While I was in school, one of my professors set this problem to me and my classmates and challenged us to solve it over the next few days. I found the challenge intriguing and it fascinated me, so I thought it was worth sharing. The problem was this: Show that where has finite support and […]
An overview and review of some of the results of one of my observing projects
In this post, I continue to introduce tensor calculus by discussing coordinates and transformations of coordinates.
In my final semester, my course load included a graduate course that had two modules: astronomical instrumentation and numerical modeling. The latter focused on developing the equations of motion of geophysical fluid dynamics (See Research in Magnetohydrodynamics). Such equations are then converted into an algorithm based on a specific type of numerical method of solving […]
SOURCE FOR CONTENT: Davidson, P.A., 2001, An Introduction to Magnetohydrodynamics. 3. The purpose of this post is to introduce the concepts of helicity as an integral invariant and its magnetic analog. More specifically, I will be showing that is invariant and thus correlates to the conservation of vortex line topology using the approach given in […]
SOURCES: Tricomi, F.G., Integral Equations. 1985. Dover. 1. Wazwaz, A.M., A First Course in Integral Equations. 2015. 3.6 In regards to solving integral equations, there are two main types of equations: Volterra and Fredholm equations. The first of which is the topic of this post. First, a brief introduction. Just as there are equations which deal with […]
SOURCE FOR CONTENT: Choudhuri, A.R., 2010. Astrophysics for Physicists. Ch. 8. In the previous post we saw the consequences of different regimes of the magnetic Reynolds’ number under which either diffusion or advection of the magnetic field dominates. In this post, I shall be doing a “proof” of Alven’s Theorem of Flux Freezing. (I hesitate to call […]