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Pattern formation on the free surface of a ferrofluid: spatial dynamics and homoclinic bifurcation

Groves, MD, Lloyd, David and Stylianou, A (2017) Pattern formation on the free surface of a ferrofluid: spatial dynamics and homoclinic bifurcation Physica D: Nonlinear Phenomena, 350. pp. 1-12.

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Abstract

We establish the existence of spatially localised one-dimensional free surfaces of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisation law. It is shown that the ferrohydrostatic equations can be derived from a variational principle that allows one to formulate them as an (infinite-dimensional) spatial Hamiltonian system in which the unbounded free-surface direction plays the role of time. A centremanifold reduction technique converts the problem for small solutions near onset to an equivalent Hamiltonian system with finitely many degrees of freedom. Normal-form theory yields the existence of homoclinic solutions to the reduced system, which correspond to spatially localised solutions of the ferrohydrostatic equations.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Groves, MDUNSPECIFIEDUNSPECIFIED
Lloyd, DavidD.J.Lloyd@surrey.ac.ukUNSPECIFIED
Stylianou, AUNSPECIFIEDUNSPECIFIED
Date : 23 March 2017
Identification Number : 10.1016/j.physd.2017.03.004
Copyright Disclaimer : © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 14 Mar 2017 15:42
Last Modified : 05 Jul 2017 11:25
URI: http://epubs.surrey.ac.uk/id/eprint/813770

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