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Fig. 1. Manifold arrangement for flow distribution. Traditionally, most of theoretical models are based on Bernoulli equation after taking the frictional losses into account using a control volume (Fig. 2). The frictional loss is described using the Darcy–Weisbach equation. One obtains a governing equation of dividing flow as follows: Fig. 2 ...
In dynamical systems, a branch of mathematics, an invariant manifold is a topological manifold that is invariant under the action of the dynamical system. [1] Examples include the slow manifold , center manifold , stable manifold , unstable manifold , subcenter manifold and inertial manifold .
Flow processes (also called -diffusions) are the probabilistic counterpart of integral curves of vector fields. In contrast, a flow process is defined with respect to a second-order differential operator, and thus, generalises the notion of deterministic flows being defined with respect to a first-order operator.
Flag manifold; Grassmann manifold; Stiefel manifold; Lie groups provide several interesting families. See Table of Lie groups for examples. See also: List of simple Lie groups and List of Lie group topics.
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 manifold") An engine part that supplies the air or fuel/air mixture to the cylinders Scuba manifold In a scuba set, connects two or more diving cylinders Vacuum gas manifold
An n-manifold M is called null-cobordant if there is a cobordism between M and the empty manifold; in other words, if M is the entire boundary of some (n + 1)-manifold. For example, the circle is null-cobordant since it bounds a disk. More generally, a n-sphere is null-cobordant since it bounds a (n + 1)-disk.
Since, as is trivial to show, any orbit of a Hamiltonian flow is contained in a level set, the Weinstein conjecture is a statement about contact manifolds. It has been known that any contact form is isotopic to a form that admits a closed Reeb orbit; for example, for any contact manifold there is a compatible open book decomposition , whose ...
A cylinder manifold is system of pipes and valves for using a group of gas cylinders, or boil-off from vacuum insulated evaporators, to feed a single supply line.The advantages of the manifold system as compared with using a single cylinder are increased capacity and reliability, and also the possibility of a centralized supply for multiple users.