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  1. Z

    Associativity of Hadamard and matrix product

    I couldn't solve it, so the post can be reworded.
  2. Z

    Associativity of Hadamard and matrix product

    Hi, Let us suppose we have three real matrices A, B, C and let \circ denote the Hadamard product, while AB is the conventional matrix product. Is this relation true for all A, B, C matrices: C \circ (AB) = A( C\circ B)? I looked at it more thoroughly and I realized that this assumption is...
  3. Z

    LaTeX What is wrong in this Latex code?

    Your code works for me. I got no error messages with MikTeX 2.9 using TeXStudio.
  4. Z

    LaTeX LaTeX - dfrac with textstyle numerator

    If I understand well, you want to make the counter smaller than the denominator. It can be done winthin an inline environment as eg. Let us see the following equation: $\frac{a}{\displaystyle a}$
  5. Z

    LaTeX Latex presentations

    I use the same math style in presentations as in articles because - in my opinion - it is much nicer.
  6. Z

    Work done by gravity - what is wrong?

    Yes, I surmised that I changed the path of integration, since \mathrm{d}\,\varphi is negative. I forgot the idea of the potential function. Thank you.
  7. Z

    Determine particle position knowing the velocity field

    Using this idea, I managed to perform what I wanted. Thank you!
  8. Z

    Work done by gravity - what is wrong?

    I would like the determine the work done by gravity on a mass attached to a rod (see the attached image). The rod is assumed to be weightless and rigid. I start from the definition of work: W_{AB} = \int_{\mathbf{r}_A}^{\mathbf{r}_B} \mathbf{G}\cdot \mathrm{d}\,\mathbf{r}. In the x-y coordinate...
  9. Z

    Determine particle position knowing the velocity field

    So if I am not mistaken I should do the following for each particle: 1. Solve the initial-value problem to gain \vec{r}(t,\vec{R}) at different time steps. For this I must solve an IVP consisting of 2 equations because of the 2D-problem. But I have \vec{v} at discrete points at each time. 2...
  10. Z

    Determine particle position knowing the velocity field

    Dear all, I solved the Navier-Stokes equations in Eulerian description. I would like to illustrate it as follows: I thought to place particles in the domain which will characterize the fluid flow. However I must know the particle position in the Lagrangian specification. As I place the...
  11. Z

    Why incompressible fluid flow is advantageous in numerical computation

    I do not know the finite difference approach, but I speak about the steady-state spectral or finite element solution of the problem. To prevent the checkerboard pressure distribution, one should use elements that satisfies the Babuska-Brezzi condition.
  12. Z

    Why incompressible fluid flow is advantageous in numerical computation

    Spurious pressure values come up when we use the non-staggered approximation for the velocity and pressure. However programming spectral methods (as I deal with the spectral collocation of the Stokes-equations) is hard for staggered-grids except the case when we apply homogeneous boundary...
  13. Z

    Why incompressible fluid flow is advantageous in numerical computation

    Hi, When we want to solve the Navier-Stokes equations coupled with the conservation of mass for incompressible fluids using the primitive-variable approach, we have to face to the problem that the equation for the continuity equation does not contain the pressure which leads to spurious...
  14. Z

    Steady-state incompressible Navier-Stokes discretization

    Hi, I would like to solve the steady-state incompressible Navier-Stokes equations by a spectral method. When I saw the classic primitive-variable finite element discretization of the time-dependent incompressible N-S, it turned out that the coefficient matrix of the derivatives of the unknowns...
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    What is the advantage of Hamilton's canonical equations?

    1. Why are they linear PDEs? See http://encyclopedia2.thefreedictionary.com/Hamilton%27s+Canonical+Equations+of+Motion. I do not refer to the Hamilton-Jacobian equation: http://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equation 2. So you mean that it has nice properties when we use apply...
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    What is the advantage of Hamilton's canonical equations?

    Hi! I would like to know that in what circumstances Hamilton's canonical equations are superior to the Lagrange-equations of the second kind. We know that every second order equation can be rewritten as a system of first order equations. Thanks, Zoli
  17. Z

    Dimensional Analysis with non-dimensional initial parameter

    I realised that a dependent parameter (the consistency index: K[Pa s^n]) includes this non-dimensional parameter and this is the only one that changes when we consider a power-law fluid instead of a Newtonian fluid. Therefore we do not have to take this non-dimensional parameter into account as...
  18. Z

    Dimensional Analysis with non-dimensional initial parameter

    I would like non-dimensionalize the equations which describe a non-Newtonian fluid model. In the constitutive equation (power-law model) there is a non-dimensional parameter: n. According to Buckingham's Pi theory, I must take all the relevant independent parameters (variables, constants, etc.)...
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