New post - Conformal Mapping Example, the Eccentric Coax
https://comphysblog.wordpress.com/2020/06/28/conformal-mapping-1/
This post is different from all my others. Rather than stepping through solving a problem with FEniCS, I step through solving a problem with the mathematical method of conformal mapping.
I introduce the method by solving the far easier problem of a pair of slanted parallel plates with a potential difference.
After that I get to the main point of the post: finding the characteristic impedance of a coaxial cable where the centre conductor isn't in the middle; where the cylinders are eccentric. Although the process has quite a lot of algebra, the final solution is simple and very usable.
I've really enjoyed doing this example, because I think it's a great demonstration of using analytical methods to solve a problem with strange boundaries. These days we'd probably just solve this kind of thing numerically, but the analytical solution gives insight and a formula that can be used over-and-over.
I'll add a numerical comparison in the coming days.
