| Slide 1 |
| Òenergy condensationÓ in matter |
| Elastic focusing: sharp structure from smooth forcing |
| Singularities in thin sheets I |
| Conditions for crumpling: thin elastic manifold |
| Bending vs stretching when thickness h ¨ small |
| Confining an unstretchable object |
| When does curvature create stretching in d dimensions? |
| For what dimensions does confinement make vertices? ridges? |
| Isometric (unstretchable) limit accounts for singularities |
| Slide 11 |
| Energy of an isolated vertex is logarithmic |
| Òkite shapeÓ explains emergent width scale w of ridge |
| numerics confirm scaling of curvature profile with thickness |
| virial theorem confirms stretching-bending competition |
| implications of stretching ridges |
| growth of ridge energy with opening angle a |
| Induced edge singularities |
| Induced edges are weaker than real ridges |
| Unstretchable d-cone: sets stage for d-cone puzzles |
| D-cone core: what limits the focusing? |
| Simulation tests scaling of Rc |
| Slide 23 |
| Gaussian charge optimisation confirms ridge scaling |
| Curvature constraints from Gauss Bonnet theorem |