Active Matter

How do locally driven particles and chemical reactions generate motion, stresses and changing shapes? Covers active materials and physical models of them, including robotic swarms. Software organisms belong in Digital Life; robot control belongs in Embodiment.

Physical foundations and collective motion

  • Vicsek model - Constant-speed particles align locally under noise. Later work finds a discontinuous transition through dense traveling bands in a disordered gas. Fluctuations select this microphase separation, unlike bulk separation in the active Ising model. Vicsek et al. 1995, Grégoire and Chaté 2004, Solon et al. 2015.
    • Vicsek phase coexistence - Continuous-time simulations find several phase-separation regimes and split the coexistence region in two. Ordered liquid coexists steadily or intermittently with bands. Part of the ordered-liquid region is metastable. Duan et al. 2026, Duan et al. 2026.
  • Active-matter hydrodynamics - Reviews theories connecting local energy consumption to collective motion, stresses and instabilities. Distinguishes polar and nematic order and systems with or without momentum-conserving fluid coupling. Marchetti et al. 2013.
  • Colloidal flocks - Electrically driven microscopic rollers develop collective directed motion in confined racetracks. Experiments and interaction modeling connect hydrodynamic coupling to flocks at low density and a polar liquid at higher density. Bricard et al. 2013.
  • Active nematic tissue defects - In cultured epithelial sheets, defects in cell alignment concentrate compressive stress before cell death and extrusion. Patterned confinement moves the defects and extrusion hotspots, linking tissue geometry to cell removal. Saw et al. 2017.

Chemical motion and division

  • Self-propelled oil droplets - Hydrolysis of supplied precursor creates surfactant gradients and flow that sustain droplet movement. Experiments also show directional motion in chemical gradients, coupling chemical fuel to locomotion. Hanczyc et al. 2007; video.
  • Active droplets - Theory and simulations show that externally fueled chemical reactions can sustain droplets and destabilize their shape into division. Provides a compartment-growth mechanism without a lipid membrane. Zwicker et al. 2017.

Active membranes

  • Active membrane deformations - Motor-driven microtubule bundles inside lipid vesicles generate large, travelling membrane deformations. Experiments and simulations connect bundle forces to shape fluctuations; activity lasts about an hour with supplied ATP. Sciortino et al. 2025.

Open questions

  • Which mechanisms transfer between idealized particle models and driven physical or biological systems?
  • When do recurring structures acquire heritable variation, rather than only persist, move or split?