scholarly journals Observing the Rosensweig instability of a quantum ferrofluid

Nature ◽  
2016 ◽  
Vol 530 (7589) ◽  
pp. 194-197 ◽  
Author(s):  
Holger Kadau ◽  
Matthias Schmitt ◽  
Matthias Wenzel ◽  
Clarissa Wink ◽  
Thomas Maier ◽  
...  
Keyword(s):  
Rosensweig Instability

scholarly journals Linear and nonlinear approach to the Rosensweig instability

2007 ◽  
Vol 30 (1) ◽  
pp. 171-184 ◽  
Author(s):  
Adrian Lange ◽  
Reinhard Richter ◽  
Lutz Tobiska
Keyword(s):  
Nonlinear Approach ◽  
Rosensweig Instability ◽  
Linear And Nonlinear

scholarly journals Small-amplitude static periodic patterns at a fluid–ferrofluid interface

2018 ◽  
Vol 474 (2216) ◽  
pp. 20180038
Author(s):  
M. D. Groves ◽  
J. Horn
Keyword(s):  
Small Amplitude ◽  
Bifurcation Theory ◽  
Elliptic Boundary ◽  
Local Bifurcation ◽  
Periodic Patterns ◽  
Elliptic Boundary Value ◽  
Nonlinear Elliptic ◽  
Nonlinear Elliptic Boundary ◽  
Rosensweig Instability ◽  
Nonlinear Magnetization

We establish the existence of static doubly periodic patterns (in particular rolls, squares and hexagons) on the free surface of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetization law. A novel formulation of the ferrohydrostatic equations in terms of Dirichlet–Neumann operators for nonlinear elliptic boundary-value problems is presented. We demonstrate the analyticity of these operators in suitable function spaces and solve the ferrohydrostatic problem using an analytic version of Crandall–Rabinowitz local bifurcation theory. Criteria are derived for the bifurcations to be sub-, super- or transcritical with respect to a dimensionless physical parameter.

Non-linear analysis of the Rosensweig instability

2003 ◽  
Vol 63 (6) ◽  
pp. 826-832 ◽  
Author(s):  
R Friedrichs ◽  
A Engel
Keyword(s):  
Linear Analysis ◽  
Non Linear ◽  
Rosensweig Instability

scholarly journals Homoclinic snaking near the surface instability of a polarisable fluid

2015 ◽  
Vol 783 ◽  
pp. 283-305 ◽  
Author(s):  
David J. B. Lloyd ◽  
Christian Gollwitzer ◽  
Ingo Rehberg ◽  
Reinhard Richter
Keyword(s):  
Magnetic Field ◽  
Specific Area ◽  
Energy Functional ◽  
Numerical Continuation ◽  
Strength Parameter ◽  
Physical Systems ◽  
Rosensweig Instability ◽  
Homoclinic Snaking ◽  
Maxwell Points ◽  
Unstable Branch

We report on localised patches of cellular hexagons observed on the surface of a magnetic fluid in a vertical magnetic field. These patches are spontaneously generated by jumping into the neighbourhood of the unstable branch of the domain-covering hexagons of the Rosensweig instability upon which the patches equilibrate and stabilise. They are found to coexist in intervals of the applied magnetic field strength parameter around this branch. We formulate a general energy functional for the system and a corresponding Hamiltonian that provide a pattern selection principle allowing us to compute Maxwell points (where the energy of a single hexagon cell lies in the same Hamiltonian level set as the flat state) for general magnetic permeabilities. Using numerical continuation techniques, we investigate the existence of localised hexagons in the Young–Laplace equation coupled to the Maxwell equations. We find that cellular hexagons possess a Maxwell point, providing an energetic explanation for the multitude of measured hexagon patches. Furthermore, it is found that planar hexagon fronts and hexagon patches undergo homoclinic snaking, corroborating the experimentally detected intervals. Besides making a contribution to the specific area of ferrofluids, our work paves the ground for a deeper understanding of homoclinic snaking of two-dimensional localised patches of cellular patterns in many physical systems.

Pattern formation in ferrogels: analysis of the Rosensweig instability using the energy method

2006 ◽  
Vol 18 (38) ◽  
pp. S2671-S2684 ◽  
Author(s):  
Stefan Bohlius ◽  
Harald Pleiner ◽  
Helmut R Brand
Keyword(s):  
Pattern Formation ◽  
Energy Method ◽  
Rosensweig Instability
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