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In 1970, an astrophysicist alleged Koryo Miura conceived what would become one of the best acclaimed and well-studied folds in origami: the Miura-ori. The arrangement of creases forms a arrangement of parallelograms, and the accomplished anatomy collapses and unfolds in a distinct motion—providing an affected way to angle a map. It additionally accepted an able way to backpack a solar console for a spacecraft, an abstraction Miura proposed in 1985 and again launched into absoluteness on Japan’s Space Flyer Unit accessory in 1995.
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Origami Evening Dress. Origami instructions, how to make a paper ... | Origami Dress Step By StepOriginal adventure reprinted with permission from Quanta Magazine, an editorially absolute advertisement of the Simons Foundation whose mission is to enhance accessible compassionate of science by accoutrement assay developments and trends in mathematics and the concrete and activity sciences.
Back on Earth, the Miura-ori has connected to acquisition added uses. The angle imbues a billowing area with anatomy and stiffness, authoritative it a able metamaterial—a absolute whose backdrop depend not on its agreement but on its structure. The Miura-ori is additionally different in accepting what’s alleged a abrogating Poisson’s ratio. Back you advance on its sides, the top and basal will contract. But that’s not the case for best objects. Try binding a banana, for example, and a blend will eject out from its ends.
Researchers accept explored how to use Miura-ori to body tubes, curves and added structures, which they say could accept applications in robotics, aerospace and architecture. Alike appearance designers accept been aggressive to absorb Miura-ori into dresses and scarves.
Now Michael Assis, a physicist at the University of Newcastle in Australia, is demography a acutely abnormal access to compassionate Miura-ori and accompanying folds: by examination them through the lens of statistical mechanics.
Assis’ new analysis, which is beneath assay at Concrete Assay E, is the aboriginal to use statistical mechanics to alarm a accurate origami pattern. The assignment is additionally the aboriginal to archetypal origami application a pencil-and-paper access that produces exact solutions—calculations that don’t await on approximations or after computation. “A lot of people, myself included, alone all achievement for exact solutions,” said Arthur Evans, a algebraic physicist who uses origami in his work.
Traditionally, statistical mechanics tries to accomplish faculty of appearing backdrop and behaviors arising from a accumulating of particles, like a gas or the baptize molecules in an ice cube. But bulge patterns are additionally networks—not of particles, but of folds. Application these conceptual accoutrement commonly aloof for gases and crystals, Assis is accepting some arresting insights.
Assis at the University of Newcastle in Australia.
JAMES HORAN/QUANTA MAGAZINE
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Origami Evening Dress. Origami instructions, how to make a paper ... | Origami Dress Step By StepIn 2014, Evans was allotment of a aggregation that advised what happens to Miura-ori back you bandy in a few defects. The advisers showed that by inverting a few creases, by blame on a arched articulation to accomplish it biconcave and carnality versa, they could accomplish the anatomy stiffer. Instead of actuality a flaw, they found, defects could be a feature. Aloof by abacus or adding defects, you can configure—and reconfigure—a Miura-ori to be as annealed as you want.
This drew the absorption of Assis. “No one had absolutely anticipation about defects until this paper,” he said.
His ability is in statistical mechanics, which applies artlessly to a filigree arrangement like Miura-ori. In a crystal, atoms are affiliated by actinic bonds. In origami, vertices are affiliated by creases. Alike with a filigree as baby as 10 units wide, Assis said, such a statistical access can still abduction its behavior adequately well.
Defects arise in crystals back you crank up the temperature. In an ice cube, for example, the calefaction break the bonds amid baptize molecules, basal defects in the filigree structure. Eventually, of course, the filigree break bottomward absolutely and the ice melts.
Similarly, in Assis’ assay of origami, a college temperature causes defects to appear. But in this case, temperature doesn’t accredit to how hot or algid the filigree is; instead, it represents the activity of the system. For example, by again aperture and closing a Miura-ori, you’re injecting activity into the filigree and, in the accent of statistical mechanics, accretion its temperature. This causes defects because the connected folding and advance ability account one of the creases to angle the amiss way.
But to accept how defects grow, Assis accomplished that it’s bigger not to appearance anniversary acme as a particle, but rather anniversary defect. In this picture, the defects behave like free-floating particles of gas. Assis can alike account quantities like body and burden to alarm the defects.
A birthmark in a Miura-ori pattern.
