Could someone explain the assignment of work in detail? Thanks.

You can find a more detailed explanation in this slide, but I believe the gist is:

1. At time step t, each processor traverses their section of the tree with DFS, computing gravitational force for their particles, and keeping track of the work done (in terms of computations for each body).
2. Sum total work = W.
3. Periodically recompute assignment so processor P_i gets all the nodes between iW/P and (i+1)W/P.