#lattices

MIT engineers use kirigami to make ultrastrong, lightweight structures

Produced with techniques borrowed from Japanese paper-cutting, the strong metal lattices are lighter than cork and have customizable mechanical properties.

Cellular solids are materials composed of many cells that have been packed together, such as a honeycomb. The shape of those cells largely determines the material’s mechanical properties, including its stiffness or strength. Bones, for instance, are filled with a natural material that enables them to be lightweight, but stiff and strong. Inspired by bones and other cellular solids found in nature, humans have used the same concept to develop architected materials. By changing the geometry of the unit cells that make up these materials, researchers can customize the material’s mechanical, thermal, or acoustic properties. Architected materials are used in many applications, from shock-absorbing packing foam to heat-regulating radiators.

(not the f. gen subgroups of Z^n)

Well, a lattice is a poset (X,<) for which every two elements hove a unique supremum and infimum, where x in X is the supremum of {a,b} when a<x, b<x and for all y such that a<y,b<y, we have x<y.

For example, we can have X={subgroups of G} with the ordering H<B if H is contained within B. Then sup{H,B}=<H,B> and inf{H,B} is the intersection of H and B.

The most awesomest thing is antiisomorphisms between two lattices L and M, which is a bijection f from L to M such that

f(sup{a,b})=inf{f(a),f(b)}

f(inf{a,b})=sup{f(a),f(b)}

New superconducting material discovered in transition-metal dichalcogenides materials

With the support of electrical transport and magnetic measurement systems of Steady High Magnetic Field Facility (SHMFF), a research team from Hefei Institutes of Physical Science (HFIPS), Chinese Academy of Sciences (CAS), discovered a new superconducting material called (InSe2)xNbSe2, which possesses a unique lattice structure. The superconducting transition temperature of this material reaches 11.6 K, making it the transition metal sulfide superconductor with the highest transition temperature under ambient pressure. The results were published in Journal of the American Chemical Society. TMD materials have received lots of attention due to their numerous applications in the fields of catalysis, energy storage, and integrated circuits. However, the relatively low superconducting transition temperatures of TMD superconductors have limited their potential use.