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Toward the scaling up of nanocages to trap noble gases

Over the past few years, scientists have demonstrated how cage-like, porous structures made of silicon and oxygen and measuring only billionths of a meter in size can trap noble gasses like argon, krypton, and xenon. However, ...

The secret life of baby octopuses

Some of the most amazing creatures live in the deep blue sea. Cuttlefish, squids and octopuses, for example. These soft-bodied cephalopods have a strikingly sophisticated nervous system, camera-like eyes, three hearts, and ...

Elements in liquid metals compete to win the surface

Some alloys are in the liquid state at or near room temperature. These alloys are usually composed of gallium and indium (elements used in low energy lamps), tin and bismuth (materials used in constructions). The ratio and ...

Tiny nanoparticles improve charge transport

Three-dimensional topological insulators are materials that can conduct electric current without resistance—but only on their surface. However, this effect is difficult to measure. This is because these materials usually ...

Earthly lava tubes may offer insights into extraterrestrial life

Since 1997, NASA has successfully landed five rovers on Mars. The rovers have beamed back data that indicate life cannot survive on the Martian surface; we do not know whether life persists below the ground, however. For ...

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In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball or bagel. On the other hand, there are surfaces which cannot be embedded in three-dimensional Euclidean space without introducing singularities or intersecting itself — these are the unorientable surfaces.

To say that a surface is "two-dimensional" means that, about each point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the Earth is (ideally) a two-dimensional sphere, and latitude and longitude provide coordinates on it — except at the International Date Line and the poles, where longitude is undefined. This example illustrates that not all surfaces admits a single coordinate patch. In general, multiple coordinate patches are needed to cover a surface.

Surfaces find application in physics, engineering, computer graphics, and many other disciplines, primarily when they represent the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface.

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