- Series
- School of Mathematics Colloquium
- Time
- Tuesday, September 3, 2013 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skyles 006
- Speaker
- Robert Finn – Stanford University
- Organizer
- Karim Lounici
During the 17th Century the French priest and physicist Edme Mariotte observed
that objects floating on a liquid surface can attract or repel each other, and he attempted
(without success!) to develop physical laws describing the phenomenon. Initial steps
toward a consistent theory came later with Laplace, who in 1806 examined the
configuration of two infinite vertical parallel plates of possibly differing materials, partially
immersed in an infinite liquid bath and rigidly constrained. This can be viewed as an
instantaneous snapshot of an idealized special case of the Mariotte observations. Using the
then novel concept of surface tension, Laplace identified particular choices of materials and
of plate separation, for which the plates would either attract or repel each other.
The present work returns to that two‐plate configuration from a more geometrical
point of view, leading to characterization of all modes of behavior that can occur. The
results lead to algorithms for evaluating the forces with arbitrary precision subject to the
physical hypotheses, and embrace also some surprises, notably the remarkable variety of
occurring behavior patterns despite the relatively few available parameters. A striking
limiting discontinuity appears as the plates approach each other.
A message is conveyed, that small configurational changes can have large
observational consequences, and thus easy answers in less restrictive circumstances
should not be expected.