| Slide 1 |
| Last time... |
| 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 |
| Slide 25 |