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  2. Material derivative - Wikipedia

    en.wikipedia.org/wiki/Material_derivative

    The material derivative is defined for any tensor field y that is macroscopic, with the sense that it depends only on position and time coordinates, y = y(x, t): +, where ∇y is the covariant derivative of the tensor, and u(x, t) is the flow velocity.

  3. Derivation of the Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Derivation_of_the_Navier...

    The derivative of a field with respect to a fixed position in space is called the Eulerian derivative, while the derivative following a moving parcel is called the advective or material (or Lagrangian [2]) derivative. The material derivative is defined as the linear operator:

  4. Lagrangian and Eulerian specification of the flow field

    en.wikipedia.org/wiki/Lagrangian_and_Eulerian...

    The Lagrangian and Eulerian specifications of the kinematics and dynamics of the flow field are related by the material derivative (also called the Lagrangian derivative, convective derivative, substantial derivative, or particle derivative). [1] Suppose we have a flow field u, and we are also given a generic field with Eulerian specification F ...

  5. Cauchy momentum equation - Wikipedia

    en.wikipedia.org/wiki/Cauchy_momentum_equation

    is the material derivative of , equal to +, (unit: /) is the density at a given ... The X component of the forces acting on walls of a cubic fluid element (green for ...

  6. 7 Materials ETFs to Buy Today - AOL

    www.aol.com/news/7-materials-etfs-buy-today...

    Among the 11 sectors represented in the S&P 500, materials is usually the most overlooked and it is easy to understand why. Simply put, at a weight of 2.61%, materials is the smallest sector ...

  7. What do people regret the most when they retire? [Video] - AOL

    www.aol.com/finance/people-regret-most-retire...

    The timing of retirement. Sometimes the decision to retire is a regret. About one-third of retirees regretted not working longer, according to Olivia Mitchell, co-author of a paper published in ...

  8. Jacobian matrix and determinant - Wikipedia

    en.wikipedia.org/wiki/Jacobian_matrix_and...

    [a] This means that the function that maps y to f(x) + J(x) ⋅ (y – x) is the best linear approximation of f(y) for all points y close to x. The linear map h → J(x) ⋅ h is known as the derivative or the differential of f at x. When m = n, the Jacobian matrix is square, so its determinant is a well-defined function of x, known as the ...

  9. How to safely freeze milk, according to health experts - AOL

    www.aol.com/safely-freeze-milk-according-health...

    Not being able to finish all your groceries before they expire isn't a good feeling. But how do you make sure you're safely freezing milk?

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