periodic patch API demo: synchronized coarse_steps=8, fine_steps=16
leaf mass: initial=256.000002444 final=256.000005753 drift=+3.308989e-06
leaf rho: [0.999951661, 1.00004828]
leaf ux: [-0.000877841114, 0.000877885922]
leaf uy: [-1.7034624e-05, 1.70215859e-05]
covered coarse / fine halo: NaN; functional demonstration only