# Blog

A blog of Python-related topics and code.

## Wa-Tor World on a torus The population dynamics simulation known as Wa-Tor was described in a previous post. When carried out on a grid with periodic boundary conditions, the Wa-Tor "universe" is topologically equivalent to a torus, as depicted below using the code provided here.

## Diffusion on the surface of a torus An example in Chapter 7 of the scipython book describes the numerical solution of the two-dimensional heat equation for a flat plate with edges held at a fixed temperature.

## An object-oriented SVG torus The code below, torus.py, defines a class Torus for drawing an SVG image of a torus. The Torus class itself is a subclass of Shape, a more general class for depicting 3D objects in an SVG image, defined in shape.py. A usage example is given in the code of draw_torus.py, which creates this image:

## Non-linear least squares fitting of a two-dimensional data The scipy.optimize.curve_fit routine can be used to fit two-dimensional data, but the fitted data (the ydata argument) must be repacked as a one-dimensional array first. The independent variable (the xdata argument) must then be an array of shape (2,M) where M is the total number of data points.

## ExB drift for an arbitrary electric potential As described in the previous blog post charged particle moving in crossed constant magnetic and electric fields exhibits a drift velocity, $(\boldsymbol{E}\times\boldsymbol{B})/B^2$, perpendicular to both $\boldsymbol{E}$ and $\boldsymbol{B}$. The particle's trajectory in this situation can be found analytically. For an arbitrary $\boldsymbol{E}$, some kind of numerical integration of the equation of motion is usually necessary, but the force that the particle experiences at an instant is perpendicular to to the electric field and the particle therefore undergoes its gyromotion along an isocontour of electrostatic potential, $V$ (since $\boldsymbol{E} = -\nabla V$).