume fractions, Phys. Rev. Lett. 104, 165701 (2010).
  12. J. A. Drocco, M. B. Hastings, C. J. Olson Reichhardt, and C. Reichhardt, Multiscaling at point J: Jamming is a critical phenomenon, Phys. Rev. Lett. 95, 088001 (2005).
  13. I. K. Ono, C. S. O'Hern, D. J. Durian, S. A. Langer, A. J. Liu, and S. R. Nagel, Effective temperatures of a driven system near jamming, Phys. Rev. Lett. 89, 095703 (2002).
  14. P. Olsson and S. Teitel, Critical scaling of shear viscosity at the jamming transition, Phys. Rev. Lett. 99, 178001 (2007).
  15. Z. Zhang, N. Xu, D. T. N. Chen, P. Yunker, A. M. Alsayed, K. B. Aptowicz, P. Habdas, A. J. Liu, S. R. Nagel, and A. G. Yodh, Thermal vestige of the zero-temperature jamming transition, Nature (London) 459, 230 (2009).
  16. C. F. Schreck, T. Bertrand, C. S. O'Hern, and M. D. Shattuck, Repulsive contact interactions make jammed particulate systems inherently nonharmonic, Phys. Rev. Lett. 107, 078301 (2011).
  17. A. Ikeda, L. Berthier, and G. Biroli, Dynamic criticality at the jamming transition, J. Chem. Phys. 138, 12A507 (2013).
  18. T. Bertrand, C. F. Schreck, C. S. O'Hern, and M. D. Shattuck, Hypocoordinated solids in particulate media, Phys. Rev. E 89, 062203 (2014).
  19. A. Ikeda and L. Berthier, Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids, Phys. Rev. E 92, 012309 (2015).
  20. E. DeGiuli, E. Lerner, and M. Wyart, Theory of the jamming transition at finite temperature, J. Chem. Phys. 142, 164503 (2015).
  21. A. H. Clark, J. D. Thompson, M. D. Shattuck, N. T. Ouellette, and C. S. O'Hern, Critical scaling near the yielding transition in granular media, Phys. Rev. E 97, 062901 (2018).
  22. J. D. Thompson and A. H. Clark, Critical scaling for yield is independent of distance to isostaticity, Phys. Rev. Res. 1, 012002(R) (2019).
  23. K. VanderWerf, A. Boromand, M. D. Shattuck, and C. S. O'Hern, Pressure dependent shear response of jammed packings of frictionless spherical particles, Phys. Rev. Lett. 124, 038004 (2020).
  24. P. Wang, S. Zhang, P. Tuckman, N. T. Ouellette, M. D. Shattuck, and C. S. O'Hern, Shear response of granular packings compressed above jamming onset, Phys. Rev. E 103, 022902 (2021).
  25. M. van Hecke, Jamming of soft particles: Geometry, mechanics, scaling and isostaticity, J. Phys.: Condens. Matter 22, 033101 (2010).
  26. D. Bi, J. H. Lopez, J. M. Schwarz, and M. L. Manning, A density-independent rigidity transition in biological tissues, Nat. Phys. 11, 1074 (2015).
  27. C. P. Goodrich, A. J. Liu, and J. P. Sethna, Scaling ansatz for the jamming transition, Proc. Natl. Acad. Sci. USA 113, 9745 (2016).
  28. D. B. Liarte, X. Mao, O. Stenull, and T. C. Lubensky, Jamming as a multicritical point, Phys. Rev. Lett. 122, 128006 (2019).
  29. J. D. Sartor, S. A. Ridout, and E. I. Corwin, Mean-field predictions of scaling prefactors match low-dimensional jammed packings, Phys. Rev. Lett. 126, 048001 (2021).
  30. P. Charbonneau, A. Ikeda, G. Parisi, and F. Zamponi, Glass transition and random close packing above three dimensions, Phys. Rev. Lett. 107, 185702 (2011).
  31. P. Charbonneau, E. I. Corwin, G. Parisi, and F. Zamponi, Universal microstructure and mechanical stability of jammed packings, Phys. Rev. Lett. 109, 205501 (2012).
  32. C. P. Goodrich, A. J. Liu, and S. R. Nagel, Finite-size scaling at the jamming transition, Phys. Rev. Lett. 109, 095704 (2012).
  33. P. Charbonneau, E. I. Corwin, G. Parisi, and F. Zamponi, Jamming criticality revealed by removing localized buckling excitations, Phys. Rev. Lett. 114, 125504 (2015).
  34. P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Glass and jamming transitions: From exact results to finite-dimensional descriptions, Annu. Rev. Condens. Matter Phys. 8, 265 (2017).
