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How slippery surfaces allow sticky pastes and gels to slide

An MIT research team that has already conquered the problem of getting ketchup out of its bottle has now tackled a new category of consumer and manufacturing woe: how to get much thicker materials to slide without sticking ...

Flies smell through a Gore-Tex system

A research group led by a scientist of the RIKEN Center for Biosystems Dynamics Research (BDR) has gained important insights into the nanopores that allow the fruit fly to detect chemicals in the air, and has identified the ...

Demonstrating a weak topological insulator in bismuth iodide

Topological insulators are one of the most exciting discoveries of the 21st century. They can be simply described as materials that conduct electricity on their surface or edge, but are insulating in their interior bulk. ...

Predicting tvariable carbon dioxide uptake by the ocean

Ocean CO2 uptake is predictable for two years in advance, according to new paper in Science Advances by Dr. Hongmei Li, Dr. Tatiana Ilyina, Dr. Wolfgang A. Müller, and Dr. Peter Landschützer, all scientists in the department ...

Lessons learnt from the drift analysis of MH370 debris

The precise last position of Boeing 777 of Malaysia Airlines (MH370) that disappeared from radar screens on 8 March 2014 is still unknown. Multiple large-scale search missions have failed. The discovery of several items of ...

Tuning terahertz transmission

The ability to manipulate light on a subwavelength-scale could lead to a revolution in photonic devices such as antennas, solar panels, and even cloaking devices. Nanotechnology advances have made this possible through the ...

The sticky science of underwater adhesives

Mussels stick to rocks on the seafloor, to aquatic plants, and—to the consternation of boaters—they can hitch rides fastened to seafaring vessels no matter their composition: metals, rubber, glass, wood and more.

Researchers measure puncture performance of viper fangs

A team that studies how biological structures such as cactus spines and mantis shrimp appendages puncture living tissue has turned its attention to viper fangs. Specifically, the scientists wanted to know, what physical characteristics ...

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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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