Lagrangian Mechanics of Active Systems

TL;DR

This paper develops a multi-scale Lagrangian mechanics framework for modeling the hydrodynamics of shape-changing active systems like microswimmers, enabling efficient simulation and analysis of their dynamics.

Contribution

It extends Lagrangian mechanics to active surfaces and microswimmers by incorporating shape changes as generalized coordinates and pre-computed friction coefficients.

Findings

Predicted synchronization patterns of cilia in biological systems.

Provided a computational framework for fast dynamic simulations.

Validated the approach with experimentally measured cilia beat patterns.

Abstract

We present a multi-scale modeling and simulation framework for low-Reynolds number hydrodynamics of shape-changing immersed objects, e.g., biological microswimmers and active surfaces. The key idea is to consider principal shape changes as generalized coordinates, and define conjugate generalized hydrodynamic friction forces. Conveniently, the corresponding generalized friction coefficients can be pre-computed and subsequently re-used to solve dynamic equations of motion fast. This framework extends Lagrangian mechanics of dissipative systems to active surfaces and active microswimmers, whose shape dynamics is driven by internal forces. As an application case, we predict in-phase and anti-phase synchronization in pairs of cilia for an experimentally measured cilia beat pattern.