Here you'll find an assortment of technical essays I've written over the years either as part of other research, or as teaching aids, or as pass-time exercises when I had nothing more interesting to occupy myself with. Nothing here is truly original, except perhaps for the presentation. Some of them are still works in progress.
A good friend of mine pointed me in the direction of a clustering algorithm called Dynamic Quantum Clustering, or DQC for short, which uses ideas from Quantum Mechanics to find the most likely cluster centers in a data set.
I read the original papers and had a few insights of my own, which I'm summarizing in this essay. I may yet write a couple of actual research papers about these insights but that's a decision I haven't made yet.
Did you know that you can balance a partially filled soda can when it's tilted? Here I analyse the mathematics of why and when that is possible.
I've gotten quite far on this but it's still work in progress.
An essay about light, the appearance of objects, and the theory of relativity, for non-physicists.
The goal for this project is to turn it into a book on the theory of relativity, for non-physicists, and it's still work in progress.
An article I wrote in September 2010 for an online magazine while I was spending time with my family back in my home country. Sadly for me, the article didn't get picked up for publication and, so, it remained in the proverbial drawer until August 2020 when I came across Sean Carrol's excellent video series The Biggest Ideas in the Universe.
Sean covers much of what I talk about in the article (and much more!) in the series' 17th episode, on Matter. Watching that episode, I thought it would be cool to resurrect the article since it goes through some material that Sean did not cover and it has some extra (and really cool) demonstrations of what the article and Sean's video are all about.
A non-trivial exercise in Mathematical Physics and its applications to Classical Electromagnetism, this essay solves in detail the problem of computing an analytical solution for the electrostatic potential between two conducting spheres.
A little exercise on elementary Newtonian mechanics to find out the minimum coefficient of friction required for a stack of cylinders not to collapse.
I have a complete solution for the case of 2 layers of stacked cylinders and have yet to tackle the case of more layers so this is still work in progress.
(2005) Second Quantization
What is Second Quantization and where does it fit in the overall scheme of Physics? This essay is a foray into the history of the early days of Quantum Mechanics and Quantum Field Theory.
A review of fundamental notions in linear algebra followed by some applications in Quantum Mechanics, with an emphasis on proving some very important properties of the Hamiltonian operator.
You're on a spaceship traveling at a comfortable constant acceleration of one g. A staple of science-fiction, solved correctly and in detail.
Solving the Helmholtz equation is a standard problem in almost any course in mathematical physics, and a simple way to introduce the notion of Green functions. I solve it here in full detail, explaining every step of the solution.
Nothing here is new, of course, but the formalism of Time-Independent Perturbation Theory is done in detail, with an emphasis on the degenerate case.
Have you ever wondered what objects moving close to the speed of light would look like?
(2004) Projectile Motion
A summary of results of a detailed treatment of the projectile motion problem in both one and two dimensions, including the effects of air resistance (using two different models for the velocity dependence).
I've gotten quite far on this but it's still work in progress. Originally written in 2004 based on some undergraduate work I did, now long gone.
Derivation of the differential equation, the transverse normal modes, and their frequencies, for a heavy chain hanging vertically.
(1993) Planetary Transfer Orbits
How do you transfer a satellite or other object in space from one orbit to another, say, from an orbit around the Earth to an orbit around Mars? You do it by applying an appropriate "delta-v", that is, by burning fuel to change the satellite's velocity until it has the appropriate value to "enter" the new orbit. From that point on, gravity does the rest so you can turn off the satellite's engines. But how is the necessary delta-v computed? Find out in this essay, for one particularly simple scenario.