Tombstone Example tomb-HH for the Surface Evolver

[Click for the tomb-HH.fe datafile in a second window.]

This model is the tilted chip of tomb-F.fe modified to be suitable for letting the chip move in response to the forces on it.

Notable features:

• The chip is made to move by making x0, y0, z0, and/or tilt into optimizing parameters. Optimizing parameters are free to move during evolution, just like vertex coordinates. Tilt is the most interesting, and x0 next. Everything is symmetric in y, so optimizing y0 is not interesting. And optimizing z0 just lets the chip move down through the pad, since the solder pulls it down.
• One can make tilt into an optimizing parameter by declaring it an optimizing_parameter in the datafile, or at runtime with "unfix tilt". It can be made normal again with "fix tilt".
• Gradients for optimizing parameters are found by finite differences, and motions are made by simply changing the parameter. No fancy rountines like change_tilt are used. The motions involved are small, but to make the chip move coherently, the chip display geometry has been converted to a three-parameter "boundary" representation.
• Optimizing parameters are likely to have a mismatch in the magnitude of their gradient, compared to vertex coordinates. This can make the optimizing parameter evolve much faster or much slower than vertex coordinates. To provide a better speed match, a parameter may be given a "scale" parameter in the datafile, which multiplies the parameter gradient to give the parameter velocity. The value of 1e8 was determined by experimentation to do a good job.
• With the chip free to move, gravitational forces on the chip should be taken into account. Therefore, the chip is represented as body 2, with a density for gravity to act on.