Buckling cascade accounts for broad crumpling noise
crumpling burst happens when a ridge buckles:
big ridge=big sound ... small ridge=small sound
Ridges break into successively
smaller pieces––unevenly...say, 1/3 - 2/3
length= (2/3) (1/3) (2/3) (1/3)
1
2/3
1/3
2/3
after k
stages, length is a product of k random factors: each is (1/3) or (2/3)
log(length) is a sum of random
terms
Probability of (log(length)) ¨ gaussian
Probability of length ¨ log normal
distribution ~ 1/(length) for large k
... accounts for ~1/E
distribution of energies.
If E grows eg. as a power of
length, then probability of E also ¨ gaussian