this is the way the paper crumples - mylar sheets for sale
In the past few years, when Omer Gottesman was working on his doctoral thesis at Harvard, he spent a lot of time at his desk crushing a piece of paper, especially when he was stuck
He would wrinkle a piece of paper, wrinkle it, stare deep into it, and think, "there must be something that would make all these messy things look less messy.
"Crumpled, not crumpled, crumpled.
Falling in the recycle bin one by one, each blank, but the location is chaotic.
Over time, the appearance of an order appears.
The crumpled paper Regiment is undoubtedly as old and ordinary as the paper itself --
"Sweep the tomb for the theory of failure . "
The physicist Gottesman called them.
But for him, the crumpled piece of paper was a study in itself.
The dynamics of collapse are everywhere: in the initial unfolding of insect wings;
In the way DNA is packaged into a nucleus, in the challenge of how best to plug a giant solar sail into a small satellite to make it successful.
Scientists, in turn, put a lot of effort into deciphering and trying to reduce this complexity and confusion.
Paper is an ideal model.
"Although it is obviously easy for a piece of paper to be crumpled away, crumpled dynamics are often considered a complex paradigm ,"
Gottesman noted in a research paper published in the journal Communication physics earlier this month.
"A key assumption made by physicists is that there are some common universal properties between many disordered complex systems," he said recently . ".
"Studying a complex system can also teach us a lot about other systems. ”[
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British concept artist Martin cred once said, "I think you can see the epitome of the world in a work.
"1995 of his creations have achieved as much," he said.
A ball of A4 paper.
In that crumpled sphere.
Like a planet of unstable structure seen from a distance.
Complex and chaotic, deformed and chaotic.
In the same year, two French physicists Mattin Bin Amar and Yves boméu from the Paris Higher Normal College also participated in a three-
Page magazine article, "Papier froisé.
Inside it, they introduced crumpled paper atoms, d-
Cone: the tip of the cone formed when you put a piece of paper on the cup and press it in with a pencil. (
The crumpled ball is d-
A cone connected by a ridge. )
"Papier froisé" is a 26-
The English version is "crumpled paper.
The author ends up wondering if the same topological concept of curvature applies to general relativity.
So we started an early chapter in physics and mathematics of crumpled paper.
Now, the latest progress is with Mr.
Gottesman's recent contribution to the "state variable of crumpled flakes" suggests that crumpled dynamics may not be complicated after all.
"The surprising result is that it is very, very simple," said Shmuel M . "
Rubinstein is a physicist and a major researcher in the study.
Most of the work was done by Goldman.
"What Omer is showing is that it is considered the most important aspect of the phenomenon of real confusion --
A paradigm of confusion, complexity, and uncertainty, like a butterfly --flapping-its-The metaphor of wings
Very predictable, deterministic and simple.
"The method is simple anyway. In the lab, Mr.
Goldman crushed hundreds of sheets of paper in a cylindrical container.
This is a scientific paper, the elastic-plastic Mylar sheet, which is unlikely to cause paper cuts or wither into tissue when repeatedly crumpled.
Some early commissioning was posted on his website called "interesting paper material", including a vertical tube of paper with an empty coffee can "kvetching. (
"Kvetch" is a word of Yiddish, which usually means "complaining", but literally means "squeezing" or "pressing" to become a lovely term in the lab, A stack of paper complains about their fate. )
Sir, it's like a palm reader seeing a lifeline intuitively.
Goldman analyzed the creases of crumpled paper and tried to sort out a variable, an equation, a law --
Predict what happens to the next crash.
He studied many variables: the range of the length of a single crease;
The distance between creases;
The largest patch without creases;
The sharpness of the crease, and the amount of energy required to cause the crease.
He observed that a piece of paper had never stopped forming new creases, even though their formation slowed down in numbers.
With each new fold, the paper folds along some of its existing scars, but one day it will take a new fold to continue the fold.
"I crumpled up to 70 times in the lab . "Gottesman said.
"Usually after four or five times, it's really hard for you to see the difference between a crumpled to the next crumpled.
However, he did notice a trend that after each wrinkle, the cumulative total length of all the creases on a piece of paper.
In the lab, this variable is called "Mileage ". ”As Mr.
Gottesman crumpled scanned each sheet of paper into his computer and then measured the sum of all the creases with an algorithm.
He found that if he had wrinkled two separate sheets, each sheet would have accumulated damage in a unique way as expected.
But the crease length of the two sheets is very similar.
Length seems to be a deterministic variable.
Known as a state variable, predict how the creases network will evolve.
"The detailed history of the folds is written into the intricate pattern of folds," he said.
Goldman and his colleaguesauthors wrote.
"No two crumpled sheets are the same.
However, there is actually no memory of this document.
In every crumpled state, the intricate pattern of creases and events that lead to creases are irrelevant.
All it takes to predict the next State of the paper is the total length of the crease in the current state.
"You only care about the current state ,"Gottesman said.
News of crumpled paper obeying state variables-
Or crease, or damage.
As the author points out, it represents a "significant reduction in complexity" and is therefore surprised and pleased at the college.
"The idea that crumpled can be described in simple numbers and crumpled lengths is very interesting," said the doctor . "Ben Amar.
"It would be great if this experimental work continued through theoretical treatment "-
That is, the equation derived from the law of elasticity.
Thomas Witten, a physicist at the University of Chicago, found the result shocking and confusing.
"It could be very exciting," he said . "
Witten's research shows that each material is broken in roughly the same way
A plate of construction, a cell membrane, a graphene in a pirate ball, the fabric of the right sleeve of the Mona Lisa depicted by Leonardo da Vinci, which for the doctor
Witten, folded up in a way that reminds people of human ears. For Dr.
The loss Act is encouraging.
This suggests that other complex phenomena may be presented in a similar way --
"The more mysterious system, where you don't see scars and breakage very easily," he said . ".
Why, for example, do different proteins fold so reliably into similar shapes and under what conditions do they not fold?
With the newspaper, he said, "we are doing something very arbitrary.
We're crashing, squashing, squashing.
Basically, we're just a loop system.
"Many systems, including the human body, work the same way," he said.
"We are looking at how damage and defects accumulate, which is a big problem in the field of materials science and engineering.
When will something go wrong?
How will it break?
These are things of the most uncertain statistical nature.
There is nothing we can do about them.
But at least for crumpled paper, nature seems to be going beyond that uncertainty.
"The demise of paper has been around for a while, but it seems that paper may not be done with us.
Paper goes beyond history in many ways.
Its scars and creases may even be a potential philosophy.
"This is a good metaphor . "
"Because it's hard to imagine that the future depends only on the current situation.
We are a powerful feature of history-
Personal history, global history, etc.
To say that our future really depends only on our current mindset, not how it develops, and how we get to this point, is indeed counter-intuitive.
"We have the same intuition for any complex system: its evolution is very strongly dependent on many points of time, many degrees of freedom, and you have to know many of them.
It's not a big deal to find you.