

Scrunch time: The peculiar physics of crumpled paper - lucas3677
http://www.newscientist.com/article/mg21228441.700-scrunch-time-the-peculiar-physics-of-crumpled-paper.html?full=true

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ColinWright
This reminds me of the fixed point theorem. Take a sheet of paper, scrumple it
however you choose without tearing it. Place it over an unscrumpled copy of
the original, without going outside the edges.

Some point in the scrumpled version is exactly above its original position.

~~~
noblethrasher
That's actually an illustration of the Contraction Mapping Principle.

Another way of illustrating it is that if you're in city X and place a map of
city X on the ground, then exactly one point on the map will be above the
corresponding physical point.

~~~
srean
Contraction mapping is not really required for this phenomenon. Contraction
would mean that any two points are closer after the crumpling/mapping than
before. In fact contraction will guarantee that there is only _one_ such point
which lies over the other.

For the aforesaid property any form of crumpling that does not tear the paper
would suffice. Provided no part of the crumpled paper extends beyond the
boundary of the pristine sheet (or the city, in your example). The phenomenon
relies of Browder's fixed point theorem.

If it helps to reduce one dimension: think of a continuous curve defined over
a part of the x-axis [0, 10]. As long as the curve stays inside the box [0,0],
[10,10] and every point in the [0,10] part of the x-axis is mapped, it would
be impossible to avoid the diagonal. Just try it.

Incidentally, a generalization of the theorem above, called the Kakutani fixed
point theorem underlies John Nash's proof (that won him the Nobel) of the
existence of equilibria in games.

~~~
noblethrasher
Thanks!

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szopa
This reminds me that in Argentina in primary school we would make an
improvised football (as in: soccer) by crumpling some paper and then wrapping
it in scotch tape. It was of course much smaller than the real ball, but it
worked surprisingly well (and broken windows were not an issue). Now I know
why :-)

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Jun8
If you, like me, wonder how one can even get funding for research on crumpled
paper, Prof. Menon's research area is on condensed matter, "primarily on soft-
condensed matter systems".

Article passed on the interesting tidbit about Britney Gallivan
(<http://en.wikipedia.org/wiki/Britney_Gallivan>) and her paper folding
result.

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maeon3
Understanding the physics of why crumpled paper resists with a specific force
can help you design vehicle crumple-zone systems in cars which will save
occupants from head on crashes into trees, by having the entire engine crumple
with a pre defined resistance.

<http://en.wikipedia.org/wiki/Crumple_zone>

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javajosh
I understand how guessing at the particular pattern of a crumple is a hard
physics problem. What I do not understand is why understanding the macro-
properties of crumpled paper is a hard physics problem. For example:

"Do the balls absorb vibrations by trapping pressure waves or by dissipating
them? Nobody knows, says Menon, 'but it means there are still plenty of
beautiful problems to keep me interested'."

This seems like a rather odd thing to say. What does "trapping pressure waves"
even mean? Is Menon asserting that, when I take my shipment out of the
container, all of the vibration that the package suffered on its journey is
still swirling around in all the crumpled paper?

It's laudable to study everyday physics, but at least when it comes to macro-
behavior of crumpled paper, these research questions appear laughable.

~~~
jerf
"What I do not understand is why [several things]..."

"... these research questions appear laughable."

How about before declaring these questions laughable, you try a little harder
to understand why they are interesting? For instance, the fact that we don't
have computers powerful enough to simply simulate the question being asked
provides one clue of a possible reason why this is more interesting than you
think.

Either one of "I don't understand this research" or "this research is
laughable" I might accept from a given person, but the combination is
unpleasant.

~~~
javajosh
I have a degree in physics, so I guess it was a mistake to leave out the (two)
punchlines and leave them implied:

1\. "absorb vibrations by trapping pressure waves" is a meaningless concept in
physics. Sponges, rubber, styrofoam, springs and crumpled paper all "absorb
vibration" in the same way - converting mechanical energy into heat. Apart
from a rather pedantic system in which somehow air pressure is used to add
angular velocity to a flywheel, there is no sense in which vibrations are
"stored". There is also the case of an irreversible deformation, as when a car
crumples. And in that case, the object would become monotonically less capable
of absorbing energy - a curve that would be easy to measure (place crumpled
paper in a vice, repeatedly attempt to squeeze a bit, measure maximum and
minimum circumference, repeat, graph)

2\. Thermodynamically, any excess energy is going into heat. Period. This
could be tested by very carefully measuring the temperature of the crumpled
paper before and after being deformed several times, as with the vice above.
Eventually (and with paper, sooner rather than later) there's going to be
microscopic breakdown at the fiber and even molecular levels, and that
increase in entropy must be factored in, too. (Now that is an interesting
experimental challenge: how to measure the "looseness" of paper fiber in a
crumpled sheet. There are some easy destructive ways but I cannot think of any
non-destructive ones.)

So yes, I call shenanigans on this professor and, apart with the (already
admittedly) interesting problem of describing the geometry of particular
crumples, I think his research is laughable. Although I would enjoy being
shown how I am in error, if that be the case.

~~~
jerf
"I have a degree in physics,"

... in which case you really ought to know better than to accept a popular
press summation of somebody's research as accurate.

