Towards a statistical physics of crumpled elastic structures?
Presenter
July 24, 2008
Keywords:
- Elastic
MSC:
- 74B10
Abstract
Low dimensional elastic manifolds (such as rods 1D or sheets
2D) have been drawing a lot of attention lately. When confined into
environments smaller than their size at rest, elastic objects sustain
large deformations involving many fascinating mechanisms such as energy
condensation from large length-scales to small singular structures,
topological self-avoidance, complex energetical landscapes... One only
needs to crumple a piece of paper to observe the extreme complexity of
fold patterns generated. This begs the question: Is there an underlying
statistical mechanics foundation?
By studying the isotropic compaction of elastic rods in a 2D space via
experiments and numerical simulations, we have been able to gain some
encouraging insight into this question. It turns out that the rod can be
decomposed into more basic elements whose energy distribution display a
Boltzmann-law like behavior containing an "effective" temperature. The
comparison between experiments and numerical simulations ensure of the
robustness of this result. Moreover thermal equilibration does occur
between geometrically different subsystems. These results put on firm
ground the underlying statistical nature of crumpling phenomena and their
implications will be discussed in light of some recent theoretical work.