Pattern selection in ferrofluids
type: Item
instance of: scholarly article
title: Pattern selection in ferrofluids
zbMATH Open document ID: 0639.76055
DOI: 10.1016/0167-2789(88)90099-1
author: M. Silber
author: Edgar Knobloch
published in: Physica D
publication date: 1988-01-01T00:00:00Z
review text: Pattern formation by surface instabilities in a ferrofluid is studied as a function of an applied vertical magnetic field H. The effects of sidewalls are neglected. The problem is formulated as a bifurcation problemon an appropriately chosen doubly-periodic lattice. Normal forms for both square and hexagonal lattices are given and the necessary coefficients computed from the partial differential equations. On the square lattice solutions in the form of parallel ridges are never stable near onset. For a relative magnetic permeability \(\mu <1.4\) stable squares are formed. On the hexagonal lattice a finite amplitude instability produces hexagons. Analysis of a degenerate bifurcation predicts a hysteretic transition to ridges with increasing H.
Mathematics Subject Classification ID: 76E25
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 4043461
zbMATH Keywords: Pattern formation
zbMATH Keywords: surface instabilities
zbMATH Keywords: ferrofluid
zbMATH Keywords: vertical magnetic field
zbMATH Keywords: bifurcation problem
zbMATH Keywords: doubly-periodic lattice
zbMATH Keywords: hexagonal lattices
zbMATH Keywords: square lattice solutions
MaRDI profile type: Publication
full work available at URL: 0167-2789(88)90099-1
OpenAlex ID: W1998205507
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description: scientific article; zbMATH DE number 4043461