A short post on evaluating the Fourier integral numerically. https://comphysblog.wordpress.com/2023/07/06/computing-fourier-integrals/

When I tried to look up how to do this, I almost exclusively found information on the FFT. This gave inadequate results, which I now know is expected. Numerical recipes says:

"It is a sobering exercise to implement equation (13.9.6)[DFT] for an integral that can be done

analytically, and to see just how bad it is."

@freemo I was confused earlier on by a minicircuits spec sheet for a 180 degree hybrid [1]. They only seem to sell three port varieties, I assume they fourth port is internally terminated or it isn't included somehow. Now the thing which confused me was that they referred to one of the ports as the SUM port. Hybrid couplers are often shown as 4 port devices with Sigma, Delta 1 and 2 ports. I would have thought the "SUM" port would be the sigma port, but then the output of the splitter would be two in-phase signals and it wouldn't really be much of a "180" degree" hybrid. Their SUM port must correspond to the Delta port, that is, the signal out of the "sum" port would be large if the inputs at ports 1 and 2 were entirely out of phase, I.e. the difference. It does behave this way, I tried it today, but my question is: why would they call it a "sum" port when if anything it's subtracting?! Am I alone in finding that confusing?

[1] - https://www.minicircuits.com/WebStore/dashboard.html?model=ZFSCJ-2-1

Half way through the magnetostatics post I promised a year ago. I've finished an introductory coax example and now I'm writing the intro theory for a cos(phi) magnet. I think it'll be ready in a week :) After that I see two options to progress: eigenmodes or time dependence.

If I go with the eigenmode, I can write an example for how the finite difference method works and talk about linear algebra methods. I haven't tried any time dependent problems in FEniCS yet, so that'll be a whole new area to learn.

Surprisingly, the blog is apparently getting a citation of some kind.

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.

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.

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. #physics #python #opensource #ham #radio #fenics

https://comphysblog.wordpress.com/2019/07/15/assuming-symmetry-with-boundary-conditions/

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!

This blog is dedicated to physics and computing, with a current focus on solving electromagnetic problems using open source tools.

I work in particle beam diagnostics and am a PhD student studying the interaction of particle beams with their surroundings as well as the associated dynamics.

I'm Interested in anything related to particle accelerators, beam dynamics, detectors, electromagnetism and computing for science. I also enjoy tennis, fountain pens, fantasy & sci-fi books and board games.

Joined Aug 2018