A blog of Python-related topics and code.
Simulating the Belousov-Zhabotinsky reaction
Posted by: christian on 27 Jul 2017
The Belousov-Zhabotinsky (BZ) reaction is a classical example of a non-equibrium chemical oscillator in which the components exhibit periodic changes in concentration.
The harmonically-driven pendulum
Posted by: christian on 25 Jul 2017
For the purposes of this article, the harmonically-driven pendulum is one whose anchor point moves in time according to $x_0(t) = A\cos\omega t$. As with previous posts, the position of the pendulum bob with time can be described using Lagrangian mechanics. In a coordinate system with the pendulum anchor initially at $(0,0)$ and the $y$-axis pointing up, the components of the bob position and velocity as a function of time are:
The spring pendulum
Posted by: christian on 19 Jul 2017
Following on from the previous post on the double pendulum, here is a similar Python script for plotting the behaviour of the "spring pendulum": a bob of mass $m$ suspended from a fixed anchor by a massless spring.
The double pendulum
Posted by: christian on 16 Jul 2017
In classical mechanics, a double pendulum is a pendulum attached to the end of another pendulum. Its equations of motion are often written using the Lagrangian formulation of mechanics and solved numerically, which is the approach taken here. The dynamics of the double pendulum are chaotic and complex, as illustrated below.
A very simple 2-D diffusion model
Posted by: christian on 21 May 2017
A very simple diffusion simulation can be constructed in two dimensions by following the positions of a number of "particles" which all start off at the centre of a grid of cells. Time is assumed to progress in a series of "ticks": at each tick, each particle's position changes at random by $-1$, $0$, or $+1$ cells in each of the $x$ and $y$ directions.