# Blog

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## Packing circles inside a shape

A previous blog post dealt with packing circles into a circle. To fill an arbitrary shape, a slightly different approach is needed. The code presented in my github repo.

## Packing circles in a circle

The following code attempts to pack a predefined number of smaller circles (of random radii between two given limits) into a larger one.

## Simulating two-dimensional polycrystals

The following code simulates (very approximately) the growth of a polycrystal from a number of seeds. Atoms are added to the crystal lattice of each of the resulting grains until no more will fit, creating realistic-looking boundaries where two grains meet.

## Breeding tritium for a fusion reactor

The most feasible nuclear reaction for a "first-generation" fusion reaction is the one involving deuterium (D) and tritium (T): $$\mathrm{D} + \mathrm{T} \rightarrow \alpha (3.5\;\mathrm{MeV}) + n (14.1\;\mathrm{MeV})$$ Tritium is not a primary fuel and does not exist in significant quantities naturally since it decays with a half life of 12.3 years. It therefore has to be "bred" from a separate nuclear reaction. Most fusion reactor design concepts employ a lithium "blanket" surrounding the reaction vessel which absorbs the energetic fusion neutrons to produce tritium in such a reaction.

## 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.