Viewing posts by christian
Plotting nuclear fusion cross sections
Posted by: christian in Featured on frontpage on 10 Jul 2018
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.
Constructing Reuleaux polygons
Posted by: christian on 21 Jun 2018
A Reuleaux polygon is a curvilinear polygon built up of circular arcs. For an odd number of vertices, it has a constant width, and for this reason many polygonal coins, such as the UK's 50p piece and this Bermudian dollar coin are Reuleaux polygons. This property also means they make serviceable bicycle wheels:
What happens to carbon dioxide dissolved in water?
Posted by: christian on 11 Jun 2018
Carbon dioxide ($\mathrm{CO_2}$) dissolves in water, and some of the dissolved $\mathrm{CO_2}$ forms carbonic acid, $\mathrm{H_2CO_3(aq)}$: $$ \mathrm{CO_2(g)} + \mathrm{H_2O(l)} \rightleftharpoons \mathrm{H_2CO_3(aq)}. $$ This acid can then dissociate to form bicarbonate, $\mathrm{HCO_3^-}$: $$ K_1: \mathrm{H_2CO_3(aq)} \rightleftharpoons \mathrm{HCO_3^-(aq)} + \mathrm{H^+(aq)}, $$ which may further dissociate to carbonate, $\mathrm{CO_3^{2-}}$: $$ K_2: \mathrm{HCO_3^-(aq)} \rightleftharpoons \mathrm{CO_3^{2-}(aq)} + \mathrm{H^+(aq)}. $$
The world's nuclear reactors over time
Posted by: christian on 18 May 2018
The Python program given below generates this stacked area plot of the number of nuclear reactors in different countries over the last six decades or so.
The Duffing Oscillator
Posted by: christian on 15 May 2018
The previous blog post described the motion of a quartic oscillator: a particle moving in the potential $V(x) = \frac{1}{4}x^4 - \frac{1}{2}x^2$. In this case, the motion was always periodic (since the particle's energy is conserved).