Topological correlations in Bénard-Marangoni convective structures

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Abstract
Bénard-Marangoni convection displays a two-dimensional (2D) hexagonal pattern. A topological analysis of these structures is presented. We describe the elementary topological transformations involved in such patterns (neighbor switching process, cell disappearance or creation, and cellular division) and the typical defects [pentagon-heptagon pair, ‘‘flower’’ (a cluster of more than three polygons incident on the same vertex), etc.]. Usual topological laws (Lewis’s, Aboav-Weaire’s, Peshkin’s, and Lemaître’s laws) are satisfied. For Von Neumann’s law, a modification which takes into account a physical effect specific to the dynamics of Bénard-Marangoni structures (selection of average cell size in steady regime) has been introduced. We also compare topological correlations in Bénard-Marangoni structures with those derived from biological tissues or simulated structures (2D hard disk tessellations, Ising mosaics, distributions of maximum entropy formalism, etc.). The agreement is fair for pentagons, hexagons, and heptagons. © 1996 The American Physical Society.