Surface Evolver Manual

Total Page:16

File Type:pdf, Size:1020Kb

Surface Evolver Manual Surface Evolver Manual Version 2.26 August 25, 2005 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 ................................................. 11 1.6 Acknowledgements ............................................ 11 2 Installation. 12 2.1 Microsoft Windows ............................................ 12 2.2 Macintosh ................................................. 13 2.3 Unix/Linux ................................................ 13 2.3.1 Compiling ............................................ 14 2.4 Geomview graphics ............................................ 14 2.5 X-Windows graphics ........................................... 15 3 Tutorial 16 3.1 Basic Concepts .............................................. 16 3.2 Example 1. Cube evolving into a sphere ................................. 17 3.3 Example 2. Mound with gravity ..................................... 20 3.4 Example 3. Catenoid ........................................... 22 3.5 Example 4. Torus partitioned into two cells ............................... 24 3.6 Example 5. Ring around rotating rod ................................... 26 3.7 Example 6. Column of liquid solder ................................... 31 3.8 Example 7. Rocket fuel tank ....................................... 34 3.8.1 Surface energy .......................................... 34 3.8.2 Volume .............................................. 35 3.8.3 Gravity .............................................. 36 3.8.4 Running .............................................. 37 3.9 Example 8. Spherical tank ........................................ 39 3.9.1 Surface energy .......................................... 40 3.9.2 Volume .............................................. 41 3.9.3 Gravity .............................................. 42 3.9.4 Running .............................................. 43 3.10 Example 9. Crystalline integrand ..................................... 45 3.11 Tutorial in Advanced Calculus ...................................... 46 2 Surface Evolver Manual 3 4 The Model 50 4.1 Dimension of surface ........................................... 50 4.2 Geometric elements ............................................ 50 4.2.1 Vertices .............................................. 50 4.2.2 Edges ............................................... 51 4.2.3 Facets ............................................... 52 4.2.4 Bodies. .............................................. 53 4.2.5 Facetedges ............................................ 53 4.3 Quadratic model .............................................. 53 4.4 Lagrange model .............................................. 54 4.5 Simplex model .............................................. 54 4.6 Dimension of ambient space ....................................... 54 4.7 Riemannian metric ............................................ 54 4.8 Torus domain. .............................................. 55 4.9 Quotient spaces and general symmetry .................................. 55 4.9.1 TORUS symmetry group ..................................... 56 4.9.2 ROTATE symmetry group .................................... 56 4.9.3 FLIP ROTATE symmetry group ................................. 56 4.9.4 CUBOCTA symmetry group ................................... 57 4.9.5 XYZ symmetry group ...................................... 57 4.9.6 GENUS2 symmetry group .................................... 57 4.9.7 DODECAHEDRON symmetry group .............................. 57 4.9.8 CENTRAL SYMMETRY symmetry group ........................... 58 4.9.9 SCREW SYMMETRY symmetry group ............................. 58 4.10 Symmetric surfaces ............................................ 58 4.11 Level set constraints ............................................ 58 4.12 Boundaries ................................................ 59 4.13 Energy. .................................................. 59 4.14 Named quantities and methods ...................................... 61 4.15 Pressure .................................................. 62 4.16 Volume or content ............................................. 62 4.17 Diffusion ................................................. 62 4.18 Motion ................................................... 63 4.19 Hessian .................................................. 63 4.20 Eigenvalues and eigenvectors ....................................... 64 4.21 Mobility .................................................. 65 4.21.1 Vertex mobility .......................................... 65 4.21.2 Area normalization ........................................ 65 4.21.3 Area normalization with effective area .............................. 66 4.21.4 Approximate polyhedral curvature ................................ 66 4.21.5 Approximate polyhedral curvature with effective area ...................... 66 4.21.6 User-defined mobility ...................................... 66 4.22 Stability .................................................. 66 4.22.1 Zigzag string ........................................... 66 4.22.2 Perturbed sheet with equilateral triangulation .......................... 67 4.23 Topology changes ............................................. 67 4.24 Refinement ................................................ 67 4.25 Adjustable parameters and variables ................................... 67 4.26 The String Model ............................................. 68 3 Surface Evolver Manual 4 5 The Datafile 69 5.1 Datafile organization ........................................... 