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