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In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh [1]) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. [ 2 ] [ 3 ] [ 4 ] It characterises the fluid's flow regime: [ 5 ] a value in a certain lower range denotes laminar flow ; a value in a higher range ...
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 .
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
In mathematics, the Rayleigh quotient [1] (/ ˈ r eɪ. l i /) for a given complex Hermitian matrix and nonzero vector is defined as: [2] [3] (,) =. For real matrices and vectors, the condition of being Hermitian reduces to that of being symmetric , and the conjugate transpose x ∗ {\displaystyle x^{*}} to the usual transpose x ...
By doing so we obtain the scalar (), also known as Rayleigh's quotient: [1] = = = Therefore, the Rayleigh's quotient is a scalar whose value depends on the vector u {\displaystyle {\textbf {u}}} and it can be calculated with good approximation for any arbitrary vector u {\displaystyle {\textbf {u}}} as long as it lays reasonably far from the ...
The constants σ, ρ, and β are system parameters proportional to the Prandtl number, Rayleigh number, and certain physical dimensions of the layer itself. [3] The Lorenz equations can arise in simplified models for lasers, [4] dynamos, [5] thermosyphons, [6] brushless DC motors, [7] electric circuits, [8] chemical reactions [9] and forward ...
The equation is named after Lord Rayleigh, who introduced it in 1880. [2] The Orr–Sommerfeld equation – introduced later, for the study of stability of parallel viscous flow – reduces to Rayleigh's equation when the viscosity is zero. [3] Rayleigh's equation, together with appropriate boundary conditions, most often poses an eigenvalue ...
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 ...