Murray, J. D. Mathematical Biology: I. An Introduction (Springer, 2007).
Budrene, E. O. & Berg, H. C. Complex patterns formed by motile cells of Escherichia coli. Nature 349, 630–633 (1991).
Kessler, D. A. & Levine, H. Pattern formation in Dictyostelium via the dynamics of cooperative biological entities. Phys. Rev. E 48, 4801 (1993).
Liu, C. et al. Sequential establishment of stripe patterns in an expanding cell population. Science 334, 238–241 (2011).
Riedel, I. H., Kruse, K. & Howard, J. A self-organized vortex array of hydrodynamically entrained sperm cells. Science 309, 300–303 (2005).
Petroff, A. P., Wu, X.-L. & Libchaber, A. Fast-moving bacteria self-organize into active two-dimensional crystals of rotating cells. Phys. Rev. Lett. 114, 158102 (2015).
Mongera, A. et al. A fluid-to-solid jamming transition underlies vertebrate body axis elongation. Nature 561, 401–405 (2018).
Qin, B. et al. Cell position fates and collective fountain flow in bacterial biofilms revealed by light-sheet microscopy. Science 369, 71–77 (2020).
Parry, B. R. et al. The bacterial cytoplasm has glass-like properties and is fluidized by metabolic activity. Cell 156, 183–194 (2014).
Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).
Angelini, T. E. et al. Glass-like dynamics of collective cell migration. Proc. Natl Acad. Sci. USA 108, 4714–4719 (2011).
Delarue, M. et al. Self-driven jamming in growing microbial populations. Nat. Phys. 12, 762–766 (2016).
Geyer, D., Martin, D., Tailleur, J. & Bartolo, D. Freezing a flock: motility-induced phase separation in polar active liquids. Phys. Rev. 9, 031043 (2019).
Henkes, S., Fily, Y. & Marchetti, M. C. Active jamming: self-propelled soft particles at high density. Phys. Rev. E 84, 040301 (2011).
Bi, D., Lopez, J. H., Schwarz, J. M. & Manning, M. L. A density-independent rigidity transition in biological tissues. Nat. Phys. 11, 1074–1079 (2015).
Mandal, R., Bhuyan, P. J., Chaudhuri, P., Dasgupta, C. & Rao, M. Extreme active matter at high densities. Nat. Commun. 11, 2581 (2020).
James, M., Suchla, D. A., Dunkel, J. & Wilczek, M. Emergence and melting of active vortex crystals. Nat. Commun. 12, 5630 (2021).
Wensink, H. H. et al. Meso-scale turbulence in living fluids. Proc. Natl Acad. Sci. USA 109, 14308–14313 (2012).
Dunkel, J., Heidenreich, S., Bär, M. & Goldstein, R. E. Minimal continuum theories of structure formation in dense active fluids. New J. Phys. 15, 045016 (2013).
Reinken, H., Heidenreich, S., Bär, M. & Klapp, S. H. L. Anisotropic mesoscale turbulence and pattern formation in microswimmer suspensions induced by orienting external fields. New J. Phys. 21, 013037 (2019).
Doostmohammadi, A., Adamer, M. F., Thampi, S. P. & Yeomans, J. M. Stabilization of active matter by flow-vortex lattices and defect ordering. Nat. Commun. 7, 10557 (2016).
Aranson, I. Bacterial active matter. Rep. Prog. Phys. 85, 076601 (2022).
Zahn, K., Maret, G., Ruß, C. & von Grünberg, H. H. Three-particle correlations in simple liquids. Phys. Rev. Lett. 91, 115502 (2003).
Wioland, H., Woodhouse, F. G., Dunkel, J., Kessler, J. O. & Goldstein, R. E. Confinement stabilizes a bacterial suspension into a spiral vortex. Phys. Rev. Lett. 110, 268102 (2013).
Nishiguchi, D., Aranson, I. S., Snezhko, A. & Sokolov, A. Engineering bacterial vortex lattice via direct laser lithography. Nat. Commun. 9, 4486 (2018).
Liu, S., Shankar, S., Marchetti, M. C. & Wu, Y. Viscoelastic control of spatiotemporal order in bacterial active matter. Nature 590, 80–84 (2021).
Xu, H., Huang, Y., Zhang, R. & Wu, Y. Autonomous waves and global motion modes in living active solids. Nat. Phys. 19, 46–51 (2023).
Ramaswamy, S. The mechanics and statistics of active matter. Annu. Rev. Condens. Matter Phys. 1, 323–345 (2010).
