Surface Evolver Manual Version 2.70 August 25, 2013 Kenneth A. Brakke Mathematics Department Susquehanna University Selinsgrove, PA 17870 [email protected] http://www.susqu.edu/brakke Contents 1 Introduction. 9 1.1 General description ............................................ 9 1.2 Portability ................................................. 9 1.3 Bug reports ................................................ 10 1.4 Web home page .............................................. 10 1.5 Newsletter ................................................. 10 1.6 Acknowledgements ............................................ 10 2 Installation. 11 2.1 Microsoft Windows ............................................ 11 2.1.1 Modern GUI installation ..................................... 11 2.1.2 Old-fashioned installation by hand ................................ 12 2.2 Macintosh ................................................. 12 2.3 Unix/Linux ................................................ 12 2.3.1 Compiling ............................................ 13 2.4 Geomview graphics ............................................ 14 2.5 X-Windows graphics ........................................... 14 3 Tutorial 15 3.1 Basic Concepts .............................................. 15 3.2 Example 1. Cube evolving into a sphere ................................. 16 3.3 Example 2. Mound with gravity ..................................... 19 3.4 Example 3. Catenoid ........................................... 21 3.5 Example 4. Torus partitioned into two cells ............................... 23 3.6 Example 5. Ring around rotating rod ................................... 25 3.7 Example 6. Column of liquid solder ................................... 30 3.8 Example 7. Rocket fuel tank ....................................... 32 3.8.1 Surface energy .......................................... 33 3.8.2 Volume .............................................. 34 3.8.3 Gravity .............................................. 35 3.8.4 Running .............................................. 36 3.9 Example 8. Spherical tank ........................................ 38 3.9.1 Surface energy .......................................... 39 3.9.2 Volume .............................................. 40 3.9.3 Gravity .............................................. 41 3.9.4 Running .............................................. 42 3.10 Example 9. Crystalline integrand ..................................... 44 3.11 Tutorial in Advanced Calculus ...................................... 45 2 Surface Evolver Manual 3 4 Geometric elements 49 4.1 Vertices .................................................. 49 4.2 Edges ................................................... 50 4.3 Facets ................................................... 50 4.4 Bodies .................................................. 51 4.5 Facetedges ................................................ 51 4.6 Common element attributes ........................................ 51 4.7 Vertex attributes .............................................. 54 4.8 Edge attributes .............................................. 60 4.9 Facet attributes .............................................. 65 4.10 Body attributes .............................................. 70 4.11 Facetedge attributes ............................................ 72 5 The Model 74 5.1 Dimension of surface ........................................... 74 5.2 Quadratic model .............................................. 74 5.3 Lagrange model .............................................. 74 5.4 Simplex model .............................................. 75 5.5 Dimension of ambient space ....................................... 75 5.6 Riemannian metric ............................................ 75 5.7 Torus domain. .............................................. 75 5.8 Quotient spaces and general symmetry .................................. 77 5.8.1 TORUS symmetry group ..................................... 77 5.8.2 ROTATE symmetry group .................................... 77 5.8.3 FLIP ROTATE symmetry group ................................. 78 5.8.4 CUBOCTA symmetry group ................................... 78 5.8.5 CUBELAT symmetry group ................................... 78 5.8.6 XYZ symmetry group ...................................... 78 5.8.7 GENUS2 symmetry group .................................... 79 5.8.8 DODECAHEDRON symmetry group .............................. 79 5.8.9 CENTRAL SYMMETRY symmetry group ........................... 79 5.8.10 SCREW SYMMETRY symmetry group ............................. 79 5.8.11 QUARTER_TURN symmetry group ............................... 79 5.9 Symmetric surfaces ............................................ 80 5.10 Level set constraints ............................................ 80 5.11 Boundaries ................................................ 81 5.12 Energy. .................................................. 82 5.13 Named quantities and methods ...................................... 83 5.14 Pressure .................................................. 84 5.15 Volume or content ............................................. 84 5.16 Diffusion ................................................. 85 5.17 Motion ................................................... 85 5.18 Hessian .................................................. 86 5.19 Eigenvalues and eigenvectors ....................................... 86 5.20 Mobility .................................................. 87 5.20.1 Vertex mobility .......................................... 88 5.20.2 Area normalization ........................................ 88 5.20.3 Area normalization with effective area .............................. 88 5.20.4 Approximate polyhedral curvature ................................ 88 5.20.5 Approximate polyhedral curvature with effective area ...................... 88 5.20.6 User-defined mobility ...................................... 89 3 Surface Evolver Manual 4 5.21 Stability .................................................. 89 5.21.1 Zigzag string ........................................... 89 5.21.2 Perturbed sheet with equilateral triangulation .......................... 89 5.22 Topology changes ............................................. 90 5.23 Refinement ................................................ 90 5.24 Adjustable parameters and variables ................................... 90 5.25 The String Model ............................................. 90 6 The Datafile 91 6.1 Datafile organization ........................................... 91 6.2 Lexical format ............................................... 91 6.2.1 Comments ............................................ 91 6.2.2 Lines and line splicing ...................................... 91 6.2.3 Including files .......................................... 92 6.2.4 Macros .............................................. 92 6.2.5 Case ................................................ 92 6.2.6 Whitespace ............................................ 92 6.2.7 Identifiers ............................................. 92 6.2.8 Strings .............................................. 92 6.2.9 Numbers ............................................. 92 6.2.10 Keywords ............................................. 93 6.2.11 Colors ............................................... 93 6.2.12 Expressions ............................................ 93 6.3 Datafile top section: definitions and options ............................... 94 6.3.1 Macros .............................................. 94 6.3.2 Version check ........................................... 94 6.3.3 Element id numbers ....................................... 94 6.3.4 Variables ............................................. 95 6.3.5 Arrays ............................................... 95 6.3.6 Dimensionality .......................................... 96 6.3.7 Domain .............................................. 96 6.3.8 Length method .......................................... 97 6.3.9 Area method ........................................... 97 6.3.10 Volume method .......................................... 98 6.3.11 Representation .......................................... 98 6.3.12 Hessian special normal vector .................................. 98 6.3.13 Dynamic load libraries ...................................... 99 6.3.14 Extra attributes .......................................... 99 6.3.15 Surface tension energy ...................................... 100 6.3.16 Squared mean curvature ..................................... 100 6.3.17 Integrated mean curvature .................................... 100 6.3.18 Gaussian curvature ........................................ 100 6.3.19 Squared Gaussian curvature ................................... 101 6.3.20 Ideal gas model .......................................... 101 6.3.21 Gravity .............................................. 101 6.3.22 Gap energy ............................................ 101 6.3.23 Knot energy ............................................ 101 6.3.24 Mobility and motion by mean curvature ............................. 101 6.3.25 Annealing ............................................. 102 6.3.26 Diffusion ............................................. 102 6.3.27 Named method instances ..................................... 102 4 Surface Evolver Manual 5 6.3.28 Named quantities ......................................... 103 6.3.29 Level set constraints ......................................