A little investment into building a GUI for live visualizations and control provides huge improvements in iteration speed.

I recently came across the excellent video Coding Adventure: Simulating Fluids wonderfully explained by Sebastian Lague. The video walks through the steps to build a simple smoothed particle hydrodynamics simulation from nothing …

In the previous post I discussed how, when measuring the frequency (tempo) of a signal that itself changes in time, there is necessarily a tradeoff between the precision in the measured frequency and precision in the time at which the measurement is taken: A more precise measurement of frequency requires …

Most people are introduced to the term 'uncertainty principle' in the context of quantum mechanics. It is usually described as the idea that a particle's position and momentum cannot be simultaneously measured to arbitrary precision, but that improved precision in one must be traded off against increased uncertainty in the …

This page is intended to give a little context behind the "Bohr model" that is introduced in the first Quantum Mechanics sheet.

Background

Like all atomic models, the Bohr model attempts to answer the question "Why do atoms exhibit the properties that they do?", proposing a mechanical or mathematical description …

What is a variational principle?

A variational principle is a mathematical or physical law expressed in terms of maximising or minimising a certain quantity. The simplest example was known to ancient Egyptian builders and surveyers: a taut rope stretched between two points takes the shape that minimises its length. This …