We consider a single spike of ferrofluid, arising in a small cylindrical
container, when a vertically oriented magnetic field is applied. The height of
the spike as well as the surface topography is measured experimentally by two
different technologies and calculated numerically using the finite element
method. As a consequence of the finite size of the container, the numerics
uncovers an imperfect bifurcation to a single spike solution, which is forward.
This is in contrast to the standard transcritical bifurcation to hexagons,
common for rotational symmetric systems with broken up-down symmetry. The
numerical findings are corroborated in the experiments. The small hysteresis
observed is explained in terms of a hysteretic wetting of the side wall.Comment: accepted to New Journal of Physic
