# Search results

1. ### Associativity of Hadamard and matrix product

I couldn't solve it, so the post can be reworded.
2. ### 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. ### 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. ### 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. ### LaTeX Latex presentations

I use the same math style in presentations as in articles because - in my opinion - it is much nicer.
6. ### 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. ### Determine particle position knowing the velocity field

Using this idea, I managed to perform what I wanted. Thank you!
8. ### 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. ### 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. ### 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. ### Why incompressible fluid flow is advantageous in numerical computation

Thank you, now it is clear.
12. ### 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.
13. ### 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...
14. ### 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...
15. ### 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...
16. ### 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...
17. ### 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
18. ### 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...
19. ### Dimensional Analysis with non-dimensional initial parameter

I managed to solve it.
20. ### 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.)...