Sanchez, T. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).
Guillamat, P. Active nematic emulsions. Sci. Adv. 4, eaao1470 (2018).
Tan, A. J. Topological chaos in active nematics. Nat. Phys. 15, 1033–1039 (2019).
Kumar, N. Tunable structure and dynamics of active liquid crystals. Sci. Adv. 4, eaat7779 (2018).
Sokolov, A. Swimming bacteria power microscopic gears. Proc. Natl Acad. Sci. USA 107, 969–974 (2010).
Beta, C. From actin waves to mechanism and back: how theory aids biological understanding. eLife 12, e87181 (2023).
Marchetti, M. C. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).
Giomi, L. Geometry and topology of turbulence in active nematics. Phys. Rev. X 5, 031003 (2015).
Zhou, S. Living liquid crystals. Biophys. J. 106, 420a (2014).
Serra, M. Defect-mediated dynamics of coherent structures in active nematics. Nat. Phys. 19, 1355–1361 (2023).
Guillamat Bassedas, P., Ignés i Mullol, J. & Sagués i Mestre, F. Taming active turbulence with patterned soft interfaces. Nat. Commun. 8, 564 (2017).
Li, H. Data-driven quantitative modeling of bacterial active nematics. Proc. Natl Acad. Sci. USA 116, 777–785 (2019).
Yashunsky, V. Topological defects in multi-layered swarming bacteria. Soft Matter 20, 4237–4245 (2024).
Shimaya, T. & Takeuchi, K. A. Tilt-induced polar order and topological defects in growing bacterial populations. PNAS Nexus 1, pgac269 (2022).
Copenhagen, K. Topological defects promote layer formation in Myxococcus xanthus colonies. Nat. Phys. 17, 211–215 (2021).
Genkin, M. M. Topological defects in a living nematic ensnare swimming bacteria. Phys. Rev. X 7, 011029 (2017).
Saw, T. B. Topological defects in epithelia govern cell death and extrusion. Nature 544, 212–216 (2017).
Balasubramaniam, L. Investigating the nature of active forces in tissues reveals how contractile cells can form extensile monolayers. Nat. Mater. 20, 1156–1166 (2021).
Blanch-Mercader, C. Turbulent dynamics of epithelial cell cultures. Phys. Rev. Lett. 120, 208101 (2018).
Be’er, A. & Ariel, G. A statistical physics view of swarming bacteria. Mov. Ecol. 7, 9 (2019).
Aranson, I. S. Bacterial active matter. Rep. Prog. Phys. 85, 076601 (2022).
Doostmohammadi, A. & Ladoux, B. Physics of liquid crystals in cell biology. Trends Cell Biol. 32, 140–150 (2022).
Duclos, G. Topological defects in confined populations of spindle-shaped cells. Nat. Phys. 13, 58–62 (2017).
Kawaguchi, K., Kageyama, R. & Sano, M. Topological defects control collective dynamics in neural progenitor cell cultures. Nature 545, 327–331 (2017).
Ienaga, R., Beppu, K. & Maeda, Y. T. Geometric confinement guides topological defect pairings and emergent flow in nematic cell populations. Soft Matter 19, 5016–5028 (2023).
Venkatesh, V., de Graaf Sousa, N. & Doostmohammadi, A. The interplay of polar and nematic order in active matter: implications for non-equilibrium physics and biology. J. Phys. A: Math. Theor. 58, 263001 (2025).
Shi, X. Q. & Chaté, H. Self-propelled rods: linking alignment-dominated and repulsion-dominated active matter. Preprint at https://arxiv.org/abs/1807.00294 (2018).
Großmann, R., Aranson, I. S. & Peruani, F. A particle-field approach bridges phase separation and collective motion in active matter. Nat. Commun. 11, 5365 (2020).
de Graaf Sousa, N. Self-propulsive active nematics. Philos. Trans. A 383, 20240272 (2025).
Han, E. Local polar order controls mechanical stress and triggers layer formation in Myxococcus xanthus colonies. Nat. Commun. 16, 952 (2025).
Huber, L. Emergence of coexisting ordered states in active matter systems. Science 361, 255–258 (2018).
Meacock, O. J. Bacteria solve the problem of crowding by moving slowly. Nat. Phys. 17, 205–210 (2021).
Maroudas-Sacks, Y. Topological defects in the nematic order of actin fibres as organization centres of hydra morphogenesis. Nat. Phys. 17, 251–259 (2021).
Amiri, A., Mueller, R. & Doostmohammadi, A. Unifying polar and nematic active matter: emergence and co-existence of half-integer and full-integer topological defects. J. Phys. A: Math. Theor. 55, 094002 (2022).
