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Perfect optics through light scattering

Innovative technologies are the key to tackling some of society's key challenges—and many of these technologies have an optical system at their core. Examples include semiconductor lithography systems designed to create ...

Universal virus detection platform to expedite viral diagnosis

The quick, accurate detection of a virus on a wide scale is the key to combating infectious diseases such as COVID-19. A new viral diagnostic strategy using reactive polymer-grafted, double-stranded RNAs will serve as a pre-screening ...

The hidden underwater map of the past

Major climate changes leading to great fluctuations in sea levels took place during the Quaternary period 2.58 million years ago. The sea receded during the glaciations, because the water ended up stored in huge ice masses; ...

Jeddah gets caught in the rain

Urbanization could cause 26 percent more rain to fall over Jeddah city than over the surrounding desert during storms.

A new horizon for vibrational circular dichroism spectroscopy

Vibrational circular dichroism (VCD) spectroscopy is an extension of circular dichroism spectroscopy into the infrared and near-infrared regions where vibrational transitions occur in the ground electronic state of a molecule. ...

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Surface

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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