TOPOLOGICAL CORRELATIONS IN BENARD-MARANGONI CONVECTIVE STRUCTURES

Bernard-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 p atterns (neighbor switching process, cell disappearance or creation, a nd cellular division) and the typical defects [pentagon-heptagon pair, ''flower'' (a cluster of more than three polygons incident on the sam e vertex), etc.]. Usual topological laws (Lewis's, Aboav-Weaire's, Pes hkin's, and Lemaitre's laws) are satisfied. For Von Neumann's law, a m odification which takes into account a physical effect specific to the dynamics of Benard-Marangoni structures (selection of average cell si ze in steady regime) has been introduced. We also compare topological correlations in Bernard-Marangoni structures with those derived from b iological 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.