Abstract
Convection due to two competing or cooperating mechanisms, displays a fascinating variety of dynamical phenomena [1]. One of the physical mechanisms is usually a thermal gradient, and the other may be as diverse as a concentration, rotation, or magnetic field gradient. The transition from a conductive to a convective state is via either a steady or a Hopf bifurcation; the point separating the two was one of the first codimension-two points explored [2] The bifurcation may be super or sub-critical, and the convection amplitude may undergo a transition from weak to strong. We show [3] that all of these features can be explained as manifestations of the behavior of the eigenvalues of generic 2 × 2 matrix near the point where the eigenvalues intersect.
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Tuckerman, L.S. (2004). Binary fluid convection as a 2 x 2 matrix problem. In: Descalzi, O., Martínez, J., Rica, S. (eds) Instabilities and Nonequilibrium Structures IX. Nonlinear Phenomena and Complex Systems, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0991-1_22
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DOI: https://doi.org/10.1007/978-94-007-0991-1_22
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