Embedding
singularities via nonuniform metric
–E. Sharon,et. al. Nature 419
579 (2002); B. Audoly & A.
Boudaoud. Phys. Rev. Lett. 91, 096105 (2003).
ds02= (1 + g0(y)) dx2 + dy2
y
x
g0
y
flat sheet is compressed
at the boundary
stress can be relaxed
by bending, with gaussian curvature C0
C0 È ¦y ¦y g0
(Gauss embedding
theorem)
actual gaussian
curvature c1c2: balance bending and stretching energy ~ g2(area)
narrow strip: single
wave suffices
b
wide strip: more waves
needed to counter increasing
g near edges
g ~ c1c2 b2
hierarchy of waves
edge of torn plastic
bag