Polar form for an ellipse offset from the origin

I recently needed a polar-form equation for an ellipse, where the center of the ellipse is offset from the origin. I couldn’t easily find such an equation, so I derived it and am posting it here. (It’s easy to find expressions for ellipses where the focus is at the origin.) Read more 16 Feb 2021

Scaling of relative neutron fluxes at inboard and outboard midplane with aspect ratio

The most intense neutron flux in a tokamak is normally found at the midplane. The flux on the inboard side is often a critical value, since inboard space is scarce. The magnets need to be shielded so that they remain operational for the lifetime of the machine, but extra shielding thickness is wasted space. Read more 06 Feb 2021

Magnetic field at the surface of a long conductor with a square cross section

Assume an infinite conductor with a square cross-section. It has side length $l$ and carries a current along its length with uniform density $J$. Read more 21 Oct 2020

OpenRCT2 operations research: how many mechanics should I hire?

OpenRCT2 breathes new life into a classic game Read more 31 Aug 2020

The wrong (and right) way to select random velocities of particles moving through a surface

Part of my thesis is about simulating gases inside a box: their flow and how they interact with a plasma that is also inside a box. In order to do this, I’m using a FORTRAN code that’s been developed by generations of graduate students. I ran a simple test case in which I should end up with a gas of a uniform temperature and density inside my b... Read more 28 Apr 2019