Nonlinear physics
Cahn–Hilliard equation
We now study the Cahn–Hilliard equation with an extra reaction term,
\[\pd{u}{t} = r\nabla^2 (u^3ug\nabla^2u)+uu^3,\]with periodic boundary conditions.

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The initial condition is taken to be random noise at the level of the discretised system, and the initial timescale, given by $r$, is small. Increase $r$ by one or two orders of magnitude to speed up the simulation, and observe the coarsening process as described in this 2001 article.