  Several algorithms have been used for mass transfer between particles
undergoing advective and macro-dispersive random walks. The mass transfer
between particles is required for general reactions on, and among, particles.
The mass transfer is shown to be diffusive, and may be simulated using
implicit, explicit, or mixed methods. All algorithms investigated are accurate
to $\mathcal{O}(\Delta t)$. For $N$ particles, the implicit and semi-implicit
methods require inverse matrix solutions and $\mathcal{O}(N^3)$ calculations.
The explicit methods use forward matrix solves and require only
$\mathcal{O}(N^2)$ calculations. Practically, this means that naive
implementations with more than about 5,000 particles run more reliably using
explicit methods
