Recent simulations [1,2] of binary fluid convection with a
negative separation ratio reveal the presence of multiple numerically
stable spatially localized steady states we have called 'convectons'.
These states consist of a finite number of convection rolls embedded
in a nonconvecting background and are present at supercritical Rayleigh
numbers. The convecton length decreases with decreasing Rayleigh number;
below a critical Rayleigh number the convectons are replaced by
relaxation oscillations in which the steady state is gradually eroded
until no rolls are present (the slow phase), whereupon a new steady state
regrows from small amplitude (the fast phase) and the process repeats.
Both He3-He4 mixtures [1] and water-ethanol mixtures [2] exhibit
this remarkable behavior. Stability requires that the convectons are
present in the regime where the conduction state is convectively unstable
but absolutely stable. The multiplicity of stable convectons can be attributed
to the presence of a 'pinning' region in parameter space, or equivalently
to a process called homoclinic snaking [3]. In the pinning region the
fronts bounding the convecton are pinned to the underlying roll structure;
outside it the fronts depin and allow the convecton to grow at the
expense of the small amplitude state (large Rayleigh numbers) or shrink
back to the small amplitude state (low Rayleigh numbers). The convectons
may exist beyond the onset of absolute instability but the background
state is then filled with small amplitude traveling waves. A theoretical
understanding of these results will be developed.

[1] O. Batiste and E. Knobloch. Simulations of localized states of
stationary convection in He3-He4 mixtures. Phys. Rev. Lett. 95, 244501 (2005).
[2] O. Batiste, E. Knobloch, A. Alonso, I. Mercader. Spatially localized
binary fluid convection. J. Fluid Mech. 560, 149 (2006).
[3] J. Burke and E. Knobloch. Localized states in the generalized
Swift-Hohenberg equation. Phys. Rev. E 73, 056211 (2006)