Jeffrey Elms



At the start of the REU program I was interested in two experiments involving
the rotation of liquids.  One is Plateau's rotating drop and the other the
rotation of a cylindrical container of liquid.

Plateau's rotating drop is the rotation of an independent drop of a liquid free
of the effects of gravity.  This experiment is performed by suspending a drop
of oil in an equally dense immiscible liquid.  We used a ethanol/water mix to
achieve this.

Several questions were raised during seminars given by Dr. McCuan at the
beginning of the summer.  Several variational problems are known to have
solutions that can be obtained by rolling a curve on an axis and following the
path of a point in relation to the curve.  The most famous of these are
Delaunay's minimal surfaces.  We asked if such an interpretation is possible
with Plateau's rotating drop.

The second experiment was the rotation of a cylindrical container of liquid. 
This is simple in concept but difficult due to the fact that it must be rotated
on the exact center of the container.  The experiment was postponed because of
the difficulties and the need to focus efforts on Plateau's experiment.  

To answer whether we reached our goals, the answers is clearly that we didn't. 
However, to answer whether our efforts paid off is still to be seen. 
Unfortunately we have not seen our research bear fruit, but it perhaps it
will.  For the short period of time and the steep learning curve, I think we
did quite well.

As the ACE lab is very new, we had to figure out ways to build the apparatus
and take data.  Sometimes we had to wait for equipment.  To compute the
solutions, we created a model, from mathematics and physics. To compute the
solutions to our equations we used computers but ran into problems, as we had
little experience solving complex problems.  To analyze our experiments we
asked specific questions about the relationship of our solutions to the rolling
of curves on an axis.  If we didn't remain focused we could easily find
ourselves attacking many problems simultaneously, which I often found myself
doing.

I started this summer with a rigid schedule in mind.  I learned very quickly
that research is everything but rigid: The questions aren't static, they
multiply.  I learned how one can put a lot of effort and get no results and
other times results seem to be immediate.  

I hope the ACE lab will be more productive in the future now that it has a
large base of equipment available and will likely have more students.