Deformable Elastic Surface

Helfrich membrane energy: F = ∫[κ(2H)² + σ] dA — bending rigidity κ and surface tension σ

Parameters

1.00
0.50
0.30
0.10

Energy

0
Bending κ
0
Tension σ
0
Pressure
0
Total F

Interaction

Click and drag on the surface to apply a local force. The membrane responds according to Helfrich elasticity.

Physics

F = κ∫(2H)² dA
+ σ∫ dA
+ P∫ dV

H = mean curvature
κ ~ 10-30 kT (lipid bilayer)
Undulation modes:
⟨|h_q|²⟩ = kT/(κq⁴+σq²)