Videos

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.