Figure 1: Visual representation of the mappings.
From: Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting
The flow lines of the ordered phase of a 2D incompressible polar active fluid, the magnetization lines of the ordered phase of divergence-free 2D XY magnets, dislocation-free 2D smectic layers and the surfaces of a growing one-dimensional crystal (which can be obtained by taking equal-time-interval snap shots) undulate in exactly the same way over space; their fluctuations share exactly the same asymptotic scaling behaviour at large-length scales. Note that the vertical axis is time for KPZ surface growth and the y Cartesian coordinate for the other three systems.
