What I’m trying to do
I am trying to export a file containing Latex formulas in pdf format. One line of my display math code didn’t get rendered, (it just appears as a line o fLatex code in red in the pdf file) and several lines after it are missing.
I tried to export it in different page sizes, with all community plugins turned off. But it didn’t seem to work.
If you switch to Reading view, do you see the error / red text there are well? Reading view is going to be closest to the PDF export.
If you paste that section and just above it here, in a code block, hopefully folks can spot the issue. It may be as simple as adding a newline or two between some sections to sort it out.
Thank you for your suggestions. Since I’m not very familiar with this forum, I don’t know if I include the code correctly. This is the code for the part that I’m having trouble with. The issue still exits in preview mode. Here I attached a screen shot of what this part looks like in preview mode.
The vorticity is:
$$\boldsymbol{\omega}=\nabla \times \begin{pmatrix}
\frac{\beta}{2}x_{2} \\
-\frac{\beta}{2}x_{1} \\
0
\end{pmatrix}
=-\beta \hat{\mathbf{z}}$$This corresponds to a clockwise rotation, consistent with the plot in the problem. For the straining part, the eigenvalues of the straining part are $\pm \frac{\beta}{2},0$, with eigen vectors $\frac{1}{\sqrt{ 2 }} \begin{pmatrix}1 \\ 1 \\ 0\end{pmatrix},\ \frac{1}{\sqrt{ 2 }}\begin{pmatrix}1 \\ -1 \\ 0\end{pmatrix},\ \begin{pmatrix}0 \\ 0 \\ 1\end{pmatrix}$. So the "deformation" happens only in the xy-plane. There is a stretch of $\frac{\beta}{2}$ is the $\frac{1}{\sqrt{ 2 }}\begin{pmatrix}1 \\ 1 \\ 0 \end{pmatrix}$ direction, and a contraction of $- \frac{\beta}{2}$ in the $\frac{1}{\sqrt{ 2 }}\begin{pmatrix}1 \\ -1 \\ 0 \end{pmatrix}$ direction. This is also consistent with the plot in the problem.
# Acheson 6.12
The total viscous force on $dV$ is given by $\mu \nabla^{2}\mathbf{u}dV$. Indeed, if the flow is irrotational, we have:
$$\begin{align}
\nabla^{2}\mathbf{u} & = \nabla(\nabla \cdot \mathbf{u})- \nabla \times(\nabla \times \mathbf{u})=0
\end{align}$$
However, it just means that the total viscous force is zero. It does not imply that the force exerted on the particle in contact with the cylinder by the cylinder is zero. It could be non-zero, and is just canceled out by viscous forces on that particle by other particles. Then by Newton's third law, the net viscous force on the cylinder could be non-zero, which exerts a torque.
Yup, that’s great. Give this a shot. For mathblocks, and markdown in general, if something isn’t working try adding a newline above and below the issue.
The vorticity is:
$$\boldsymbol{\omega}=\nabla \times \begin{pmatrix}
\frac{\beta}{2}x_{2} \\
-\frac{\beta}{2}x_{1} \\
0
\end{pmatrix}
=-\beta \hat{\mathbf{z}}$$
This corresponds to a clockwise...
or
The vorticity is:
$$
\boldsymbol{\omega}=\nabla \times \begin{pmatrix}
\frac{\beta}{2}x_{2} \\
-\frac{\beta}{2}x_{1} \\
0
\end{pmatrix}
=-\beta \hat{\mathbf{z}}
$$
This corresponds to a clockwise...
with the $$ on their own lines. Both of these seem fine in this case.
source mode | reading view
Thank you! It worked.