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

, , , ,

comphysblog.wordpress.com/2019

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

ComPhys boosted

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!

ComPhys boosted
ComPhys boosted

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 :)

Small update to the TEM mode analysis with example.

I've added in a calculation for the mutual capacitance and self-inductance per unit length of the transmission line.

comphysblog.wordpress.com/2018

I've just finished my new post: TEM mode analysis with an finite element differential equation solver. comphysblog.wordpress.com/2018

In this post I calculate the electric and magnetic fields on a coaxial cable, characteristic impedance of the line, the Poynting vector, the conductor and dielectric loss, an estimated loss coefficient, Q-factor and s-parameter for a given length of cable.

Coax has been a useful example for comparisons with analytical results but the methods are very general. TEM modes of systems with different geometries can also be analysed with the exact same techniques!

Very happy to hear any comments, corrections or suggestions.

ComPhys boosted

@arteteco haha I know, its all Einsteins fault :)

I mixed up the conversion rate for weight and length :)

Starting my next post which will be about the TEM mode on a two-conductor transmission line. Specifically I'll be looking at a coaxial geometry and using to calculate the field distributions, the characteristic impedance and the Poynting vector. Just had a go and it all seems to be working.

While I'll focus on a coaxial geometry the method can be extended to more complicated geometries just by changing the mesh & boundaries. I've just had a go at an odd mode impedance and it came out just right!

The best thing about this post will be how easy it is.

I use wxmaxima as a mathematica alternative. I don't consider it to be as polished as mathematica but in general it's pretty amazing.

The syntax of sympy puts me off (too much like programming) and I find sage to be a bit too huge and clunky.

What computer algebra systems does everybody else use?

3D electrostatics example using . In this example I solve the Laplace equation for two concentric spheres to obtain an electric potential and take the gradient to find the electric field. The results are then compared with an analytical solution.

The geometry is produced in FreeCAD and the mesh/ boundaries produced with Gmsh.

comphysblog.wordpress.com/2018

Please let me know if you have comments or corrections!

QOTO Mastodon

Welcome to the QOTO instance

QOTO: Question Others, Teach Others

A Mastodon instance for scholars in Science, Technology, Engineering, and Mathematics (STEM) and all yearning to learn.

A free speech space. No censorship here.
We do not silence or block any instances.


Unique Features
  • Inline math Latex support - Use \ ( and \ ) for inline LaTeX, and \ [ and \ ] for display mode.
  • 65,535 character limit for toots (usually 500)
  • 65,535 character limit for profile bio (usually 160)
  • Full text searches - usually you can only search hashtags and usernames
  • Halcyon / Twitter clone front-end - Want the interface to look exactly like the Twitter interface? After you signed up just go here to login: https://halcyon.qoto.org.
  • PeerTube - We host our own PeerTube server with open registration for up to 100MB, but all of our active users get unlimited quotas. Sign up here: https://video.qoto.org.
  • Professionally hosted with nightly backups
  • light modern theme with full width columns (not fixed)
  • Several extra themes - including mastodon default and mastodon default with full width columns (not fixed)

Message to New Members

Welcome to the Qoto Mastodon instance, its like twitter but better!

Please don't hesitate to Direct Message me or tag me in Toots (what we call tweets here) if you have any questions or even if you just want to chat.

If you are new to Mastodon you may want to check out this official getting started guide: https://github.com/tootsuite/documentation/blob/master/Using-Mastodon/User-guide.md

We are a free speech, no censorship zone. Feel free to talk about whatever you want, say whatever you want, as long as it is legal you wont ever get banned from the server. With that said we do have a few rules: No spam, and no using multiple accounts to circumvent personal bans.

This server isnt a typical mastodon server either. I have personally modified the code on this server to give it several unique features you wont find on other servers.

If you are new to Mastodon here is some useful info.

First off, if your coming from Twitter and you'd prefer an interface that looks exactly like twitter, then just go here and login with your Qoto credential: https://halcyon.qoto.org/ No need to create an account there, your account on this server will work just fine. Just enter your username in the following format @[username]@qoto.org so for me it would be @freemo But personally I think our default skin here is way better.

Basically Mastodon is a decentralized twitter. That means anyone can run a server (like Qoto) that people can sign up to and use just like twitter. The unique part is how the servers talk to each other.

If you want to tag someone on the same server as you then you can just do @user however if you want to specify someone on a different server you can do @user@server. If someone follows you or mentions you on any server on the internet you'll get notified right here. So my full tag is @freemo@qoto.org.

So now a bit about the timelines, there are three (unlike twitter there is just one): Home, Local, Federated.

The Home timeline is just like what you'd expect on twitter, that is, everyone you are following.

The local timeline is any post made by anyone on your local server.

The federated timeline is what is cool. It combines the timeline of everyone on the server into one. This way you can see the posts of everyone that is followed by anyone on the server (assuming the post is public). So this timeline is a close representation of everyone on the internet who has Mastadon (though not really). Moreover we have a bot here that goes around and federates with everyone it can find, so our Federated Feed is rather robust covering thousands of instances.

Only other thing that is unique is listed vs unlisted posts. You have normal privacy settings like on twitter but you also can set a post to be listed or unlisted. If it is listed it acts just as i described. If it is unlisted then it acts just as a normal tweet would but it doesnt show up on local or federated timelines anywhere.

Also this goes without saying, but don't be racist, sexist, hateful, and don't harass people. Its a pretty shitty thing to do, don't be shitty!

The following is the list of QOTO administrators/moderators.
  • @freemo@qoto.org
  • @absolutus@qoto.org
  • @arteteco@qoto.org
  • @Surasanji@qoto.org
  • @hashtaggrammar@qoto.org
Note: The account @QOTO@qoto.org listed as the administrator is NOT an actively monitored account. It was selected so as not to show favoritism among our moderator group, we are a democracy and even our administrators and moderators are held to the same high standards of decency as the rest of the community.

***We will never advertise on QOTO or sell your information to third-parties***