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The structure and dynamics of patterns of Benard convection cells

Benard-Marangoni convection, in containers with large aspect ratio, exhibits space-filling cellular structures, highly deformable, but crystallized. They contain dislocations and grain boundaries generated and moved by elementary topological transformations, and are subjected to a weak shear stress due to the earth's rotation. The cellular structure and its fluctuations are analysed from a crystallographic viewpoint, by using two complementary approaches. One is a global analysis of cellular structures in cylindrical symmetry. Their structural stability and defect pattern are obtained as topological mode-locking of a continuous structural parameter. The other, a local, molecular dynamics of the cells, gives a realistic parametrization of the forces and the transformations by generalizing the Voronoi cell construction in one extra dimension.