Two-dimensional magnetic liquid froth: Coarsening and topological correlations

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 56, Issue 3, 1997, Pages 3310-3318

  Elias, Florence ^a   Flament, Cyrille ^a   Bacri, Jean Claude ^a   Cardoso, Olivier ^b   Graner, François ^c  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

^c UNIV GRENOBLE ALPES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000183057     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.3310     Document Type: Article

References (25)

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20. The mean value of the number of sides of the cells, (Formula presented) is in fact less than 6, because of the finite size of our experimental system (the Euler theorem is established for an infinite two-dimensional Euclidean space). (Formula presented) is generally about 5.95 at the beginning of the experiment, when the number of cells is maximum, and decreases toward 5.6 to 5.8 at the end of the coarsening process, because the statistics are measured on less than ten cells.
21. This home-made software program consists of a user module for NIH Image by Wayne Rasband, National Institutes of Health. Both source code and compiled application for Mac OS are available at http://www.lps.ens.fr/∼cardoso/
22. Here again, the mean area is proportional to the topological charge (Formula presented) Consequently, the average area of the cells with (Formula presented) is less than that of the cells with (Formula presented) and, furthermore, as a consequence of the Aboav-Weaire law, the smaller cells are surrounded by larger cells (i.e., (Formula presented)). This fact is a crucial property of the cellular patterns.
23. M. Seul, N. Y. Morgan, and C. Sire, Phys. Rev. Lett. 73, 2284 (1994).PRLTAO
24. gives the period of the stripe pattern as a function of the external field. Using a truncated formula we get (Formula presented) With (Formula presented) and (Formula presented) we obtain (Formula presented)
25. P. Mohlo (private communication).