# Blog

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## Types of plasma

Two important parameters in plasma physics are the electron Debye length, $\lambda_{\mathrm{D}e}$, a measure of the distance over which charge-screening effects occur and deviations from quasi-neutrality are observed, and the number of paricles in a "Debye cube" (of side length $\lambda_{\mathrm{D}e}$), $N_\mathrm{D}$.

## Plotting nuclear fusion cross sections

In a nuclear fusion reaction two atomic nuclei combine to form a single nucleus of lower total mass, the difference in mass, $\Delta m$ being released as energy in accordance with $E = \Delta m c^2$. It is this process which powers stars (in our own sun, hydrogen nuclei are fused into helium), and nuclear fusion has been actively pursued as a potential clean and cheap energy source in reactors on Earth for over 50 years.

## Simulating the Belousov-Zhabotinsky reaction

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 double pendulum

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.

## Visualizing the bivariate Gaussian distribution

The multivariate Gaussian distribution of an $n$-dimensional vector $\boldsymbol{x}=(x_1, x_2, \cdots, x_n)$ may be written