Buckling
cascade accounts for broad crumpling noise
crumpling burst happens when a
ridge buckles:
big ridge=big sound ... small ridge=small soundRidges 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