A Hamiltonian Formulation of Membrane Dynamics under Axial Symmetry
Biological Membranes Biological membranes are important in many cellular processes such as endocytosis and protein diffusion. We seek to model the dynamic properties of membranes. We use a surface model since membrane thickness is small compared to lateral length scales.
Geometric Model
Membrane Parameterization
Surface Constraint
Membrane Free Energy
Variational Problem
Hamilton-Jacobi Formalism
Euler-lagrange Equations
Lagrangian Dynamic Formulation
Membrane Shape Equation Under Dynamic Equilibrium