"Everybody believes in the law of errors [the final result of many small, independent, random errors is normally distributed], the experimenters because they think it is a mathematical theorem, the mathematicians because they think it is an experimental fact" - Poincare, Calcul des Probabilites

I've just compared my formula for the characteristic impedance of an eccentric coax with results from a series of finite element simulations with FEniCS. They look excellent. I've added them to my post comphysblog.wordpress.com/2020

New post - Conformal Mapping Example, the Eccentric Coax


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.

I also discovered that WordPress.com supports latex. Excellent.

I haven't written a blog post for a long time. Although I'm aware that I never posted the magnetostatic solutions, my next post is going to be a bit different to all my previous ones. I'm going to introduce conformal mapping with a very simple example, then demonstrate finding the characteristic impedance of a coaxial cable where the inner and outer conductors aren't concentric. I've done the maths and written about half of it :)

What is everybody's view of the FCC project?

The opinions on YC seemed pretty critical in general. While I see some validity to the point that it's a shot in the dark, I also think that shots in the dark might be the best way to go. We know there are problems with our current model of the universe and aren't sure how to resolve them, maybe it'll give us some direction. The final price tag €21B sounds like a lot, but that is spread over a number of years and across multiple governments. Finally, if we don't fund a large project now, then 50 years into the future when we need a big collider for something specific we won't have the skills or expertise to build one. To me, that seems like reason enough to build something.

Does anybody know the name of this type of usb connector? (Not the HDMI)

Just made a short post about how to simulate electrostatic nonuniform charge density distributions with FEniCS; that is spatially varying charge density distributions. This could be useful for simulating things like particle beams which are commonly assumed to have Gaussian (or similar) distributions. This is a small extension of a previous post about how to simulate uniform charge density distributions.


WordPress.com offers a pretty good service, but its limiting in terms of access to WordPress features and puts pretty intrusive advertisements on my blog. I was thinking of moving to a different WordPress host.

I got magnetostatic simulations working yesterday, so I made a cos(theta) style dipole magnet with an iron yoke. The fields looked sensible although I didnt check the amplitudes, for the post I'll see if I can recreate the LHC dipoles!

My latest post is about using boundary conditions to assume symmetry in a finite element electrostatics problem.

To demonstrate Neumann boundaries I solve the Laplace equation for a coaxial geometry using 1/4 of the cross section. I then find the fields of a differential pair transmission line using half the cross section and a Dirichlet boundary.

This is all done with FEniCS, the open source finite element solver.


Finally finished my post on electrostatics with linear dielectrics using the open source finite element solver FEniCS. It's surprisingly easy!

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Here's the electric potential and field overlaid for a uniform cylindrical charge distribution created using FEniCS, an opensource finite element solver. Although this is a simple analytical problem, this technique can be used for much more complicated geometries.

Next up: linear dielectrics, I've tested in both 2D and 3D and I'm ready to write it up =] surprisingly easy!

New post: electrostatic problems with charge densities in FEniCS. A domain is specified within the mesh to have a uniform charge density, the fields both inside and outside the region are then solved. The finite element solution is then compared with the analytical result. All materials available as a repo. wp.me/p8Kvfs-cX

After a couple of months without a new post I've started writing about simulating charge distributions, rather than just boundary value problems. I'll explain how can calculate the electrostatic fields of arbitrarily shaped charge densities, which are specified with mesh subdomains. These will have hard edges for now but I want to look into having more general charge distributions.

I've also run 3D simulations for calculating capacitances between arbitrarily shaped conductors and 2D linear dielectrics. I need to do some more testing & comparison with other FEA tools/ analytical methods before I publish any posts. Seems to be going well though!

I was reading the help files of a well-known commercial microwave FEA package and it suggested calculating characteristic impedance from the power and voltage rather than finding the current directly.

This way doesn't require surface normals or line integrals which my previous methods did, so it's probably better (easier to do anyway). I've added this into my TEM mode post - comphysblog.wordpress.com/2018

Just made a bow tie, surprisingly easy. Actually putting it on is another matter.

@aparrish always happy to try and help with maths :)

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