# Efficient reactive Brownian dynamics

## Abstract

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 dissociation 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 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-limited and diffusion-limited irreversible association in three dimensions and compare tomore »

- Authors:

- New York Univ. (NYU), NY (United States)
- New York Univ. (NYU), NY (United States); Univ. of California, Berkeley, CA (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1435110

- Alternate Identifier(s):
- OSTI ID: 1417424

- Grant/Contract Number:
- AC02-05CH11231; SC0008271

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 148; Journal Issue: 3; Related Information: © 2018 Author(s).; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Donev, Aleksandar, Yang, Chiao-Yu, and Kim, Changho.
```*Efficient reactive Brownian dynamics*. United States: N. p., 2018.
Web. doi:10.1063/1.5009464.

```
Donev, Aleksandar, Yang, Chiao-Yu, & Kim, Changho.
```*Efficient reactive Brownian dynamics*. United States. doi:10.1063/1.5009464.

```
Donev, Aleksandar, Yang, Chiao-Yu, and Kim, Changho. Sun .
"Efficient reactive Brownian dynamics". United States.
doi:10.1063/1.5009464.
```

```
@article{osti_1435110,
```

title = {Efficient reactive Brownian dynamics},

author = {Donev, Aleksandar and Yang, Chiao-Yu and Kim, Changho},

abstractNote = {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 dissociation 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 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-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also 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.},

doi = {10.1063/1.5009464},

journal = {Journal of Chemical Physics},

number = 3,

volume = 148,

place = {United States},

year = {Sun Jan 21 00:00:00 EST 2018},

month = {Sun Jan 21 00:00:00 EST 2018}

}