Gaussian Units
CGS and Gaussian Units are the bane of my existence, so I decided to make a page that compiles all the useful information I can find about them in one place.
Shape Functions
In PIC simulations, we are solving for quantities on a discrete grid. So, for example, if we are looking at charge, it would seem that all the charge would be concentrated in macroscopic point charges. However, this is not capturing the true physical picture of a simulation, because each of these simulation charges are macroparticles and represent many, many real particles. It would make more sense to smooth these charges out into some type of shape function that represents the charge density. Closer to the macroparticle location, we should expect a higher value of the shape function and further away, it should be lower.
Relativity and E&M
In an introductory Electricity and Magnetism Class, we learn that the magnetic force on a charge in a magnetic field is dependendent on its velocity. This is an issue because if we move into an inertial reference frame moving with the particle, the magnetic force will appear to vanish!