ReactLD.jl

ReactLD.jl is a Julia package for performing stochastic simulations of particle-based reactive Brownian and Langevin dynamics using the Stochastic Simulation Algorithm (SSA).

This project focuses on the fundamental reversible reaction A + B ⇌ C but the methodology can be extended to more general reactions (see our paper below for details).

We consider randomly diffusing particles of species A, B, or C that evolve according to either:

• Brownian Dynamics (BDs): $$\dot{X}_t = \sqrt{2D} \dot{W}_t$$

• Langevine Dynamics (LDs): $$\dot{X}_t = V_t, \quad \dot{V}_t = -\beta V_t + \beta \sqrt{2D} \dot{W}_t,$$

where $X_t$ and $V_t$ denote positions and velocities of particles, $D$ is diffusion coefficient, and $\beta$ is the scaled friction constant.

Installation

Prerequisites

• Julia (v1.0 or later) installed on your system.
• Git installed.

1. Clone the repository

git clone https://github.com/chenyaomath/ReactLD.jl.git
cd ReactLD.jl

2. Install the packages in Julia

cd env
julia setup.jl

Quick Start

The repository contains several subfolders for running simulations of the A + B ⇌ C reaction:

• AB_C_V_large/ and AB_C_V_small/: Langevin Dynamics simulations in large/small domains
• AB_C_X_large/ and AB_C_X_small/: Brownian Dynamics simulations in large/small domains

To run a simulation, use the following command (customize the parameters as needed):

nohup JULIA_NUM_THREADS=5 julia ReactLD.jl --num_sim 11000 --beta 1.0e19 --time_step 1.0e-7 > ABCV_sim11000_beta1.0e19_time_step1.0e-7_24072210.log 2>&1 &

Main Results

Convergence of Reactive LDs to BDs	Error between Reactive LDs and BDs as β → ∞

Support and citation

If you use this package in your work, please cite the following paper. Open-source development in academia depends heavily on proper attribution. Also, consider starring the repository—this helps us demonstrate impact and secure funding:

@misc{isaacson2025macroscopicallyconsistentreactivelangevin,
  title     = {A Macroscopically Consistent Reactive Langevin Dynamics Model},
  author    = {Samuel A. Isaacson and Qianhan Liu and Konstantinos Spiliopoulos and Chen Yao},
  year      = {2025},
  eprint    = {2501.09868},
  archivePrefix = {arXiv},
  primaryClass  = {physics.bio-ph},
  url       = {https://arxiv.org/abs/2501.09868}
}