![]() B.: 1946, `The Three-Dimensional Shape of Bubbles in Foam’. Stong: 1993, ‘Combinatorics of Triangulations of 3-Manifolds’. Sullivan: 1996, `Comparing the Weaire-Phelan Equal-Volume Foam to Kelvin’s Foam’. Schmitt: 1996, `On the Spinor Representation of Minimal Surfaces’. Kusner, R.: 1992, `The Number of Faces in a Minimal Foam’. Reinelt: 1996, `Elastic-Plastic Behavior of a Kelvin Foam’. Sullivan, ‘TCP Structures as Equal-Volume Foams’ In preparation. Solomon: 1989, `The Structure of Complete Embedded Surfaces with Constant Mean Curvature’. Lipowsky: 1993, `Conformal Degeneracy and Conformal Diffusion of Vesicles’. Sullivan: 1992, `Minimizing the Squared Mean Curvature Integral for Surfaces in Space Forms’. Meeks, III: 1990, `Embedded Minimal Surfaces of Finite Topology’. Hildebrandt, S.: 1970, `On the Plateau problem for surfaces of constant mean curvature’. Schlafiy: 1995, `The Double Bubble Conjecture’. To appear in the Springer proceedings of VisMath’97. Sullivan: 1998, `Constant Mean Curvature Surfaces with Cylindrical Ends’. Sullivan: 1997, `Classification of Embedded Constant Mean Curvature Surfaces with Genus Zero and Three Ends’. Analysis and Classification of Representative Structures’. Kasper: 1959, `Complex Alloy Structures Regarded as Sphere Packings. Kasper: 1958, `Complex Alloy Structures Regarded as Sphere Packings. 295 of Grundlehren der Mathematischen Wissenschaften. Journal de mathématiques 6, 309–320.ĭierkes, U., S. ĭelaunay, C.: 1841, `Sur la surface de révolution, dont la courbure moyenne est constante’. 95–117.Ĭhoe, J.: 1989, `On the Existence and Regularity of Fundamental Domains with Least Boundary Area’. Hege (eds.): Visualization andMathematics. Sullivan: 1997, `Using Symmetry Features of the Surface Evolver to Study Foams’. Morgan: 1996, `Instability of the Wet X Soap Film’. Rivier: 1996, `From One Cell to the Whole Froth: A Dynamical Map’. J.: 1976, `Existence and Regularity Almost Everywhere of Solutions to Elliptic Variational Problems with Constraints’. D.: 1958, `Uniqueness Theorems for Surfaces in the Large, I’. This process is experimental and the keywords may be updated as the learning algorithm improves.Īlexandrov, A. These keywords were added by machine and not by the authors. These include the one used by Weaire and Phelan in their counterexample to the Kelvin conjecture, and they all seem useful for generating good equal-volume foams. Finally, we examine particular structures, like the family of tetrahedrally close-packed structures. We examine certain restrictions on the combinatorics of triangulations and some useful ways to construct triangulations. The possible singularities are described by Plateau’s rules this means that combinatorially a foam is dual to some triangulation of space. The resulting surfaces have constant mean curvature and an invariant notion of equilibrium forces. We consider mathematical models of bubbles, foams and froths, as collections of surfaces which minimize area under volume constraints.
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