Controlling the collective dynamics in systems of active oscillators through geometry and hydrodynamic entrainment
type: CreativeWork
description: Synchronisation is broadly defined as the coordinated action of two or more individual elements that exhibit some time periodic behaviour. It is widely observed across different systems, where it is often a help or hindrance. Here the focus is on synchronisation facilitated by hydrodynamic coupling, with the viscous forces dominating. This style of coupling is spatially dependent, and so the steady state dynamics of the oscillators can be controlled using their positions. I study 'rower' oscillators, a highly simplified model for motile cilia that approximates each cilium by a rigid sphere that is driven by a geometrically updated force. The simplicity of the model lends itself to generic results that could be observed in many systems with hydrodynamic coupling. This thesis is broken into two main parts. The first focuses on developing an analytical framework to further understand the synchronisation between two oscillators coupled through hydrodynamic forces. To achieve this a phase reduction is applied to the geometric oscillators. To apply a phase reduction first the transformation the natural phase is determined; the natural phase is characterised by constant phase velocity and involves a moving reference frame. Following the transformation, the interaction is subjected to an averaging process. The result is a continuous interaction function characterised by the phase difference of two oscillators. This dramatically simplifies the system and allows standard dynamical system techniques to be applied. The new interaction is verified through a comparison of relaxation time, before it is used to predict the steady state through the examination of fixed points. This framework is then used to demonstrate the ability to entrain a rower is not sensitive to changes in the characteristics of the rower motion, while the synchronisation between rowers is susceptible. Estimates of the relative synchronisation strength vis-a-vis the entrainment were calculated for two single …
abstract: Synchronisation is broadly defined as the coordinated action of two or more individual elements that exhibit some time periodic behaviour. It is widely observed across different systems, where it is often a help or hindrance. Here the focus is on synchronisation facilitated by hydrodynamic coupling, with the viscous forces dominating. This style of coupling is spatially dependent, and so the steady state dynamics of the oscillators can be controlled using their positions. I study 'rower' oscillators, a highly simplified model for motile cilia that approximates each cilium by a rigid sphere that is driven by a geometrically updated force. The simplicity of the model lends itself to generic results that could be observed in many systems with hydrodynamic coupling. This thesis is broken into two main parts. The first focuses on developing an analytical framework to further understand the synchronisation between two oscillators coupled through hydrodynamic forces. To achieve this a phase reduction is applied to the geometric oscillators. To apply a phase reduction first the transformation the natural phase is determined; the natural phase is characterised by constant phase velocity and involves a moving reference frame. Following the transformation, the interaction is subjected to an averaging process. The result is a continuous interaction function characterised by the phase difference of two oscillators. This dramatically simplifies the system and allows standard dynamical system techniques to be applied. The new interaction is verified through a comparison of relaxation time, before it is used to predict the steady state through the examination of fixed points. This framework is then used to demonstrate the ability to entrain a rower is not sensitive to changes in the characteristics of the rower motion, while the synchronisation between rowers is susceptible. Estimates of the relative synchronisation strength vis-a-vis the entrainment were calculated for two single …
author: Hamilton, Evelyn Alexandra Waterhouse
language: en
keywords: rower model, hydrodynamic forces, synchronisation, cilia
license: https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/e58f89ab-b4e8-4b5b-9e28-c901cf592501/download
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
date published: 2019-07-19
date modified: 2026-07-22T22:24:14Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.46269