Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the collective dynamics of active self-attracting particles. We identify a sequence of size-controlled transitions that generate characteristic slow modes, leading to exponential increase of patterning timescales. Experimental measurements of multicellular dynamics confirm our predictions.
Categories: nlin.PS cond-mat.soft nlin.AO physics.bio-ph q-bio.CB