Oza, A. U., Heidenreich, S. & Dunkel, J. Generalized Swift-Hohenberg models for dense active suspensions. Eur. Phys. J. E 39, 97 (2016).
Cisneros, L. H., Cortez, R., Dombrowski, C., Goldstein, R. E. & Kessler, J. O. Fluid dynamics of self-propelled microorganisms, from individuals to concentrated populations. Exp. Fluids 43, 737–753 (2007).
Cisneros, L. H., Kessler, J. O., Ganguly, S. & Goldstein, R. E. Dynamics of swimming bacteria: transition to directional order at high concentration. Phys. Rev. E 83, 061907 (2011).
Sokolov, A. & Aranson, I. S. Reduction of viscosity in suspension of swimming bacteria. Phys. Rev. Lett. 103, 148101 (2009).
López, H. M., Gachelin, J., Douarche, C., Auradou, H. & Clément, E. Turning bacteria suspensions into superfluids. Phys. Rev. Lett. 115, 028301 (2015).
Martinez, V. A. et al. A combined rheometry and imaging study of viscosity reduction in bacterial suspensions. Proc. Natl Acad. Sci. USA 117, 2326–2331 (2020).
Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I. & Shochet, O. Novel type phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995).
Toner, J., Tu, Y. & Ramaswamy, S. Hydrodynamics and phases of flocks. Ann. Phys. 318, 170–244 (2005).
Dunkel, J. et al. Fluid dynamics of bacterial turbulence. Phys. Rev. Lett. 110, 228102 (2013).
Heidenreich, S., Dunkel, J., Klapp, S. H. & Bär, M. Hydrodynamic length-scale selection in microswimmer suspensions. Phys. Rev. E 94, 020601 (2016).
Sumino, Y. et al. Large-scale vortex lattice emerging from collectively moving microtubules. Nature 483, 448–452 (2012).
Nakane, D., Odaka, S., Suzuki, K. & Nishizaka, T. Large-scale vortices with dynamic rotation emerged from monolayer collective motion of gliding Flavobacteria. J. Bacteriol. 203, e0007321 (2021).
Patra, P. et al. Collective migration reveals mechanical flexibility of malaria parasites. Nat. Phys. 18, 586–594 (2022).
Supekar, R. et al. Learning hydrodynamic equations for active matter from particle simulations and experiments. Proc. Natl Acad. Sci. USA 120, e2206994120 (2023).
James, M., Bos, W. J. & Wilczek, M. Turbulence and turbulent pattern formation in a minimal model for active fluids. Phys. Rev. Fluids 3, 061101 (2018).
Yan, J. et al. Reconfiguring active particles by electrostatic imbalance. Nat. Mater. 15, 1095 (2016).
Jacobson, A. G. Somitomeres: mesodermal segments of vertebrate embryos. Development 104, 209–220 (1988).
Voiculescu, O., Bertocchini, F., Wolpert, L., Keller, R. E. & Stern, C. D. The amniote primitive streak is defined by epithelial cell intercalation before gastrulation. Nature 449, 1049–1052 (2007).
Słomka, J. & Dunkel, J. Geometry-dependent viscosity reduction in sheared active fluids. Phys. Rev. Fluids 2, 043102 (2017).
Mukherjee, A., Walker, J., Weyant, K. B. & Schroeder, C. M. Characterization of flavin-based fluorescent proteins: an emerging class of fluorescent reporters. PLoS ONE 8, e64753 (2013).
Zuo, W. & Wu, Y. Dynamic motility selection drives population segregation in a bacterial swarm. Proc. Natl Acad. Sci. USA 117, 4693–4700 (2020).
Chen, C., Liu, S., Shi, X. Q., Chate, H. & Wu, Y. Weak synchronization and large-scale collective oscillation in dense bacterial suspensions. Nature 542, 210–214 (2017).
Lauga, E., DiLuzio, W. R., Whitesides, G. M. & Stone, H. A. Swimming in circles: motion of bacteria near solid boundaries. Biophys. J. 90, 400–412 (2006).
Swift, J. & Hohenberg, P. C. Hydrodynamic fluctuations at the convective instability. Phys. Rev. A 15, 319–328 (1977).
Banerjee, D., Souslov, A., Abanov, A. G. & Vitelli, V. Odd viscosity in chiral active fluids. Nat. Commun. 8, 1573 (2017).
Danaila, I., Joly, P., Kaber, S. M. Postel, M. (eds) An Introduction to Scientific Computing: Twelve Computational Projects Solved with MATLAB (Springer, 2007).