A Hamiltonian Formulation of Membrane Dynamics under Axial Symmetry

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Presentation transcript:

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

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