Nonlinear dynamics, bifurcations and collective motion of active filaments
File(s)
Author(s)
Clarke, Bethany
Type
Thesis
Abstract
This thesis investigates the nonlinear dynamics of active filaments submerged in viscous fluids through a combination of initial-value-problem studies and bifurcation analysis. The central focus of this work is the follower force model, in which filament deformation is driven through compressive forces which act along the tangent of the filament centreline. This model provides a powerful framework for understanding biologically relevant systems, such as molecular motor-driven biopolymer filaments and the beating of cilia and flagella.
We begin by examining the behaviour of a single filament, systematically exploring the parameter space of several variants of the follower force model, starting with its simplest formulation. Numerical simulations, complemented with computational dynamical systems techniques, are used to identify new dynamical behaviours and map the bifurcations in the state space. Following studies investigate the influence of the domain, the forcing distribution, and the mechanical properties of the filament, uncovering new solution types and highlighting the differences between modelling approaches.
Building on these results, we extend the study to filament ensembles to examine the stability of coordinated states. We observe multistability between metachronal wave solutions of different wavelengths in arrays of asymmetrically beating filaments, suggesting that while hydrodynamic interactions can facilitate these patterns, additional regulatory mechanisms are required in biological systems to select the desired wavelength solution. Overall, this work provides new insights into the mechanical principles underlying both individual and collective filament dynamics, revealing the rich nonlinear behaviours that emerge from simple forcing mechanisms.
We begin by examining the behaviour of a single filament, systematically exploring the parameter space of several variants of the follower force model, starting with its simplest formulation. Numerical simulations, complemented with computational dynamical systems techniques, are used to identify new dynamical behaviours and map the bifurcations in the state space. Following studies investigate the influence of the domain, the forcing distribution, and the mechanical properties of the filament, uncovering new solution types and highlighting the differences between modelling approaches.
Building on these results, we extend the study to filament ensembles to examine the stability of coordinated states. We observe multistability between metachronal wave solutions of different wavelengths in arrays of asymmetrically beating filaments, suggesting that while hydrodynamic interactions can facilitate these patterns, additional regulatory mechanisms are required in biological systems to select the desired wavelength solution. Overall, this work provides new insights into the mechanical principles underlying both individual and collective filament dynamics, revealing the rich nonlinear behaviours that emerge from simple forcing mechanisms.
Version
Open Access
Date Issued
2025-09-09
Date Awarded
01/12/2025
License URL
Advisor
Keaveny, Eric
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
EP/W523872/1
Publisher Department
Department of Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)