Calculations of the minimal perimeter for N deformable cells of equal area confined in a circle

Philosophical Magazine Letters

Volumn 86, Issue 9, 2006, Pages 569-578

  Cox, S J ^a  

^a ABERYSTWYTH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CONSTRAINT THEORY; DEFORMATION; PROBLEM SOLVING; RANDOM PROCESSES;

DEFORMABLE CELLS; LEAST PERIMETER PARTITION; UNCONSTRAINED PROBLEMS; VORONOI CONSTRUCTION;

PARAMETER ESTIMATION;

EID: 33748789316     PISSN: 09500839     EISSN: 13623036     Source Type: Journal    
DOI: 10.1080/09500830600929083     Document Type: Article

References (21)

1. D. Weaire and S. Hutzler, The Physics of Foams (Clarendon Press, Oxford, 1999).
2. T.C. Hales, Discrete Comput. Geom. 25 1 (2001).
3. F. Morgan, Geometric Measure Theory: A Beginner's Guide, 3rd ed. (Academic Press, San Diego, 2000).
4. W. Wichiramala and J. Reine, Angew. Math. 567 1 (2004).
5. M. Alfaro, J. Brock, J. Foisy, et al., Compound Soap Bubbles in the Plane, SMALL Geometry Group report (1990).
6. F. Morgan, Amer. Math. Monthly 101 343 (1994).
7. M.F. Vaz and M.A. Fortes, J. Phys.: Condens. Matt. 13 1395 (2001).
8. S.J. Cox, F. Graner, M.F. Vaz, et al., Phil. Mag. 83 1393 (2003).
9. A. Heppes and F. Morgan, Phil. Mag. 85 1333 (2005).
10. S.J. Cox and F. Graner, Phil. Mag. 83 2573 (2003).
11. F. Graner, Y. Jiang, E. Janiaud, et al., Phys. Rev. E 63 011402 (2001).
12. A. Cañete and M. Ritore, Indiana Univ. Math. J. 53 883 (2004).
13. Y. Tomonaga, Geometry of Length and Area (Department of Mathematics, Utsunomiya University, Japan, 1974).
14. M.N. Bleicher, in Intuitive Geometry, Colloq. Math. Soc. János Bolyai, Vol. 48 (North-Holland, Amsterdam, 1987), pp. 63-84.
15. T. Hayashi and R.W. Carthew, Nature 431 647 (2004).
16. T. Tarnai, in Symmetry 2000, edited by I. Hargittai and T. Laurent (Portland, 2002), pp. 121-132.
17. T. Tarnai and K. Miyazaki, Leonardo 36 145 (2003).
18. J.E. Taylor, Ann. Math. 103 489 (1976).
19. J.A.F. Plateau, Statique Experimentale, et Théorique des Liquides Soumis aux Seules Forces Moléculaires (Gauthier-Villars, Paris, 1873).
20. M. Emília Rosa and M.A. Fortes, Phil. Mag. A 79 1871 (1999).
21. K. Brakke, Exp. Math. 1 141 (1992).