# gst: complexity of a flat-foldings random origami

AA << give the result of approximate enumeration of the total number of flat-foldings of single-vertex origami diagram with random width of angles gathering around the central vertex, and obtain its size dependence for an asymptotic prediction towards the limit of infinite size. >>️

<< In addition, an outlook with respect to the chained determination of local stacking orders of facets caused by the constraint that prohibits the penetration of them is also provided from the viewpoint of organizing the terms included in the physical model. A method to efficiently solve the problem of the determination or enumeration of flat-foldings is discussed based on the above perspectives. >>️

Chihiro Nakajima. An Efficient Enumeration of Flat-Foldings : Study on Random Single Vertex Origami. arXiv: 2409.03240v1 [cond-mat.stat-mech]. Sep 5, 2024.

https://arxiv.org/abs/2409.03240

Also: origami, kirigami, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, origami, kirigami 

# gst: kirigami exposed to external flows.

<< Kirigami patterned materials have found several applications in recent years due to their ability to assume complicated shapes and exhibit emergent physical properties when exposed to external forces. >>️

<< Consisting of an array of cuts in a thin material, fabrication of these patterns can be quite simple. Here (AA) show that when they are placed in fluid flow, kirigami cut sheets with various patterns produce a verity of flow patterns in the wake. Through several sets of experiments, (AA) show that the kirigami sheets placed in flow can undergo static or dynamic flow-induced instabilities as a result of which they can buckle or undergo limit cycle oscillations, or they can remain stable while undergoing very large elongations. >>️

<< The ability to create controlled small-scale vortex shedding, induce desired flow-induced instabilities on structures, and form specifically-angled jets will enable several future applications in flow mixing (e.g., by producing small vortices in uniform flow at low Reynolds numbers), flow control (e.g., by controlling the direction and the number of jets that are produced downstream), and underwater soft robotics (e.g., by imposing desired flow-induced oscillations on structures). >>

️

Adrian G. Carleton, Yahya Modarres-Sadeghi. Kirigami Sheets in Fluid Flow.  arXiv: 2311.09381v1 [physics.flu-dyn]. Nov 15, 2023. 

https://arxiv.org/abs/2311.09381

Also: kirigami, origami, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, kirigami, origami, fluid flows, vortex

# gst: shape-shifting architecture inspired by metamorphosis, the metamorphosis kirigami system.

<< Kirigami is a variation of origami that involves cutting and folding paper. But while kirigami traditionally uses two-dimensional materials, Yin (Jie Yin) applies the same principles to three-dimensional materials. The metamorphosis system starts with a single unit of 3D kirigami. Each unit can form multiple shapes in itself. But these units are also modular—they can be connected to form increasingly complex structures. Because the individual units themselves can form multiple shapes, and can connect to other units in multiple ways, the overall system is capable of forming a wide variety of architectures. >>

<< The system we've developed was inspired by metamorphosis, (..) With metamorphosis in nature, animals change their fundamental shape. We've created a class of materials that can be used to create structures that change their fundamental architecture. (..) Think of what you can build with conventional materials, (..) Now imagine what you can build when each basic building block is capable of transforming in multiple ways.  (..) The metamorphosis kirigami system does not allow you to disassemble a structure, (..) And because the sides of each cubic unit are rigid and fixed at 90-degree angles, the assembled structure does not bend or flex very much. However, the finished structure is capable of transforming into different architectures.>> Jie Yin.️

Matt Shipman. Inspired by metamorphosis, researchers create materials for shape-shifting architecture. North Carolina State University. Sep 08, 2021. 

https://phys.org/news/2021-09-metamorphosis-materials-shape-shifting-architecture.html  

Yanbin Li, Jie Yin. Metamorphosis of three-dimensional kirigami-inspired reconfigurable and reprogrammable architected matter. Materials Today Physics, 21, 100511. doi: 10.1016/ j.mtphys.2021.100511.

https://www.sciencedirect.com/science/article/abs/pii/S2542529321001723

Also

keyword 'origami' in FonT

https://flashontrack.blogspot.com/search?q=origami

Keywords: gst, origami, kirigami, architecture, bifurcation, metamorphosis,  reconfigurability, reprogrammability.

# gst: apropos of the structure of natural codes, a RNA folding knot (origami-style) dance

 << Every second, a myriad of shapeless strands of RNA fold, origami-style, into intricate structures inside living cells. Now, for the first time, researchers can watch a data-driven video of this folding as RNA molecules are made by the cellular machinery. >> 

<< as the RNA strand grows, it twists, forming knot-like structures. But as more RNA building blocks are added to the strand, the knots unravel, allowing the molecule’s structure to emerge. >> 

Ground-breaking films show RNA’s complex curves take shape. Experimental data and predictive algorithms combine to reveal the essential biomolecule’s shape-shifting.

Nature. Jan 19, 2021. 

https://www.nature.com/articles/d41586-021-00126-8

AA << model the folding of an RNA called SRP, an ancient RNA found in all kingdoms of life. The molecule is well-known for its signature hairpin shape. When watching the videos, the researchers discovered that the molecule ties itself into a knot and unties itself very quickly. Then it suddenly flips into the correct hairpin-like structure using an elegant folding pathway called toehold mediated strand displacement. >>

<< To the best of our knowledge, this has never been seen in nature, (..) We think the RNA has evolved to untie itself from knots because if knots persist, it can render the RNA nonfunctional. The structure is so essential to life that it had to evolve to find a way to get out of a knot. >> Julius Lucks. 

Amanda Morris. New Videos Show RNA as it's Never Been Seen. First-ever data-driven movies illuminate RNA's mysterious folding process.  McCormick School of Engineering. Jan 15, 2021.

https://www.mccormick.northwestern.edu/news/articles/2021/01/new-videos-show-rna-as-its-never-been-seen.html 

https://youtu.be/2XTi9LG9NnU

Angela M Yu, Paul M. Gasper, et al. Computationally reconstructing cotranscriptional RNA folding from experimental data reveals rearrangement of non-native folding intermediates. Molecular Cell. doi: 10.1016/ j.molcel.2020.12.017

Jan 15, 2021. 

https://www.cell.com/molecular-cell/fulltext/S1097-2765(20)30936-9

# gst: dealing with bistability (through hyperbolic paraboloid origami)

<< Origami offers an avenue to program three-dimensional shapes via scale-independent and non-destructive fabrication. >>

Using theoretical model, << which connects geometry to mechanics, (AA) prove that a folded hypar origami exhibits bistability between two symmetric configurations. Further, (AA) tessellate the hypar origami and harness its bistability to encode multi-stable metasurfaces with programmable non-Euclidean geometries. >>

Ke Liu, Tomohiro Tachi, Glaucio H. Paulino. Invariant and smooth limit of discrete geometry folded from bistable origami leading to multistable metasurfaces. Nature Comm. volume 10, Article number: 4238, 17 Sep 17, 2019.    https://www.nature.com/articles/s41467-019-11935-x  

Josh Brown. Hyperbolic paraboloid origami harnesses bistability to enable new applications. Georgia Institute of Technology. Sep 17, 2019.    https://m.techxplore.com/news/2019-09-hyperbolic-paraboloid-origami-harnesses-bistability.html