69 5.2 Lexical format ............................................... 69 5.2.1 Comments ............................................ 69 5.2.2 Lines and line splicing ...................................... 69 5.2.3 Including files .......................................... 69 5.2.4 Macros .............................................. 70 5.2.5 Case ................................................ 70 5.2.6 Whitespace ............................................ 70 5.2.7 Identifiers ............................................. 70 5.2.8 Strings .............................................. 70 5.2.9 Numbers ............................................. 70 5.2.10 Keywords ............................................. 70 5.2.11 Colors ............................................... 71 5.2.12 Expressions ............................................ 71 5.3 Datafile top section: definitions and options ............................... 72 5.3.1 Macros .............................................. 72 5.3.2 Version check ........................................... 72 5.3.3 Element id numbers ....................................... 72 5.3.4 Variables ............................................. 73 5.3.5 Arrays ............................................... 73 5.3.6 Dimensionality .......................................... 73 5.3.7 Domain .............................................. 74 5.3.8 Length method .......................................... 74 5.3.9 Area method ........................................... 75 5.3.10 Volume method .......................................... 75 5.3.11 Representation .......................................... 75 5.3.12 Hessian special normal vector .................................. 76 5.3.13 Dynamic load libraries ...................................... 76 5.3.14 Extra attributes .......................................... 76 5.3.15 Surface tension energy ...................................... 77 5.3.16 Squared mean curvature ..................................... 77 5.3.17 Integrated mean curvature .................................... 77 5.3.18 Gaussian curvature ........................................ 77 5.3.19 Squared Gaussian curvature ................................... 78 5.3.20 Ideal gas model .......................................... 78 5.3.21 Gravity .............................................. 78 5.3.22 Gap energy ............................................ 78 5.3.23 Knot energy ............................................ 78 5.3.24 Mobility and motion by mean curvature ............................. 78 5.3.25 Annealing ............................................. 79 5.3.26 Diffusion ............................................. 79 5.3.27 Named method instances ..................................... 79 5.3.28 Named quantities ......................................... 80 5.3.29 Level set constraints ....................................... 81 5.3.30 Constraint tolerance ....................................... 82 5.3.31 Boundaries ............................................ 83 5.3.32 Numerical integration precision ................................. 83 5.3.33 Scale factor ............................................ 83 5.3.34 Mobility ............................................. 83 5.3.35 Metric ............................................... 84 4 Surface Evolver Manual 5 5.3.36 Autochopping ........................................... 84 5.3.37 Autopopping ........................................... 84 5.3.38 Total time ............................................. 84 5.3.39 Runge-Kutta ........................................... 84 5.3.40 Homothety
Recommended publications
  • Surface Evolver Manual
    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 ..............................
    [Show full text]
  • Computational Modelling of a Spanning Drop in a Wedge with Variable Angle Caio Rondon Federal University of ABC, [email protected]
    CORE Metadata, citation and similar papers at core.ac.uk Provided by CommonKnowledge International Journal of Undergraduate Research and Creative Activities Volume 8 Article 3 April 2016 Computational Modelling of a Spanning Drop in a Wedge with Variable Angle Caio Rondon Federal University of ABC, [email protected] Valerio Ramos Batista Federal University of ABC, [email protected] Follow this and additional works at: http://commons.pacificu.edu/ijurca Recommended Citation Rondon, Caio and Ramos Batista, Valerio (2016) "Computational Modelling of a Spanning Drop in a Wedge with Variable Angle," International Journal of Undergraduate Research and Creative Activities: Vol. 8, Article 3. DOI: http://dx.doi.org/10.7710/2168-0620.1064 Computational Modelling of a Spanning Drop in a Wedge with Variable Angle Peer Review This work has undergone a double-blind review by a minimum of two faculty members from institutions of higher learning from around the world. The faculty reviewers have expertise in disciplines closely related to those represented by this work. If possible, the work was also reviewed by undergraduates in collaboration with the faculty reviewers. Abstract In this work, mathematical and computational techniques were used to model the phenomenon of a bubble or liquid drop as it slides to the narrowest side between two tilted plates. Practical applications of this phenomenon, such as the adjustment of liquid propellant tanks, are also discussed. Computations involved the use of Surface Evolver—a fully open, interactive program that allows the simulation of physical experiments in a virtual environment. Keywords Surface Evolver, Computational Modeling, Spanning Drop, Wedge Acknowledgements Editor's Note: Dr.
