implications
of stretching ridges
Condensation: ridge energy occupies arbitrarily small
fraction w/X of system
Self-consistency: Bending radius
w >> h, strain << 1,
... justifying smooth deformation (linear elasticity)
assumption
Ridge energy ~ (X/h)1/3
>> vertex energy ~
log (X)
ridges dominate the
energy of thin sheets
ridge creates a confining potential between vertices
X
energy
separation X
robust: ridges occur
whenever high curvature is imposed at two separate points