bot.md

Bump-on-tail:

$$ f_0(x,v) = \left(\frac{9}{10 \sqrt{2\pi}} \mathrm{e}^{-0.5 v^2}

• \frac{2}{10 \sqrt{2\pi}} \mathrm{e}^{-2 (v-4.5)^2} \right) (1+\alpha \cos(kx)), $$