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The S-parameter matrix describing an N-port network will be square of dimension N and will therefore contain elements. At the test frequency each element or S-parameter is represented by a unitless complex number that represents magnitude and angle , i.e. amplitude and phase .
The S-matrix is closely related to the transition probability amplitude in quantum mechanics and to cross sections of various interactions; the elements (individual numerical entries) in the S-matrix are known as scattering amplitudes. Poles of the S-matrix in the complex-energy plane are identified with bound states, virtual states or resonances.
By assuming a form of Coulomb's law in which the Coulomb constant k e is taken as unity, Maxwell then determined that the dimensions of an electrostatic unit of charge were Q = T −1 L 3/2 M 1/2, [15] which, after substituting his M = T −2 L 3 equation for mass, results in charge having the same dimensions as mass, viz. Q = T −2 L 3.
m⋅s L T: vector Acceleration: a →: Rate of change of velocity per unit time: the second time derivative of position m/s 2: L T −2: vector Angular acceleration: ω a: Change in angular velocity per unit time rad/s 2: T −2: pseudovector Angular momentum: L: Measure of the extent and direction an object rotates about a reference point kg ...
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.
A Z-parameter matrix describes the behaviour of any linear electrical network that can be regarded as a black box with a number of ports.A port in this context is a pair of electrical terminals carrying equal and opposite currents into and out-of the network, and having a particular voltage between them.
The oldest and best-known is the so-called rescaled range (R/S) analysis popularized by Mandelbrot and Wallis [3] [10] and based on previous hydrological findings of Hurst. [1] Alternatives include DFA, Periodogram regression, [11] aggregated variances, [12] local Whittle's estimator, [13] wavelet analysis, [14] [15] both in the time domain and ...
Loosely, the theorem states that if there is a physically meaningful equation involving a certain number n physical variables, then the original equation can be rewritten in terms of a set of p = n − k dimensionless parameters π 1, π 2, ..., π p constructed from the original variables, where k is the number of physical dimensions involved ...