The demonstration of conformal maps with two-dimensional foams

European Journal of Physics

Volumn 25, Issue 3, 2004, Pages 429-438

  Drenckhan, W ^a   Weaire, D ^a   Cox, S J ^a  

^a TRINITY COLLEGE DUBLIN   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BUBBLE FORMATION; CONFORMAL MAPPING; CRYSTAL GROWTH; HONEYCOMB STRUCTURES;

HONEYCOMB LATTICE; ISOGONALITY;

FOAMS;

EID: 2542636420     PISSN: 01430807     EISSN: None     Source Type: Journal    
DOI: 10.1088/0143-0807/25/3/010     Document Type: Article

References (29)

1. Aref H and Herdtle T 1990 Topological Fluid Mechanics ed H Moffat and A Tsinober (Cambridge: Cambridge University Press) p 745
2. Atela P, Golé C and Hotton S 2003 Phyllotaxis, An Interactive Site for the Mathematical Study of Plant Pattern Formation http://http://www.math.smith.edu/~phyllo
3. Bolton F and Weaire D 1992 The effects of Plateau borders in the two-dimensional soap froth: II. General simulation and analysis of rigidity loss transition Phil. Mag. B 65 473-87
4. Bragg L and Nye J F 1947 A dynamical model of a crystal structure Proc. R. Soc. Lond. A 190 474-81
5. Brakke K 1992 The surface evolver Exp. Math. 1 141-65.
6. Brakke K 2002 Private communication
7. Cox S J and Graner F 2003 Large two-dimensional clusters of equal-area bubbles Phil. Mag. 83 2573-84
8. Cox S J, Vaz M F and Weaire D 2003 Topological changes in a two-dimensional foam cluster Eur. Phys. J. E 11 29-35
9. Cox S J, Weaire D and Vaz M F 2002 The transition from two-dimensional to three-dimensional foam structures Eur. Phys. J. E 7 311-5.
10. Drenckhan W, Elias F, Hutzler S, Weaire D, Janiaud E and Bacri J C 2003 Bubble size control and measurement in the generation of ferrofluid foams J. Appl. Phys. 93 10078-83
11. Elias F, Bacri J-C, de Mougins F H and Spengler T 1999 Two-dimensional ferrofluid foam in an external force field: gravity arches and topological defects Phil. Mag. Lett. 79 389-97
12. Glazier J A, Gross S P and Stavans J 1987 Dynamics of two-dimensional soap froths Phys. Rev. A 36 306-12
13. Hales T C 2001 The honeycomb conjecture Discrete Comput. Geom 25 1-22
14. Jean R V 1984 Mathematical Approach to Patterns and Form in Plant Growth (New York: Wiley)
15. Kolosov V Yu 1995 Nontranslation atom ordering in crystals growing in amorphous films Aperiodic '94 ed G Chapius (Singapore: World Scientific) p 26
16. Pierański P 1989 Phase Transitions in Soft Condensed Matter (Nato Advanced Study Institute Series B: Physics vol 211) ed T Riste and D Sherington (Dordrecht: Kluwer)
17. Pittet N, Boltenhagen R, Rivier N and Weaire D 1996 Structural transitions in ordered, cylindrical foams Europhys. Lett. 35 547-52
18. Plateau J A F 1873 Statique Expérimentale et Théoretique des Liquides Soumis aux Seules Forces Moléculaires 2 vol (Paris: Gauthiers-Villars)
19. Prandt L and Tietjens O G 1934 Applied Hydro- and Aeromechanics (New York: McGraw-Hill)
20. Rivier N, Occelli R, Pantaloni J and Lissowski A 1984 Structure of Bénard convection cells, phyllotaxis and crystallography in cylindrical symmetry J. Physique 45 49-63
21. Rowlinson J S 2002 Cohesion: A Scientific History of Intermolecular Forces (Cambridge: Cambridge University Press) p 13
22. Rothen F and Pierański P 1996 Mechanical equilibrium of conformal crystals Phys. Rev. E 53 2828-42
23. Rothen F, Pieranski P, Rivier N and Joyet A 1993 Cristaux conformes Eur. J. Phys. 14 227-33
24. Smith C S 1952 Grain shapes and other metallurgical applications of topology Metal Interfaces (Cleveland, OH: American Society for Metals) pp 65-108
25. Weaire D 1999 The equilibrium structure of soap froths: inversion and decoration Phil. Mag. Lett. 79 491-5
26. Weaire D and Phelan R 1994 Optimal design of honeycombs Nature 367 123
27. Weaire D, Hutzler S and Pittet N 1992 Cylindrical packings of foam cells Forma 7 259
28. Weaire D and Rivier N 1984 Soap, cells and statistics-random patterns in two dimensions Contemp. Phys. 25 59-99
29. Wolfram Research, Inc. 1999 Mathematica Version 4 edition Champaign, Illinois