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 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231  Surface Evolver Documentation - Newsletter 2
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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