  35. S. Ramaswamy, The mechanics and statistics of active matter, Annu. Rev. Condens. Matter Phys. 1, 323 (2010).
  36. 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. Mod. Phys. 85, 1143 (2013).
  37. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  38. P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, and L. Schimansky-Geier, Active brownian particles, Eur. Phys. J.: Spec. Top. 202, 1 (2012).
  39. A. P. Solon, M. E. Cates, and J. Tailleur, Active Brownian particles and run-and-tumble particles: A comparative study, Eur. Phys. J.: Spec. Top. 224, 1231 (2015).
  40. C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).
  41. Y. Fily and M. C. Marchetti, Athermal phase separation of self-propelled particles with no alignment, Phys. Rev. Lett. 108, 235702 (2012).
  42. G. S. Redner, M. F. Hagan, and A. Baskaran, Structure and dynamics of a phase-separating active colloidal fluid, Phys. Rev. Lett. 110, 055701 (2013).
  43. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett. 75, 1226 (1995).
  44. A. Bricard, J.-B. Caussin, N. Desreumaux, O. Dauchot, and D. Bartolo, Emergence of macroscopic directed motion in populations of motile colloids, Nature (London) 503, 95 (2013).
  45. T. Bertrand and C. F. Lee, Diversity of phase transitions and phase separations in active fluids, Phys. Rev. Res. 4, L022046 (2022).
  46. C. F. Lee, Active particles under confinement: Aggregation at the wall and gradient formation inside a channel, New J. Phys. 15, 055007 (2013).
  47. I. D. Vladescu, E. J. Marsden, J. Schwarz-Linek, V. A. Martinez, J. Arlt, A. N. Morozov, D. Marenduzzo, M. E. Cates, and W. C. K. Poon, Filling an emulsion drop with motile bacteria, Phys. Rev. Lett. 113, 268101 (2014).
  48. T. Bertrand, Y. Zhao, O. Bénichou, J. Tailleur, and R. Voituriez, Optimized diffusion of run-and-tumble particles in crowded environments, Phys. Rev. Lett. 120, 198103 (2018).
  49. T. Bertrand, P. Illien, O. Bénichou, and R. Voituriez, Dynamics of run-and-tumble particles in dense single-file systems, New J. Phys. 20, 113045 (2018).
  50. G. Mahmud, C. J. Campbell, K. J. M. Bishop, Y. A. Komarova, O. Chaga, S. Soh, S. Huda, K. Kandere-Grzybowska, and B. A. Grzybowski, Directing cell motions on micropatterned ratchets, Nat. Phys. 5, 606 (2009).
  51. N. Sadati, N. Taheri Qazvini, R. Krishnan, C. Young Park, and J. J. Fredberg, Collective migration and cell jamming, Differentiation 86, 121 (2013).
  52. D. Bi, X. Yang, M. C. Marchetti, and M. L. Manning, Motility-driven glass and jamming transitions in biological tissues, Phys. Rev. X 6, 021011 (2016).
  53. J.-A. Park, J. H. Kim, D. Bi, J. A. Mitchel, N. T. Qazvini, K. Tantisira, C. Y. Park, M. McGill, S.-H. Kim, B. Gweon, J. Notbohm, R. Steward Jr, S. Burger, S. H. Randell, A. T. Kho, D. T. Tambe, C. Hardin, S. A. Shore, E. Israel, D. A. Weitz et al., Unjamming and cell shape in the asthmatic airway epithelium, Nat. Mater. 14, 1040 (2015).
  54. S. Garcia, E. Hannezo, J. Elgeti, J.-F. Joanny, P. Silberzan, and N. S. Gov, Physics of active jamming during collective cellular motion in a monolayer, Proc. Natl. Acad. Sci. USA 112, 15314 (2015).
  55. C. Malinverno, S. Corallino, F. Giavazzi, M. Bergert, Q. Li, M. Leoni, A. Disanza, E. Frittoli, A. Oldani, E. Martini, T. Lendenmann, G. Deflorian, G. V. Beznoussenko, D. Poulikakos, K. H. Ong, M. Uroz, X. Trepat, D. Parazzoli, P. Maiuri, W. Yu et al., Endocytic reawakening of motility in jammed epithelia, Nat. Mater. 16, 587 (2017).
  56. A. Mongera, P. Rowghanian, H. J. Gustafson, E. Shelton, D. A. Kealhofer, E. K. Carn, F. Serwane, A. A. Lucio, J. Giammona, and O. Campàs, A fluid-to-solid jamming transition underlies vertebrate body axis elongation, Nature (London) 561, 401 (2018).
