Long-ranged forces

[ElliotB256]

Long-ranged forces are important for 3D MOTs with lots of atoms, as the repulsive forces reduce the phase space density.

Some thoughts:

• May need to use a MacroAtom approach, where relevant quantities like repulsive forces are scaled so that a small number of atoms can simulate the PSD of an (intractable) larger number of atoms.
• Force goes as 1/r^2 which is long ranged and a real pain to parallelise.

Possible implementation:

• Hash spatial position to sort atoms into bins.
• Use a tree structure to allow fine-grained forces at close range, and coarse-grained forces for long range.
  • Atoms are sorted into each leaf of the tree.
  • Each leaf in the tree calculates total 'charge' and 'centre-of-mass'.
  • The tree structure is traversed to aggregate charges into each branch.
  • Tree structure from this point is immutable.
  • Calculate force exerted on each leaf due to tree structure (parallel over each leaf). Only calculate leaves which are occupied (total charge > 0). Iterate branches and leaves, to depth based on distance from calculated leaf.
  • For each atom, determine force by looking up leaf node. Use leaf.force + force calculated pair-wise between other atoms in the leaf.

Building tree will be O(L) O(N).

[ElliotB256]

Turns out the tree method has a name, it's called Barnes-Hut https://en.wikipedia.org/wiki/Barnes%E2%80%93Hut_simulation

[ElliotB256]

There is a recent repo for implementing this algorithmn, wouldn't hurt to try it and see how it performs. I expect it may need a bit of profiling https://docs.rs/nbody_barnes_hut/0.1.0/nbody_barnes_hut/

[ElliotB256]

Good overview in Leyuan Wu, Geophys. J. Int.(2018)215,1865–1886