Elastic Interface Depinning

An elastic line driven through a disordered medium. Below the depinning threshold F_c the interface is pinned. Above F_c it moves with velocity v ~ (F−F_c)^β — a non-equilibrium critical transition.

Interface (blue line) in disorder landscape (yellow = strong pinning)

Velocity v vs driving force F (depinning curve)

Parameters

Driving force F: 0.50 Elasticity c: 1.0 Disorder strength σ: 0.8 System size N: 100

v = 0
Pinned

Equation of motion:
∂_t h = c∇²h + F + η(x,h)

Depinning exponent β≈0.625 (1D)
Roughness ζ≈1.25 (1D)

Applications: domain walls, crack fronts, contact lines, vortex lattices