LaTeX Rendering Test Post

This post exists only to verify that the blog renders LaTeX correctly inside Markdown content.

Inline math should work inside a paragraph, for example $R_{\mathrm{interface}} = R_{\mathrm{chem}} + R_{\mathrm{mech}}$ and $\gamma_{\mathrm{SL}} = \gamma_{\mathrm{SV}} - \gamma_{\mathrm{LV}}\cos\theta$.

Display math should also render cleanly:

$$\Delta G_{\mathrm{eff}}(T) = \Delta G_{\mathrm{ox}}(T) + \gamma \, \Delta \varepsilon(T)$$

For a very simple transport-style note, a one-dimensional flux can be written as:

$$J = -D \frac{\partial c}{\partial x}$$

A minimal matrix example:

$$\mathbf{A} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$

And a basic materials-science notation example:

$$\mathrm{Ga_2O_3} + 6e^- \rightarrow 2\mathrm{Ga} + 3\mathrm{O}^{2-}$$

If you can read all formulas above without raw dollar signs leaking into the page, the LaTeX pipeline is working.