    [Show full text]
  • Simulating External Compressions of the Breast with the Surface Evolver
    Simulating External Compressions of the Breast with the Surface Evolver M. Zanchetta & V. Ramos Batista UFU/UFABC Talk IC-MSQUARE, Prague, Sep 2013 Project Financed by FAPESP proc.No.12/16244-3 (UFU/UFABC) Virtual Mammography Talk 1 / 31 DEDICAT ION T HE 2nd AUT HOR DEDICAT ES T HIS WORK T O HIS WIFE; T HE WOMAN T HAT CON CEDED HER MEASUREMEN T S FOR OUR RESEARCH: (UFU/UFABC) Virtual Mammography Talk 2 / 31 1. Introduction 1.1. Breast Cancer The 2nd main cause of obits among women in the globe. At the 1st place: lung cancer. For details, browse on the web for Cancer Fact Sheets - World Health Organization. In Brazil, the Cancer National Institute predicted 53,000 cases of breast tumours in 2012, with an estimate risk of 52 cases per 100,000 women. In our country, the population has ca. 100 million women. Some statistics show these cases have been increasing. (UFU/UFABC) Virtual Mammography Talk 3 / 31 1. Introduction 1.2. Mammography To date, this technique still has the best cost-benefit. It's largely applied in developing countries. Other techniques: resonance and ultrasonography. But all of them have a common disadvantage: the breast shape deforms drastically. For the surgery, tumour location is highly uncertain. A great portion of the breast has to be removed. (UFU/UFABC) Virtual Mammography Talk 4 / 31 2. Surface Evolver 2.1. Brief History It was created by Prof Ken Brakke (nowadays at Susquehanna University - USA). First release: 1989. Evolver allows to simulate physical experiments in a virtual environment.
    [Show full text]
  • A Laboratory for Geometric Performance 1
    A Laboratory for Geometric Performance 1 Sha Xin Wei June 1998 I. Introduction: Creating Geometry Why is it that when two students of differential geometry work together, itÕs more natural to turn to a blackboard than to a keyboard? How do we inscribe and work out mathematics with marks on paper or on a blackboard, and how is this different from typing math in TeX? Is mathematical creativity mediated by freehand writing and sketching in ways that are not captured by traditional keyboard-and-mouse writing systems? How do computation or automated symbol manipulation augment or degrade a writing system for mathematical work? What forms of writing, computation and symbolic encoding help or hinder the practices of inventing new mathematical structures, making new conjectures, or convincing oneself of the truth of a claim? I would like to consider these questions in the context of a specific subdomain of geometry. This is a proposal to construct a formalism and an experimental computational environment that supports as well as possible a fragment of differential geometersÕ practice. I would like to analyze in detail what geometrical work can or cannot be performed easily in a hybrid medium provided by a generalized writing system (a so-called multi-modal geometrical liveboard) spanning freehand sketches, mathematical text, symbolic and numeric computation, and manipulable diagrams or graphics. The critical part of this project will be informed by insights from literary and performance studies as well as the mathematical sciences. Practically, this work benefits students of differential geometry or topology, people who need to work with nonlinear or multi-dimensional information, and artists and designers who wish to shape computational material using freehand sketches.
    [Show full text]