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Lecture 2: more singularities and ways to understand them
Estimating stretching energy from gaussian curvature
Numerical representation: Seung-Nelson lattice
d-cone from pushing sheet into container:
rim structure
Curvature cancellation is robust
Experiment shows curvature cancellation
Distant changes alter curvature cancellation
Known forces constrain rim curvature
What principle underlies the vanishing curvature?
Curvature cancellation conjecture
Foppl van Karmann equations
Foppl von Karmann equations dictate the equilibrium shape
Scaling of minimal ridge
Lobkovsky scaling prediction: strong focusing near vertex
Embedding singularities via nonuniform metric
The crumpled state: how strong? how heterogeneous?
Buckling ridges cause crumpling noise
Buckling cascade accounts for broad crumpling noise
How strong are real crumpled sheets? Mylar experiment
Open questions about the crumpled state
Conclusions about embedding singularities
Slide 23
Gaussian charge optimisation confirms ridge scaling
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