Crystal Surface Roughening — KPZ Growth

Simulate crystal surface growth via the Kardar-Parisi-Zhang (KPZ) equation. Watch the roughening transition and measure the interface width W ~ t^β.

Growth Model

Controls

Time t0
Width W(t)0.00
β (exponent)
Mean height0.0
KPZ Equation:
∂h/∂t = ν∇²h + (λ/2)(∇h)² + η(x,t)

Scaling exponents:
KPZ (1D): β=1/3, α=1/2, z=3/2
EW (1D): β=1/4, α=1/2, z=2
Random: β=1/2 (no correlations)

W(t) ~ t^β until saturation W_sat ~ L^α