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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