James Horan/Quanta Magazine
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origami folds in dresses - Google Search | Flat Pattern Drafting ... | Origami Dress Step By StepAt about low temperatures, the defects behave in an alike fashion. And at aerial abundant temperatures, back defects awning the absolute lattice, the origami anatomy becomes about uniform.
But in the middle, both the Miura-ori and addition trapezoidal origami arrangement arise to go through an brusque about-face from one accompaniment to another—what physicists would alarm a appearance transition. “Finding that origami can accept a appearance alteration to me was very, absolute exciting,” Assis said. “In a sense, it shows origami is complex; it has all the complexities of real-world materials. And at the end of the day, that’s what you want: real-world metamaterials.”
Without accomplishing experiments, Assis said, it’s adamantine to say absolutely how the origami changes at this alteration point. But he hypothesizes that as defects multiply, the filigree steadily becomes added disordered. Beyond the alteration point, there are so abounding defects that the accomplished origami anatomy becomes ample in clutter. “It’s about as if you’ve absent all order, and globally, it’s behaving affectionate of randomly,” he said.
Yet appearance transitions don’t necessarily appearance up in all types of origami. Assis additionally advised a arrangement of squares and parallelograms alleged Barreto’s Mars. This arrangement doesn’t abide a appearance transition, which agency you can add added defects after breeding boundless disorder. If you appetite a metamaterial that can bear added defects, this arrangement ability be the way to go, Assis said.
Defects additionally abound abundant faster on the Miura-ori and trapezoid patterns than on Barreto’s Mars. So if you’d rather accept a metamaterial on which you can accomplished tune the cardinal of defects, the Miura-ori or a trapezoid would be a bigger design.
Whether these abstracts absolutely administer to real-world origami is up for debate. Robert Lang, a physicist and origami artist, thinks that Assis’ models are too arcadian to be of abundant use. For example, Lang said, the archetypal assumes the origami can be fabricated to angle collapsed alike with defects, but in reality, defects can anticipate the area from flattening. The assay additionally doesn’t absorb the angles of the folds themselves, nor does it forbid the area from intersecting with itself as it folds, which can’t appear in absolute life. “This cardboard doesn’t absolutely appear abutting to anecdotic the behavior of absolute origami with these bulge patterns,” Lang said.
But the assumptions in the archetypal are reasonable and necessary, abnormally if we appetite exact solutions, Assis said. In abounding engineering applications, such as the folding of a solar panel, you appetite the area to angle flat. The act of folding can additionally force defects to flatten. The angles of the folds may be important about defects, abnormally back you additionally accede that the faces of the filigree can warp. Assis affairs to abode such “face bending” in consecutive work.
Unfortunately, the catechism of all-around flat-foldability is one of the hardest mathematics problems around, which is why best advisers in the acreage accept bounded collapsed foldability, said Thomas Hull, a mathematician at Western New England University and a co-author of the 2014 study. These kinds of assumptions, he said, accomplish sense. But he admits that the gap amid approach and designing absolute metamaterials and structures charcoal wide. “It’s still not bright whether assignment like Michael’s is activity to advice accord us things that we can do in practice,” he said.
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Natalie Wolchover
Natalie Wolchover
To acquisition out, advisers will charge to backpack out abstracts to analysis Assis’ account and barometer whether the models can absolutely acquaint the architecture of origami structures, or if they’re toy models of absorption alone to theorists in statistical mechanics. Still, this affectionate of abstraction is a footfall in the appropriate direction, Hull said. “These are the basal architecture blocks we charge in adjustment to use this being for real.”
Christian Santangelo, a physicist at the University of Massachusetts, Amherst, who additionally collaborated on the 2014 paper, agrees. Not abundant advisers are arrest the botheration of defects in origami, in his opinion, and if anything, he hopes this assignment will get added bodies to anticipate about the problem. “Of the bodies who are absolutely architecture things, it doesn’t assume to be on their radar,” he said. Whether it is or not, origami technology will crave a accurate application of defects. “These structures,” he said, “aren’t aloof activity to angle themselves.”
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Making Cocktail Dress Origami | Paper Origami Guide | Origami Dress Step By StepOriginal adventure reprinted with permission from Quanta Magazine, an editorially absolute advertisement of the Simons Foundation whose mission is to enhance accessible compassionate of science by accoutrement assay developments and trends in mathematics and the concrete and activity sciences.
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