Figure 17: Mathematics is essential to designing electrolyte membranes that lie at the heart of
fuel cells. The green areas of this image are crystallized polymer, the white areas are
uncrystallized polymer, and the blue areas are water. The charges on the polymer force the water
into this convoluted shape. Credit: Zhengfu Xu, Keith Promislow, Andrew Christlieb, and Nir
Gavish.
The traditional approach has been to do an atom-by-atom simulation, butthis is untenably slow. Techniques from the field of differential geometry can
create a rich language to describe the shapes that the water can form and give a
much more powerful way of modeling them.
To meet the energy challenge, we need promising technologies like these.But another huge aspect of the challenge is scaling up laboratory techniques to
make them into economical solutions that will work on a large scale, which
requires major investment. A serious challenge is choosing which technologies to
invest in.
A natural first thought would be to let many flowers bloom and invest asmall amount in every promising technology. But technologies get cheaper the
more we invest: Investment spurs innovation and innovation spurs more
investment, as we’ve seen so powerfully with, for example, the development of
personal computers over the last few decades. So with new energy technologies,
we’ll get a much bigger return on our investment if we choose a small number of