Tom Witten, U. of Chicago
Generalized crumpling: how smooth forces make sharp structures.
Physics Division Colloquium - 8 Feb. 2002

When you confine a piece of paper in a shrinking sphere, sharp points and lines of strong deformation appear: the paper crumples. Recently powerful scaling laws have shown that many features of the crumpled structure are universal properties of any elastic sheet. For example the deformation energy must condense into an arbitrarily small fraction of the sheet as its thickness diminishes: the condensed fraction varies with the thickness to the 1/3 power. This condensation is driven by a competition between bending energy and stretching energy. Analogous condensation should occur whenever a space with a preferred metric is appropriately deformed. To understand this condensation more deeply, we explore how sheets deform in general spatial dimensions. Three different forms of deformation emerge as one varies the dimension of space.

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