Diffusion-driven autocatalytic dynamics on a sphere (opens in new tab)

We study the collective dynamics of independent particles that diffuse outside a spherical surface, on which they are replicated with a prescribed catalytic rate. In spatial dimensions three and higher, the transient nature of diffusion creates the competition between autocatalytic and escape events, thus leading to a rich phase diagram between subcritical (extinction), critical (steady-state), and supercritical (growth) regimes at long times. T...