A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold.
Origami is the Japanese art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a finished sculpture through folding and sculpting techniques. Modern origami practitioners generally discourage the use of cuts, glue, or markings on the paper. Origami folders often use the Japanese word kirigami to refer to designs which use cuts.
The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability, and the use of paper folds to solve up-to cubic mathematical equations.
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.
In botany, phyllotaxis or phyllotaxy is the arrangement of leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature.
Robert J. Lang is an American physicist who is also one of the foremost origami artists and theorists in the world. He is known for his complex and elegant designs, most notably of insects and animals. He has studied the mathematics of origami and used computers to study the theories behind origami. He has made great advances in making real-world applications of origami to engineering problems.
The Little–Parks effect was discovered in 1962 by William A. Little and Roland D. Parks in experiments with empty and thin-walled superconducting cylinders subjected to a parallel magnetic field. It was one of the first experiments to indicate the importance of Cooper-pairing principle in BCS theory.
A field-reversed configuration (FRC) is a type of plasma device studied as a means of producing nuclear fusion. It confines a plasma on closed magnetic field lines without a central penetration. In an FRC, the plasma has the form of a self-stable torus, similar to a smoke ring.
The Miura fold is a method of folding a flat surface such as a sheet of paper into a smaller area. The fold is named for its inventor, Japanese astrophysicist Kōryō Miura.
Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be folded to form a flat figure. It states that the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives an alternating sum of zero. Crease patterns with more than one vertex do not obey such a simple criterion, and are NP-hard to fold.
Alexander Balankin is a Mexican scientist of Russian origin whose work in the field of fractal mechanics and its engineering applications won him the UNESCO Science Prize in 2005.
Lieb's square ice constant is a mathematical constant used in the field of combinatorics to quantify the number of Eulerian orientations of grid graphs. It was introduced by Elliott H. Lieb in 1967.
Magnetized liner inertial fusion (MagLIF) is an emerging method of producing controlled nuclear fusion. It is part of the broad category of inertial fusion energy (IFE) systems, which drives the inward movement of fusion fuel, thereby compressing it to reach densities and temperatures where fusion reactions occur. Previous IFE experiments used laser drivers to reach these conditions, whereas MagLIF uses a combination of lasers for heating and Z-pinch for compression. A variety of theoretical considerations suggest such a system will reach the required conditions for fusion with a machine of significantly less complexity than the pure-laser approach. There are currently at least two facilities testing feasibility of the MagLIF concept, the Z-machine at Sandia Labs in the US and Primary Test Stand (PTS) located in Mianyang, China.
Mechanical metamaterials are artificial structures with mechanical properties defined by their structure rather than their composition. They can be seen as a counterpart to the rather well-known family of optical metamaterials. They are often also termed elastodynamic metamaterials and include acoustic metamaterials as a special case of vanishing shear. Their mechanical properties can be designed to have values which cannot be found in nature.
This is a bibliography of works by Theodore von Kármán.
In mathematics, the Schwarz lantern is a polyhedral approximation to a cylinder, used as a pathological example of the difficulty of defining the area of a smooth (curved) surface as the limit of the areas of polyhedra. It is formed by stacked rings of isosceles triangles, arranged within each ring in the same pattern as an antiprism. The resulting shape can be folded from paper, and is named after mathematician Hermann Schwarz and for its resemblance to a cylindrical paper lantern. It is also known as Schwarz's boot, Schwarz's polyhedron, or the Chinese lantern.
Kōryō Miura is a Japanese astrophysicist, inventor, and origamist known for the Miura fold. He is a professor emeritus at the University of Tokyo and at the Institute of Space and Astronautical Science.
The FLEUR code is an open-source scientific software package for the simulation of material properties of crystalline solids, thin films, and surfaces. It implements Kohn-Sham density functional theory (DFT) in terms of the all-electron full-potential linearized augmented-plane-wave method. With this, it is a realization of one of the most precise DFT methodologies. The code has the common features of a modern DFT simulation package. In the past, major applications have been in the field of magnetism, spintronics, quantum materials, e.g. in ultrathin films, complex magnetism like in spin spirals or magnetic Skyrmion lattices, and in spin-orbit related physics, e.g. in graphene and topological insulators.
Hiroshi Suura was a Japanese theoretical physicist, specializing in particle physics.
The Kresling fold is a folding pattern which naturally arises under torsional load. It is named after Biruta Kresling, a Paris-based architect born in Berlin in 1942, who has published extensive research deployable structures, and in particular on the properties of the Kresling fold. Under the right conditions, when a sheet of paper is wrapped around two coaxial cylinders separated by a gap and the cylinders are twisted in opposite directions, the paper buckles into regular slanted folds, pulling the cylinders towards one another, and producing the so-called Kresling fold.
