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Title: 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 » 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.« less

Authors:
 [1];  [2];  [3]
  1. New York Univ. (NYU), NY (United States)
  2. New York Univ. (NYU), NY (United States); Univ. of California, Berkeley, CA (United States)
  3. 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:
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. https://www.osti.gov/servlets/purl/1435110.
@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 = {2018},
month = {1}
}

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Figures / Tables:

Fig. 1 Fig. 1: Conversion from microscopic to macroscopic reaction rates for (partially) diffusion-limited systems (ƒ = k0/kS ∼ 1/2) at finite packing densities φ. Error bars are smaller or comparable to symbol size. (Left) Correction to the low-density rate k0, given by (1) for SRBD and by (3) for RDME, formore » coagulation, A + A → A and ∅ → A. For SRBD, we use two different time step sizes (see the legend) and extrapolate to the exact result without splitting errors. For the RDME, an exact renormalization calculation gives the leading order non-analytic φ1/2 correction, which matches our numerical results for sufficiently small densities. For SRBD, the result is well fit by the empirical fit k/k0 = 1 + 1.215φ1/2 + 0.312φ (dotted black line). (Right) Deviation k/k0 = nB/nA from the low-density rate k0 given by (1) for SRBD for annihilation, A + BB and ∅ → A, for several time step sizes (see the legend). For Δt = 1, we show results obtained using a system that is twice larger (i.e., eight times the number of particles) and see no measurable finite-size effects. There is no theory for finite densities but the result is consistent with the empirical fit k/k0 ≈ 1 + 0.458φ1/2.« less

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