  57. L. Atia, D. Bi, Y. Sharma, J. A. Mitchel, B. Gweon, S. A. Koehler, S. J. DeCamp, B. Lan, J. H. Kim, R. Hirsch, A. F. Pegoraro, K. H. Lee, J. R. Starr, D. A. Weitz, A. C. Martin, J.-A. Park, J. P. Butler, and J. J. Fredberg, Geometric constraints during epithelial jamming, Nat. Phys. 14, 613 (2018).
  58. L. Yan and D. Bi, Multicellular rosettes drive fluid-solid transition in epithelial tissues, Phys. Rev. X 9, 011029 (2019).
  59. J. A. Mitchel, A. Das, M. J. O'Sullivan, I. T. Stancil, S. J. DeCamp, S. Koehler, O. H. Ocaña, J. P. Butler, J. J. Fredberg, M. A. Nieto, D. Bi, and J.-A. Park, In primary airway epithelial cells, the unjamming transition is distinct from the epithelial-to-mesenchymal transition, Nat. Commun. 11, 5053 (2020).
  60. N. I. Petridou, B. Corominas-Murtra, C.-P. Heisenberg, and E. Hannezo, Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions, Cell 184, 1914 (2021).
  61. S. Grosser, J. Lippoldt, L. Oswald, M. Merkel, D. M. Sussman, F. Renner, P. Gottheil, E. W. Morawetz, T. Fuhs, X. Xie, S. Pawlizak, A. W. Fritsch, B. Wolf, L.-C. Horn, S. Briest, B. Aktas, M. L. Manning, and J. A. Käs, Cell and nucleus shape as an indicator of tissue fluidity in carcinoma, Phys. Rev. X 11, 011033 (2021).
  62. L. Chen, J. Toner, and C. F. Lee, Critical phenomenon of the order–disorder transition in incompressible active fluids, New J. Phys. 17, 042002 (2015).
  63. J. Toner, N. Guttenberg, and Y. Tu, Swarming in the dirt: Ordered flocks with quenched disorder, Phys. Rev. Lett. 121, 248002 (2018).
  64. L. Chen, C. F. Lee, and J. Toner, Moving, reproducing, and dying beyond flatland: Malthusian flocks in dimensions d>2, Phys. Rev. Lett. 125, 098003 (2020).
  65. L. Chen, C. F. Lee, A. Maitra, and J. Toner, Packed swarms on dirt: Two-dimensional incompressible flocks with quenched and annealed disorder, Phys. Rev. Lett. 129, 188004 (2022).
  66. R. Ben Ali Zinati, M. Besse, G. Tarjus, and M. Tissier, Dense polar active fluids in a disordered environment, Phys. Rev. E 105, 064605 (2022).
  67. P. Jentsch and C. F. Lee, Critical phenomena in compressible polar active fluids: Dynamical and functional renormalization group studies, Phys. Rev. Res. 5, 023061 (2023).
  68. P. Jentsch and C. F. Lee, A new universality class describes Vicsek's flocking phase in physical dimensions, arXiv:2402.01316.
  69. M. Miller and J. Toner, Phase separation in ordered polar active fluids: A new Universality class, arXiv:2401.05996.
  70. S. Henkes, Y. Fily, and M. C. Marchetti, Active jamming: Self-propelled soft particles at high density, Phys. Rev. E 84, 040301(R) (2011).
  71. L. Berthier and J. Kurchan, Non-equilibrium glass transitions in driven and active matter, Nat. Phys. 9, 310 (2013).
  72. E. Flenner, G. Szamel, and L. Berthier, The nonequilibrium glassy dynamics of self-propelled particles, Soft Matter 12, 7136 (2016).
  73. L. Berthier, E. Flenner, and G. Szamel, How active forces influence nonequilibrium glass transitions, New J. Phys. 19, 125006 (2017).
  74. L. Berthier, E. Flenner, and G. Szamel, Glassy dynamics in dense systems of active particles, J. Chem. Phys. 150, 200901 (2019).
  75. N. Klongvessa, F. Ginot, C. Ybert, C. Cottin-Bizonne, and M. Leocmach, Active glass: Ergodicity breaking dramatically affects response to self-propulsion, Phys. Rev. Lett. 123, 248004 (2019).
  76. S. Henkes, K. Kostanjevec, J. M. Collinson, R. Sknepnek, and E. Bertin, Dense active matter model of motion patterns in confluent cell monolayers, Nat. Commun. 11, 1405 (2020).
  77. B. Loewe, M. Chiang, D. Marenduzzo, and M. C. Marchetti, Solid-liquid transition of deformable and overlapping active particles, Phys. Rev. Lett. 125, 038003 (2020).
  78. J. Yang, R. Ni, and M. P. Ciamarra, Interplay between jamming and motility-induced phase separation in persistent self-propelling particles, Phys. Rev. E 106, L012601 (2022).
