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arXiv · 2503.16701

Sub-singularities for shaping thin sheets

Thomas A. Witten·Anna Movsheva
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Abstract

The principles behind the sharp, singular structures in a crumpled sheet are well understood. Here we discuss more general ways of exploiting such sharp structures to control the shape of a sheet by deforming or forcing it elsewhere. Often, the induced shape leads to further sharp structures -- ``sub-singularities". Though weaker and softer than the primary singularities, they nevertheless provide robust ways of shaping a sheet. In simple cases we understand the reason for these and their strength. This paper surveys a broad range of other sub-structure phenomena and reports recent progress in understanding some of them.

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Thomas A. Witten, Anna Movsheva. 2025-03-20. Sub-singularities for shaping thin sheets. https://arxiv.org/abs/2503.16701

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