# Surface Evolver Newsletter no. 2

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    		      Surface Evolver Newsletter Number 2
    			      February 26, 1993

                        Editor: Ken Brakke, brakke@geom.umn.edu

    Contents:
      Announcements
      Version 1.89 features
      A student project
      Bibliography

    Announcements:

      The number of subscribers to this newsletter has passed 100.
      I really appreciate all the interest.

      Evolver version 1.89 is now available for ftp.

      There is now a Macintosh version of the Evolver.  The binary
      is available for anonymous ftp from geom.umn.edu as
      pub/evolver.sit.hqx.  This is a binhexed Stuffit 1.5.1 archive.
      It includes a README file with Mac specific information and datafiles
      in Mac format.  Thanks to Jeff Weeks for providing a sample program
      for setting up text and graphics windows and handling the event loop.

    Version 1.89 features:

      New arithmetic functions available are floor(), ceil(), and modulus.
      The modulus operator is '%' as in C. It does a real modulus operation:
        x % y = x - floor(x/y)*y,
      but it works fine on integer values.  Useful for getting multicolored
      surfaces with `set facet color id % 15'.

      A couple of items to more fully capture the current state in a dump file:
      The internal viewing matrix (used for Xwindows graphics and Postscript
      output) is now included in a dump file and can be read from a datafile.
      User-defined commands are included in the dump file in a `read'
      section at the end.

      A `rebody' command has been added that recalculates connected bodies.
      Useful when a neck has pinched out.  If original body volumes were
      fixed, new bodies have their volumes set to their current volumes.

      Some internal Evolver variables can now be used in command expressions:
    	vertex_count, edge_count, facet_count, body_count,
    	total_energy, total_area, total_length, scale.

      Knot energies have been added.  One way to get a knot to look nice
      is to endow it with `electric charge' and let it repel itself into
      shape.  The potential is some inverse power of distance and is
      integrated between all pairs of points.  Two varieties are
      implemented, corresponding to conducting or insulating wire.

     `dissolve' command added to erase elements and leave gaps in
      surface, unlike delete command, which closes gaps.  Can only
      dissolve elements not neede by higher dimensional elements.

      Command repeat numbers have been restricted to just three
      types of commands:
          1.  single letter commands that don't have optional arguments
    	  (l,t,j,m,n,w have optional arguments)
          2.  command list in braces
          3.  user-defined procedure names
      This is to prevent disasters like
    	 list vertex 1293
      which before would produce 1293 lists of all vertices.   And
      'l 2' now subdivides edges longer than 2 instead of doing 2 l commands.

      "dump" without argument will dump to default file name,
       which is datafile name with .dmp extension.

      SIGTERM is caught and causes dump to default dump file and exit.
      This is so scripts running in the background can be stopped with
      kill -TERM.  SIGHUP acts the same way, so losing a modem connection
      saves the surface.

      Fixed bug that was causing crashes on Decstations.  Bug has been
      present for a long time, but just showed up because Dec handles
      reallocation of memory a little differently from everybody else.

    A student project.
    From: "John Oprea" <OPREA@csvaxe.csuohio.edu>

    I had two grad students do a comparison, using evolver, of minimal versus
    harmonic surfaces spanning a given curve? This all arose because one
    of our professors was telling students that a least area surface was
    z=f(x,y) with f harmonic. He had done two things: (1) read Courant-
    Hilbert where they use the standard perturbation argument to show that
    a least area surface is given by a harmonic function WHEN THE CURVE
    ISN'T TOO NONPLANAR (ie I think 4 th order partials are supposed to be
    negligible) and (2) read that a parameterization of a minimal surface
    has harmonic coord functions WITHOUT PAYING ATTENTION TO THE ISOTHERMAL
    COORD CONDITION. Anyways, these students took harmonic functions
    arising as the real or imaginary parts of analytic functions, lifted a
    circle to the resulting surface as a curve on the surface and used this
    as a bounding curve. They could, by hand, calculate the area of the
    harmonic surface bounded by the curve. They then used Evolver to evolve
    the surface into a minimal surface (with fixed curve of course) and saw
    how the area decreased, measuring the percentage change. Of course, just
    as Courant - Hilbert says, for circles of small radius the harmonic
    surface is close to minimal. Actually, if the radius was too small, it
    seemed that the comparison didn't go so well --- but we think there was
    truncation error or we needed to increase the number of fixed vertices or
    something along those lines. An outside possibility is that we somehow
    jumped to a new critical point of the area functional, but I don't think
    so. Also, they looked at examples like Enneper's surface where the
    least area surface for a bounding curve on Enneper's surface (1 < r < sqrt(3))
    is NOT Enneper's surface itself --- ie Enneper is minimal but not
    least area for some curves on it. Anyway, Evolver provided very
    beautiful illustrations of these principles. 'Nuff said. Bye.
                                                             John

    Bibliography:

    Frank Morgan and Jean E. Taylor, Destabilization of the
    Tetrahedral Point Junction by Positive Triple Junction Line energy,
    Scripta Metall. Mater. {\bf 25} (1991) 1907-1910.

