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The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other. Vibration of a single normal mode of a circular disc with a pinned boundary condition along the entire outer edge.
The vibrations of the membrane are given by the solutions of the two-dimensional wave equation with Dirichlet boundary conditions which represent the constraint of the frame. It can be shown that any arbitrarily complex vibration of the membrane can be decomposed into a possibly infinite series of the membrane's normal modes.
The following table lists several common normal modal systems. The notation refers to the table at Kripke semantics § Common modal axiom schemata.Frame conditions for some of the systems were simplified: the logics are sound and complete with respect to the frame classes given in the table, but they may correspond to a larger class of frames.
The normal component of the slow shock propagates with velocity in the frame moving with the upstream plasma, that of the intermediate shock with velocity and that of the fast shock with velocity . The fast mode waves have higher phase velocities than the slow mode waves because the density and magnetic field are in phase, whereas the slow mode ...
Interface conditions describe the behaviour of electromagnetic fields; electric field, electric displacement field, and the magnetic field at the interface of two materials. The differential forms of these equations require that there is always an open neighbourhood around the point to which they are applied, otherwise the vector fields and H ...
The term "mode" in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. If there is a single mode, the distribution function is called "unimodal". If it has more modes it is "bimodal" (2), "trimodal" (3), etc., or in general, "multimodal". [2]
What does a pair of orthonormal vectors in 2-D Euclidean space look like? Let u = (x 1, y 1) and v = (x 2, y 2).Consider the restrictions on x 1, x 2, y 1, y 2 required to make u and v form an orthonormal pair.
A plasmonic nanoantenna supporting a localized surface plasmon quasinormal mode essentially behaves as a poor antenna that radiates energy rather than stores it. Thus, as the optical mode becomes deeply sub-wavelength in all three dimensions, independent of its shape, the Q-factor is limited to about 10 or less.