diff --git a/README.md b/README.md index 0429aa29ff28f67a862d85f842a5cb3c5e5dd8fe..eeaa8a2cfddad0de6e89b605111f48eaf639734c 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,7 @@ # Electromagnetic FEA Simulations +<script type="math/tex; mode=display">\sum_{n=1}^\infty \frac{(ik)^n}{n!} C_n = \log \langle e^{ikx} \rangle</script> + We can create rudimentary 2D and 3D FEA simulations of current carrying wires and permanent magnets in free space using only two equations: For current carrying wires we use [Biot-Savart](https://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law): @@ -18,7 +20,7 @@ The rest is surprisingly simple and can be implemented in about 100 lines of cod  -Examining the results above, there are some innacuracies and limitations worth noting for improvement: +Examining the results above, there are some inaccuracies and limitations worth noting for improvement: 1) First let's note that there appears to be divergence on the left and right bounds of the permanent magnet where the field changes direction. I initially assumed that this was incorrect, but it turns out [H fields are indeed divergent](https://en.wikipedia.org/wiki/Magnetic_field#H-field_and_magnetic_materials) at the boundary of a magnet, and [Gauss's law for magnetism](https://en.wikipedia.org/wiki/Gauss%27s_law_for_magnetism) applies to magnetic flux density B, but not field strength H. This should really be apparent from the fact that H = B/u_0 - M, where the magnetization vector M is just a uniform vector field that sources from one side of the magnet and sinks into the other, as shown in the image linked to above. diff --git a/images/Afield.png b/images/Afield.png new file mode 100644 index 0000000000000000000000000000000000000000..9f836dee54b6d53e1fd42f7831f76cf32c60327f Binary files /dev/null and b/images/Afield.png differ diff --git a/images/AtoB.png b/images/AtoB.png new file mode 100644 index 0000000000000000000000000000000000000000..e55ac6a16b3215024ef79d5859502b30fd3ce2a7 Binary files /dev/null and b/images/AtoB.png differ diff --git a/images/BfieldFinal.png b/images/BfieldFinal.png new file mode 100644 index 0000000000000000000000000000000000000000..b49f4f86b3428e9a28861491ebd7671940026658 Binary files /dev/null and b/images/BfieldFinal.png differ diff --git a/images/DIYsim2.png b/images/DIYsim2.png new file mode 100644 index 0000000000000000000000000000000000000000..73b3e98fd437feb3e7470ebef6af2c1ee85cb5c0 Binary files /dev/null and b/images/DIYsim2.png differ diff --git a/images/continuousDiscrete.png b/images/continuousDiscrete.png new file mode 100644 index 0000000000000000000000000000000000000000..19bdb8f6b2a91554d9b74d5f25a445b88fa3098e Binary files /dev/null and b/images/continuousDiscrete.png differ diff --git a/images/ferritic.gif b/images/ferritic.gif new file mode 100644 index 0000000000000000000000000000000000000000..d7a0813ea41f17c708f7162c1b0d46d69f8fcf10 Binary files /dev/null and b/images/ferritic.gif differ diff --git a/images/helmholtz.png b/images/helmholtz.png new file mode 100644 index 0000000000000000000000000000000000000000..792418e02afc34a3f653e7f96c7ad2f144669bf3 Binary files /dev/null and b/images/helmholtz.png differ diff --git a/images/jBound.png b/images/jBound.png new file mode 100644 index 0000000000000000000000000000000000000000..0769198b739477e5cbfb21d1853161bbccfe3016 Binary files /dev/null and b/images/jBound.png differ diff --git a/images/longboi.png b/images/longboi.png new file mode 100644 index 0000000000000000000000000000000000000000..d35bbad1aaa745311db66b340127ab02e2addab3 Binary files /dev/null and b/images/longboi.png differ diff --git a/images/validation.png b/images/validation.png new file mode 100644 index 0000000000000000000000000000000000000000..9d29de0cc1cc7e8afa2db468775a5ad0773f00c5 Binary files /dev/null and b/images/validation.png differ diff --git a/images/validationExperiment.png b/images/validationExperiment.png new file mode 100644 index 0000000000000000000000000000000000000000..a80ac5209573e22de0d36422ab3c23126e57f49f Binary files /dev/null and b/images/validationExperiment.png differ