BGA Example bga-3 for the Surface Evolver

This model is bga-2.fe with realistic surface tension and gravity.

Notable features:

• The surface tension of the liquid/air interface is defined as a parameter S_TENSION with a value of 480. This is applied as the "tension" attribute of the six side faces. A parameter is used instead of a macro so the value is conveniently available at runtime. Note that changing the parameter S_TENSION at runtime does not automatically change the surface tension of the facets.
• Gravity is implemented by defining "gravity_constant" as the appropriate value (980 here), and giving the body a density (9 here) for gravity to act on. The parameter SOLDER_DENSITY is defined for convenience at runtime.
• The Evolver itself does not know about units of measurement, so it is up to the user to use values in a consistent system of units, such as the cgs system used here.
• The dimensions of the system (height 0.12 cm and radius 0.10 cm) were chosen small enough so that gravity would not cause complete collapse of the system. To see collapse, try setting those parameters ten times higher and evolving.
• If only surface tension were involved, and not gravity, then the scale of the system would not matter, nor would the exact value of the surface tension, as far as getting the final shape, since the problem then reduces to minimizing surface area subject to a volume constraint.
• You may notice that the "gogo" command prints out an extra message

  Converting to all named quantities...Done.

  This is because the Hessian calculation for gravitational energy is implemented only as a named method, so doing "hessian" in "gogo" causes an automatic conversion of everything to named quantities and methods.