Minicourse: Calculus of Variations
I. The
parsimonious universe
The title page
of the book by
S. Hildebrandt and A. Tromba . The book contains an abundance of examples that show how
nature finds optimal shapes and forms.
The surprising elastic behavior of
shape memory wires is
related to microstrucutes
in the material that can be interpreted as minimizing sequences. Note the
needle-like
stuctures at the interfaces.
Tom Shield's
homepage has pictures that show different microstructures in Cu-Al-Ni single crystals.
Many materials display fascinating strucures at small scales. Here are
pictures from liquid crystals.
Magnetic bit structures are of
of fundamental importance in the design of mass data storage devices.
III. Bridge the scales!
Fine scale structures often have a temendous impact on the macroscopic behaviour
of the system. Here is an example in biology, the so-called
lotus effect.
Some pictures related to this:
the lotus plant
the non-wetting surface
dust on a leaf
a water drop on a leaf
A completely different system are
nematic elastomers
with potential applications to
artificial muscles.
Some figures related to experiments and numerical simulations of nematic elastomers:
the macroscopic phase diagram
the experimental stress-strain diagram
the numerical stress-strain diagram for the thin
film limit of the Verwey, Warner, and Terentjev model
recent experiments by Robert B. Meyer (Brandeis)
Georg Dolzmann
Last modified: Tue Feb 17 19:15:57 EST 2004
