We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle
simulations of reaction-diffusion systems based on the Doi or volume reactivity
model, in which pairs of particles react with a specified Poisson rate if they
are closer than a chosen reactive distance. In our Doi model, we ensure that
the microscopic reaction rules for various association and disassociation
reactions are consistent with detailed balance (time reversibility) at
thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to
separate reaction and diffusion, and solves both the diffusion-only and
reaction-only subproblems exactly, even at high packing densities. To
efficiently process reactions without uncontrolled approximations, SRBD employs
an event-driven algorithm that processes reactions in a time-ordered sequence
over the duration of the time step. A grid of cells with size larger than all
of the reactive distances is used to schedule and process the reactions, but
unlike traditional grid-based methods such as Reaction-Diffusion Master
Equation (RDME) algorithms, the results of SRBD are statistically independent
of the size of the grid used to accelerate the processing of reactions. We use
the SRBD algorithm to compute the effective macroscopic reaction rate for both
reaction- and diffusion-limited irreversible association in three dimensions.
We also study long-time tails in the time correlation functions for reversible
association at thermodynamic equilibrium. Finally, we compare different
particle and continuum methods on a model exhibiting a Turing-like instability
and pattern formation. We find that for models in which particles diffuse off
lattice, such as the Doi model, reactions lead to a spurious enhancement of the
effective diffusion coefficients.Comment: To appear in J. Chem. Phy