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The second equation, called the Codazzi equation or Codazzi-Mainardi equation, states that the covariant derivative of the second fundamental form is fully symmetric. It is named for Gaspare Mainardi (1856) and Delfino Codazzi (1868–1869), who independently derived the result, [ 3 ] although it was discovered earlier by Karl Mikhailovich ...
u ⊗ u is the dyad of the velocity. Here j and s have same number of dimensions N as the flow speed and the body acceleration, while F, being a tensor, has N 2. [note 1] In the Eulerian forms it is apparent that the assumption of no deviatoric stress brings Cauchy equations to the Euler equations.
Name Dim Equation Applications Landau–Lifshitz model: 1+n = + Magnetic field in solids Lin–Tsien equation: 1+2 + = Liouville equation: any + = Liouville–Bratu–Gelfand equation
The primitive equations may be linearized to yield Laplace's tidal equations, an eigenvalue problem from which the analytical solution to the latitudinal structure of the flow may be determined. In general, nearly all forms of the primitive equations relate the five variables u, v, ω, T, W, and their evolution over space and time.
In mathematics, an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler's equation, is a linear homogeneous ordinary differential equation with variable coefficients. It is sometimes referred to as an equidimensional equation. Because of its particularly simple equidimensional structure, the differential equation can be solved ...
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The most common way that an equilibrium distribution is established is by the interaction of the photons with matter. [1] If the photons are absorbed and emitted by the walls of the system containing the photon gas, and the walls are at a particular temperature, then the equilibrium distribution for the photons will be a black-body distribution ...
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