    Livia Racz (racz@navier.mit.edu) sends the following:

    L.M. Racz, J. Szekely, "Solder Volume Estimation" in Handbook of Fine
    Pitch Surface Mount Technology, J.H. Lau, ed., Van Nostrand Reinhold
    Publishing Co., NY (in press).

     ==>This is a book chapter we were asked to write including an algorithm
     we developed to estimate an "optimal" volume for a particular lead wire
     and substrate geometry in surface mounted integrated circuits.  We used
     the Evolver to calculate the shapes of solder fillets with the different
     volumes we proposed.

    L.M. Racz, J. Szekely, 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).

       Revised reference from Newsletter 1.

    L.M. Racz, J. Szekely, "Determination of Equilibrium Shapes and Optimal
    Volume of Solder Droplets in the Assembly of Surface Mounted Integrated
    Circuits", ISIJ International, Vol. 33, No. 2, (February, 1993).

     ==>This is the paper based on which we were asked to write the chapter.
     Basically the same contents, but more condensed and less literature
     review.

     N.L. Abbott, G.M. Whitesides, L.M. Racz, J. Szekely, "Calculating the
     Shapes of Geometrically Confined Drops of Liquid on Patterned,
     Self-Assembled Monolayers; A New Method to Estimate Small Contact
     Angles" submitted to Journal of American Chemical Society.

      ==>Abbott and Whitesides have developed a way to pattern a substrate by
      deposition and etching with which droplets of liquid (water in this
      study) can be confined to desired patterns with great control, and with
      this, a new, easier way to measure contact angles.  They were able to
      verify their method with a contact angle goniometer for angles > 15
      degrees, but for angles < 15 degrees, they compared their results to
      calculations we did with the Evolver.

      L.M. Racz, J. Szekely, "Development of Design Guidelines for Specifying
      Solder Volumes in Surface Mount Technology", Proceedings of ASME Winder
      Annual Meeting, Anaheim, CA (November, 1992).

       ==>Contents pretty much the same as that of chapter.  All the authors
       were invited to give these talks about their chapters, and these were
       published in the proceedings.

       L.M. Racz, J. Szekely, "An Alternative Method for Determining
       Wettability of Components with Dissimilar Surfaces", submitted to
       Journal of Electronic Packaging.

        ==> A very nice Evolver application.  Circuit boards, because of the way
        they are made, have two opposite sides that are wet by the solder alloy, and
        two opposite sides that are not, resulting in a rather odd looking
        meniscus.  These boards are dipped into the alloy to test for the
        wettability of the two sides that are supposed to wet.  The force of
        wetting per unit length is calculated, and that number is used as an
        "index" to determine whether that particular board is OK to use.  This
        method is fine if the two opposing non-wetting sides are proportionally
        not too large in wetted perimeter, unduly influencing the force of wetting
        determination.  Currently, with this method, they are throwing out lots
        of perfectly good boards.  We say that this method is only useful for
        certain geometries/areas.  The menisci shown as part of these arguments
        are calculated with the Evolver.

    From John Sullivan, sullivan@geom.umn.edu:

       @Article{willmore,
            Author = "Lucas Hsu and Rob Kusner and John M. Sullivan",
            Title = "Minimizing the Squared Mean Curvature Integral for
            Surfaces in Space Forms",
            Journal = "Experimental Mathematics",
            Year = 1992, Volume = 1, Number = 3, Pages = "191--208"}
       We report on numerical experiments with the evolver, minimizing the
       Willmore elastic energy for closed surfaces of different genus.

       @Article{besic,
            Author = "John M. Sullivan",
            Title = "An Explicit Bound for the Besicovitch Covering Theorem",
            Journal = "J. Geometric Analysis",
            Year = 1993, Volume = "???", Pages = "???", Note = "Submitted"}
       We show that the constant needed in the proof of the Besicovitch Theorem
       is equal to the number of spheres that can be packed into one of 5 times
       the radius; experiments with the evolver have found lower bounds for this
       packing number (which are probably optimal) in dimensions three and four.

    End of newsletter 2.

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