A symplectic integration method for elastic filaments

TL;DR

This paper introduces a novel symplectic integration method for elastic filaments that preserves Hamiltonian structure, offering improved stability and efficiency over traditional finite-difference approaches, especially for high aspect ratio filaments.

Contribution

It discretizes the Hamiltonian directly and applies explicit symplectic integrators, enabling stable, constraint-free simulations of elastic filaments with comparable complexity to molecular dynamics.

Findings

Method is more stable than finite-difference formulations.

Suitable for high aspect ratio filaments like actin.

Maintains Hamiltonian structure during integration.

Abstract

A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin.