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A hodograph is a diagram that gives a vectorial visual representation of the movement of a body or a fluid. It is the locus of one end of a variable vector, with the other end fixed. [1] The position of any plotted data on such a diagram is proportional to the velocity of the moving particle. [2] It is also called a velocity diagram.
Shock polar in the pressure ratio-flow deflection angle plane for a Mach number of 1.8 and a specific heat ratio 1.4. The minimum angle, , which an oblique shock can have is the Mach angle = (/), where is the initial Mach number before the shock and the greatest angle corresponds to a normal shock.
The mathematical basis for Bézier curves—the Bernstein polynomials—was established in 1912, but the polynomials were not applied to graphics until some 50 years later when mathematician Paul de Casteljau in 1959 developed de Casteljau's algorithm, a numerically stable method for evaluating the curves, and became the first to apply them to computer-aided design at French automaker Citroën ...
In CAD area this is a drawback, because CAD systems use polynomials or rational curves. In order to get at least rational curves, the square root of the representation of the parallel curve has to be solvable. Such curves are called pythagorean hodograph curves and were investigated by R.T. Farouki. [14]
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[4]: 289 Storm splitting becomes less pronounced as hodograph curvature increases, resulting in shorter-lived anticyclonic cells. [3] In extreme cases, where there is a strongly curving hodograph, the suppressed updraft will be so weak from the start, the splitting process will not be evident on radar, and a dominant cell will immediately be ...
The Cole–Hopf transformation is a change of variables that allows to transform a special kind of parabolic partial differential equations (PDEs) with a quadratic nonlinearity into a linear heat equation.
YouTube is an American social media and online video sharing platform owned by Google. YouTube was founded on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim, three former employees of PayPal. Headquartered in San Bruno, California, it is the second-most-visited website in the world, after Google Search.