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In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom .
In numerical linear algebra, the Rayleigh–Ritz method is commonly [12] applied to approximate an eigenvalue problem = for the matrix of size using a projected matrix of a smaller size <, generated from a given matrix with orthonormal columns. The matrix version of the algorithm is the most simple:
The example shows how the Rayleigh's quotient is capable of getting an accurate estimation of the lowest natural frequency. The practice of using the static displacement vector as a trial vector is valid as the static displacement vector tends to resemble the lowest vibration mode.
Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices.. Rayleigh fading models assume that the magnitude of a signal that has passed through such a transmission medium (also called a communication channel) will vary randomly, or fade, according to a Rayleigh distribution — the radial component of the sum of ...
In Rayleigh scatter-based distributed fiber optic sensing, a coherent laser pulse is sent along an optic fiber, and scattering sites within the fiber cause the fiber to act as a distributed interferometer with a gauge length approximately equal to the pulse length. The intensity of the reflected light is measured as a function of time after ...
Rayleigh distribution; Rayleigh fading; Rayleigh law on low-field magnetization; Rayleigh length; Rayleigh number, a dimensionless number for a fluid associated with buoyancy driven flow; Rayleigh quotient; Rayleigh–Ritz method; Plateau–Rayleigh instability explains why a falling stream of fluid breaks up into smaller packets
Using the definition of mass flux =, where denotes the flow velocity, we find M 2 = u 2 c 2 = 1 {\displaystyle M_{2}={\frac {u_{2}}{c_{2}}}=1} where M {\displaystyle M} is the Mach number and c {\displaystyle c} is the speed of sound , in other words, downstream flow is sonic with respect to the Chapman-Jouguet wave.
Hyper–Rayleigh scattering optical activity (/ ˈ r eɪ l i / RAY-lee), a form of chiroptical harmonic scattering, is a nonlinear optical physical effect whereby chiral scatterers (such as nanoparticles or molecules) convert light (or other electromagnetic radiation) to higher frequencies via harmonic generation processes, in a way that the ...