# Surface Evolver Documentation

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# Bibliography

[A] F. Almgren, "Minimal surface forms," The Mathematical Intelligencer, vol.4, no. 4 (1982), 164-172.

[AT] F. Almgren and J. Taylor, "The geometry of soap films and soap bubbles," Scientific American, July 1976, 82-93.

[AV] V. I. Arnol'd, Catastrophe Theory, 3rd ed., Springer-Verlag, 1992.

[AYC] J. Ambrose, B. Yendler, and S. H. Collicot, "Modeling to evaluate a spacecraft propellant guaging system," Spacecraft and Rockets 37 (2000) 833-835.

[B1] K. Brakke, The motion of a surface by its mean curvature, Princeton University Press, Princeton, NJ (1977).

[B2] K. Brakke, "The surface evolver," Experimental Mathematics, vol. 1, no. 2 (1992), 141-165.

[B3] K. A. Brakke, "Minimal surfaces, corners, and wires," Journal of Geometric Analysis 2 (1992) 11-36.

[B4] K. A. Brakke, "The opaque cube problem video," Computing Optimal Geometries, J. E. Taylor, ed., American Mathematical Society, Providence RI, 1991.

[B5] K. A. Brakke, "Grain growth with the Surface Evolver," Video Proceedings of the Workshop on Computational Crystal Growing, J. E. Taylor, ed., American Mathematical Society, Providence RI, 1992.

[B6] K. A. Brakke, "The opaque cube problem,", Am. Math. Monthly 99 (Nov. 1992), 866-871.

[BB] K. A. Brakke and F. Baginski, "Modeling ascent configurations of strained high-altitude balloons," AIAA Journal 36 (1998) 1901-1920.

[B7] K. A. Brakke and F. Morgan, "Instabilities of cylindrical bubble clusters,", Eur. Phys. J. E 9 (2002) 453-460.

[BS] K. A. Brakke and J. M. Sullivan, "Using Symmetry Features of the Surface Evolver to Study Foams", in Mathematics and Visualization, ed. K. Polthier and H. Hege, Springer Verlag, Berlin, (1997).

[C] M. Callahan, P. Concus and R. Finn, "Energy minimizing capillary surfaces for exotic containers," Computing Optimal Geometries, American Mathematical Society, Providence RI, 1991.

[CS] S. Collicot, "Convergence behavior of Surface Evolver applied to a generic propellant-management device," J. Propulsion and Power 17 (2001) 845-851.

[DL] D. Dobkin and M. Laszlo, "Primitives for the manipulation of three-dimensional subdivisions," technical report CS-TR-089-87, Department of Computer Science, Princeton University, Princeton, New Jersey. (April 1987).

[FHW] M. Freedman, X. He, and Z. Wang, "On the energy of knots and unknots," Annals of Mathematics 139 no. 1 (1994) 1-50.

[FS] G. Francis, J. M. Sullivan, R. B. Kusner, K. A. Brakke, C. Hartman, and G. Chappell, "The Minimax Sphere Eversion", in Mathematics and Visualization, ed. K. Polthier and H. Hege, Springer Verlag, Berlin, (1997).

[FT].H. J. Frost and C. V. Thompson, "Computer Simulation of Grain Growth," Current Opinion in Solid State and Materials Science 3, 361 (1996).

[HK] J. Hale and H. Kocak, Dynamics and Bifurcations, Springer-Verlag, 1991.

[HKS] L. Hsu, R. Kusner, and J. Sullivan, "Minimizing the squared mean curvature integral for surfaces in space forms," Experimental Mathematics 1 (1991) 191-208.

[KR1] A. Kraynik and D. Reinelt, "The linear elastic behaviour of a bidisperse Weiare-Phelan soap foam", submitted to Chem. Eng. Comm.

[KR2] A. Kraynik and D. Reinelt, "Simple shearing flow of a dry Kelvin soap foam", J. Fluid Mech. 311 (1996) 327.

[KRS] A. Kraynik, D. Reinelt, and F. van Swol, "Structure of random monodisperse foam," Phys. Rev. E 67 (2003) 031403.

