Magnetic flux tubes, elastic rods and uniformly charged loops
Magnetic flux tubes are often compared with elastic rods because the two
share similar properties. Recent results, however, show us few
surprises about the analogy. In particular, the energy of a magnetic
flux tube may decrease when local curvature of the tube axis increases;
this is in contrast with the case of an elastic rod. As a comparison,
we investigate a uniformly charged, flexible but inextensible loop
numerically. Locally, the loop behaves like an elastic rod. Globally, it
is never self-intersecting when some artifical physics are used (cf.
Freedman et al, Annal of Maths 134 (1994), pp. 189-229). The similarities
and differences of these three types of objects are discussed.
This paper (AMS paper no. 909-57-267) was presented in
The 909th AMS meeting: Special Session on
PHYSICAL KNOT THEORY, 22-23 March 1996, Iowa City, Iowa, US.
Magnetic flux tubes, elastic rods and uniformly charged loops 