Looking at the values of the parameters, I think you’re probably just under-resolving the problem in space (by many orders of magnitude). Doing some dimensional analysis, you can see that \beta / A will have units of length squared, so, heuristically, your mesh element diameter would need to be comparable to \sqrt{\beta / A} to resolve the physics. If I manually pump up \beta to 8\times 10^6, then the interface moves. (Of course this changes the physics of the problem; hopefully you’re instead planning to solve the PDE on a much smaller domain, which would have a similar effect.)
P.S. You can format code by surrounding it with backticks (and optionally specifying the language for highlighting), e.g.,
```python
Line 1
Line 2
etc.
```
For more formatting tricks, Google for “Markdown”. You can also embed equations with LaTeX notation, e.g., $\beta / A$.