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The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are called Lie Groups.
The flow in manifolds is extensively encountered in many industrial processes when it is necessary to distribute a large fluid stream into several parallel streams, or to collect them into one discharge stream, such as in fuel cells, heat exchangers, radial flow reactors, hydronics, fire protection, and irrigation. Manifolds can usually be ...
Types of manifolds in engineering include: Exhaust manifold An engine part that collects the exhaust gases from multiple cylinders into one pipe. Also known as headers. Hydraulic manifold A component used to regulate fluid flow in a hydraulic system, thus controlling the transfer of power between actuators and pumps Inlet manifold (or "intake ...
Manifolds in contemporary mathematics come in a number of types. These include: smooth manifolds, which are basic in calculus in several variables, mathematical analysis and differential geometry; piecewise-linear manifolds; topological manifolds. There are also related classes, such as homology manifolds and orbifolds, that resemble manifolds.
A manifold is composed of assorted hydraulic valves connected to each other. It is the various combinations of states of these valves that allow complex control behaviour in a manifold. [ 1 ] [ citation needed ] A hydraulic manifold is a block of metal with flow paths drilled through it, connecting various ports. [ 2 ]
This image of the open interval (with boundary points identified with the arrow marked ends) is an immersed submanifold. An immersed submanifold of a manifold is the image of an immersion map :; in general this image will not be a submanifold as a subset, and an immersion map need not even be injective (one-to-one) – it can have self-intersections.
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