[KS][KS]} R. Kusner and J. M. Sullivan, "Comparing the Weaire-Phelan Equal-Volume Foam to Kelvin's Foam", Forma (The Society for Science on Form, Japan) ed. R. Takaki and D. Weaire, KTK Scientific Publishers. As book by Taylor and Francis Ltd (1996).

[KS2]} R. Kusner and J. M. Sullivan, "Mobius Energies for Knots and Links, Surfaces and Submanifolds" in Geometric Topology, Proceedings of the Georgia International Topology Conference, August 1993, ed. W. Kazez, AMS/IP Studies in Advanced Mathematics, vol. 2, part 1 (1997) 570--604.

[MB] X. Michalet and D. Bensimon, "Observation of stable shapes and conformal diffusion in genus 2 vesicles", Science 269 (4 Aug 1995) 666-668.

[MH] H. Mittelmann, "Symmetric capillary surfaces in a cube", Math. Comp. Simulation 35 (1993) 139-152.

[MF1] F. Morgan, "Harnack-type mass bounds and Bernstein theorems for area-minimizing flat chains modulo $\nu$," Comm. Part. Diff. Eq. 11 (1986) 1257-1283.

[MT] F. Morgan and J. E. Taylor, "Destabilization of the tetrahedral point junction by positive triple junction line energy," Scripta Metall. Mater. 25 (1991) 1907-1910.

[PWB] R. Phelan, D. Weaire, and K. Brakke, "Computation of equilibrium foam structures using the Surface Evolver," Experimental Mathematics 4 (1995) 181-192.

[P] W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C, Cambridge University Press, New York, 1988.

[PP] K. Polthier and U. Pinkall,"Computing discrete minimal surfaces and their conjugates," Experimental Math. 2 (1993) 15-36.

[RN] R. J. Renka and J. W. Neuberger, "Minimal surfaces and Sobolev gradients", SIAM J. Sci. Comput. 16 (1995) 1412-1427.

[RSB] L. M. Racz, J. Szekely, and K. A. Brakke, "A General Statement of the Problem and Description of a Proposed Method of Calculation for Some Meniscus Problems in Materials Processing", ISIJ International, Vol. 33, No. 2, (February 1993).

[S] R. Sibson, "Locally equiangular triangulations", Comput. J. 21 (1978) 243-245.

[SG] G. Strang, Linear Algebra and its Applications, Academic Press.

[SJ]J. M. Sullivan, "Sphere Packings Give an Explicit Bound for the Besicovitch Covering Theorem", J. Geometric Analysis 4 (1993) 219-231.

[T1] J. E. Taylor, "The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces," Ann. Math. 103 (1976), 489-539.

[T2] J. E. Taylor, "Constructing crystalline minimal surfaces," Seminar on Minimal Submanifolds, E. Bombieri, ed., Annals of Math. Studies 105 (1983), 271-288.

[T3] J. E. Taylor, "Constructions and conjectures in crystalline nondifferentiable geometry," Proceedings of the Conference in Differential Geometry, Rio de Janiero, 1988, Pittman Publishing Ltd.

[Te] J. Tegart, "Three-dimensional fluid interfaces in cylindrical containers," AIAA paper AIAA-91-2174, 27th Joint Propulsion Conference, Sacramento, CA, June 1991.

[TW] W. Thompson (Lord Kelvin), "On the division of space with minimum partitional area," Acta Math. 11(1887), 121-134.

[U] A. Underwood, "Constructing barriers to minimal surfaces from polyhedral data," Ph.D. thesis, Princeton, 1993.

[WM] D. Weaire and S. McMurry, "Some Fundamentals of Grain Growth," in Solid State Physics: Advances in Research and Applications (eds. H. Ehrenreich and F. Spaepen), Vol. 50, Academic Press, Boston (1997).

[WP] D. Weaire and R. Phelan, "A counter-example to Kelvin's conjecture on minimal surfaces", Phil. Mag. Letters 69 (1994), 107-110.

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