A symplectic integration method for elastic filaments

摘要

A new method is proposed for integrating the equations of motion of an elastic filament. In thestandard finite-difference and finite-element formulations the continuum equations of motion arediscretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of theexact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integralover the contour of the filament. This discrete representation of the continuum filament can then beintegrated by one of the explicit symplectic integrators frequently used in molecular dynamics. Themodel systematically approximates the continuum partial differential equations, but has the samelevel of computational complexity as molecular dynamics and is constraint-free. Numerical testsshow that the algorithm is much more stable than a finite-difference formulation and can be used forhigh aspect ratio filaments, such as actin.