Lacroix, M. Emergence of bidirectional cell laning from collective contact guidance. Nat. Phys. 20, 1324–1331 (2024).
Vafa, F. & Doostmohammadi, A. Phase diagram, confining strings, and a new universality class in nematopolar matter. Europhys. Lett. 152, 57002 (2025).
Thampi, S. P., Golestanian, R. & Yeomans, J. M. Vorticity, defects and correlations in active turbulence. Philos. Trans. R. Soc. A 372, 20130366 (2014).
Shankar, S. Defect unbinding in active nematics. Phys. Rev. Lett. 121, 108002 (2018).
Patelli, A. Understanding dense active nematics from microscopic models. Phys. Rev. Lett. 123, 258001 (2019).
Bonn, L. Fluctuation-induced dynamics of nematic topological defects. Phys. Rev. E 106, 044706 (2022).
Pearce, D. Orientational correlations in active and passive nematic defects. Phys. Rev. Lett. 127, 197801 (2021).
Shankar, S. Topological active matter. Nat. Rev. Phys. 4, 380–398 (2022).
Pearce, D. J. & Kruse, K. Properties of twisted topological defects in 2D nematic liquid crystals. Soft Matter 17, 7408–7417 (2021).
Tang, X. & Selinger, J. V. Orientation of topological defects in 2D nematic liquid crystals. Soft Matter 13, 5481–5490 (2017).
Vromans, A. J. & Giomi, L. Orientational properties of nematic disclinations. Soft Matter 12, 6490–6495 (2016).
de la Cotte, A. Hidden order in active nematic defects. Proc. Natl Acad. Sci. USA 122, e2512147122 (2025).
Yashunsky, V. Chiral edge current in nematic cell monolayers. Phys. Rev. X 12, 041017 (2022).
Head, L. C. Spontaneous self-constraint in active nematic flows. Nat. Phys. 20, 492–500 (2024).
Martínez-Prat, B. Scaling regimes of active turbulence with external dissipation. Phys. Rev. X 11, 031065 (2021).
Giomi, L. Defect dynamics in active nematics. Philos. Trans. R. Soc. A 372, 20130365 (2014).
Hetrick, B. Small molecules CK-666 and CK-869 inhibit actin-related protein 2/3 complex by blocking an activating conformational change. Chem. Biol. 20, 701–712 (2013).
Lo Vecchio, S. Spontaneous rotations in epithelia as an interplay between cell polarity and boundaries. Nat. Phys. 20, 322–331 (2024).
Doostmohammadi, A. Stabilization of active matter by flow-vortex lattices and defect ordering. Nat. Commun. 7, 10557 (2016).
Vaidžiulytė, K. Persistent cell migration emerges from a coupling between protrusion dynamics and polarized trafficking. eLife 11, e69229 (2022).
Aditi Simha, R. & Ramaswamy, S. Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. Phys. Rev. Lett. 89, 058101 (2002).
Ardaševa, A. Beyond dipolar activity: quadrupolar stress drives collapse of nematic order on frictional substrates. Phys. Rev. Lett. 134, 088301 (2025).
Thampi, S. P., Golestanian, R. & Yeomans, J. M. Instabilities and topological defects in active nematics. Europhys. Lett. 105, 18001 (2014).
Seifert, U. Stochastic thermodynamics, fluctuation theorems and molecular machines. Rep. Prog. Phys. 75, 126001 (2012).
Fodor, É, Jack, R. L. & Cates, M. E. Irreversibility and biased ensembles in active matter: insights from stochastic thermodynamics. Annu. Rev. Condens. Matter Phys. 13, 215–238 (2022).
Ro, S. Model-free measurement of local entropy production and extractable work in active matter. Phys. Rev. Lett. 129, 220601 (2022).
Radhakrishnan, B. N., Serafin, F., Schmidt, T. L. & Fodor, É. Irreversibility in scalar active turbulence: the role of topological defects. New J. Phys. 28, 034601 (2026).
Farnebäck, G. Two-frame motion estimation based on polynomial expansion. In Proc. 13th Scandinavian Conference on Image Analysis 363–370 (Springer, 2003).
Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298–310 (1996).
Wang, Q., Kulkarni, S. R. & Verdú, S. Divergence estimation for multidimensional densities via k-nearest-neighbor distances. IEEE Trans. Inf. Theory 55, 2392–2405 (2009).
Beirlant, J. Nonparametric entropy estimation: an overview. Int. J. Math. Stat. Sci. 6, 17–39 (1997).