Discrete Folding
Mark Bowick, Philippe Di Francesco, Olivier Golinelli, Emmanuel, Guitter

TL;DR
This paper investigates folding models of a triangular lattice in discrete space to understand crumpling transitions in membranes, revealing a first-order transition in 3D folding on a face-centered-cubic lattice.
Contribution
It introduces a 96-vertex model for 3D folding and analyzes the phase transition from crumpled to flat states.
Findings
3D folding exhibits a first-order transition.
Model captures crumpling behavior of membranes.
Both planar and 3D folding cases are studied.
Abstract
Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a face-centered-cubic lattice are treated. The 3d-folding problem corresponds to a 96-vertex model and exhibits a first-order folding transition from a crumpled phase to a completely flat phase as the bending rigidity increases.
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Taxonomy
TopicsAdvanced Materials and Mechanics · Modular Robots and Swarm Intelligence · Structural Analysis and Optimization
