P. Cerisier et al., TOPOLOGICAL CORRELATIONS IN BENARD-MARANGONI CONVECTIVE STRUCTURES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(5), 1996, pp. 5086-5094
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.