  79. Y.-E. Keta, R. L. Jack, and L. Berthier, Disordered collective motion in dense assemblies of persistent particles, Phys. Rev. Lett. 129, 048002 (2022).
  80. S. K. Nandi, R. Mandal, P. J. Bhuyan, C. Dasgupta, M. Rao, and N. S. Gov, A random first-order transition theory for an active glass, Proc. Natl. Acad. Sci. USA 115, 7688 (2018).
  81. L. M. C. Janssen, Active glasses, J. Phys.: Condens. Matter 31, 503002 (2019).
  82. R. Mandal and P. Sollich, Multiple types of aging in active glasses, Phys. Rev. Lett. 125, 218001 (2020).
  83. R. Mandal and P. Sollich, How to study a persistent active glassy system, J. Phys.: Condens. Matter 33, 184001 (2021).
  84. G. Janzen and L. M. C. Janssen, Aging in thermal active glasses, Phys. Rev. Res. 4, L012038 (2022).
  85. E. Agoritsas, T. Maimbourg, and F. Zamponi, Out-of-equilibrium dynamical equations of infinite-dimensional particle systems I. The isotropic case, J. Phys. A: Math. Theor. 52, 144002 (2019).
  86. E. Agoritsas, T. Maimbourg, and F. Zamponi, Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain, J. Phys. A: Math. Theor. 52, 334001 (2019).
  87. E. Agoritsas, Mean-field dynamics of infinite-dimensional particle systems: global shear versus random local forcing, J. Stat. Mech.: Theory Exp. (2021) 033501.
  88. R. Mo, Q. Liao, and N. Xu, Rheological similarities between dense self-propelled and sheared particulate systems, Soft Matter 16, 3642 (2020).
  89. P. K. Morse, S. Roy, E. Agoritsas, E. Stanifer, E. I. Corwin, and M. L. Manning, A direct link between active matter and sheared granular systems, Proc. Natl. Acad. Sci. USA 118, e2019909118 (2021).
  90. L. Berthier and J.-L. Barrat, Nonequilibrium dynamics and fluctuation-dissipation relation in a sheared fluid, J. Chem. Phys. 116, 6228 (2002).
  91. H. A. Makse and J. Kurchan, Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment, Nature (London) 415, 614 (2002).
  92. N. Xu and C. S. O'Hern, Effective temperature in athermal systems sheared at fixed normal load, Phys. Rev. Lett. 94, 055701 (2005).
  93. G. Parisi and F. Zamponi, Mean-field theory of hard sphere glasses and jamming, Rev. Mod. Phys. 82, 789 (2010).
  94. F. Krzakala and J. Kurchan, Landscape analysis of constraint satisfaction problems, Phys. Rev. E 76, 021122 (2007).
  95. H. Jacquin, L. Berthier, and F. Zamponi, Microscopic mean-field theory of the jamming transition, Phys. Rev. Lett. 106, 135702 (2011).
  96. A. Ikeda, L. Berthier, and P. Sollich, Disentangling glass and jamming physics in the rheology of soft materials, Soft Matter 9, 7669 (2013).
  97. R. Mandal, P. J. Bhuyan, P. Chaudhuri, C. Dasgupta, and M. Rao, Extreme active matter at high densities, Nat. Commun. 11, 2581 (2020).
  98. W. G. Ellenbroek, E. Somfai, M. van Hecke, and W. van Saarloos, Critical scaling in linear response of frictionless granular packings near jamming, Phys. Rev. Lett. 97, 258001 (2006).
  99. M. Wyart, Marginal stability constrains force and pair distributions at random close packing, Phys. Rev. Lett. 109, 125502 (2012).
  100. E. Lerner, G. Düring, and M. Wyart, Low-energy non-linear excitations in sphere packings, Soft Matter 9, 8252 (2013).
  101. G. Parisi, P. Urbani, and F. Zamponi, Theory of Simple Glasses: Exact Solutions in Infinite Dimensions (Cambridge University Press, Cambridge, UK, 2020).
  102. V. Babu and S. Sastry, Criticality and marginal stability of the shear jamming transition of frictionless soft spheres, Phys. Rev. E 105, L042901 (2022).
  103. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022018 for further numerical details including a confirmation of the scaling behavior between pressure and excess coordination, numerically measured gap distributions for static packings, a discussion of the system size effect on the critical temperature and dynamical signatures of unjamming.
  104. P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Fractal free energy landscapes in structural glasses, Nat. Commun. 5, 3725 (2014).
  105. P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Exact theory of dense amorphous hard spheres in high dimension. III. The full replica symmetry breaking solution, J. Stat. Mech.: Theory Exp. (2014) P10009.

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Phys. Rev. Research 6, L022018– Published 22 April, 2024
  • Received 16 September 2023
  • Accepted 12 March 2024
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