Physics
Phase field φ: 1 (solid) / -1 (liquid)
T: dimensionless temperature
The surface energy anisotropy ε_a selects the growth direction: 4-fold symmetry → dendrites grow along [100] axes (like snowflakes).
Higher undercooling Δ → faster growth but more unstable tips.
Higher anisotropy → sharper, more crystalline arms.
This is the Kobayashi (1993) phase field model for dendritic solidification — the standard reference for understanding snow crystal formation.