Department of Mathematics, Ryerson University, 350 Victoria St, M5B 2K3 Toronto, Canada.
Department of Mathematics, Ryerson University, 350 Victoria St, M5B 2K3 Toronto, Canada.
Math Biosci. 2019 Jun;312:23-32. doi: 10.1016/j.mbs.2019.04.001. Epub 2019 Apr 15.
The present paper introduces a new micro-meso hybrid algorithm based on the Ghost Cell Method concept in which the microscopic subdomain is governed by the Reactive Multi-Particle Collision (RMPC) dynamics. The mesoscopic subdomain is modeled using the Reaction-Diffusion Master Equation (RDME). The RDME is solved by means of the Inhomogeneous Stochastic Simulation Algorithm. No hybrid algorithm has hitherto used the RMPC dynamics for modeling reactions and the trajectories of each individual particle. The RMPC is faster than other molecular based methods and has the advantage of conserving mass, energy and momentum in the collision and free streaming steps. The new algorithm is tested on three reaction-diffusion systems. In all the systems studied, very good agreement with the deterministic solutions of the corresponding differential equations is obtained. In addition, it has been shown that proper discretization of the computational domain results in significant speed-ups in comparison with the full RMPC algorithm.
本文提出了一种新的基于幽灵细胞方法概念的微介混合算法，其中微观子域由反应多粒子碰撞（RMPC）动力学控制。介观子域采用反应-扩散主方程（RDME）建模。RDME 通过非均匀随机模拟算法求解。迄今为止，没有混合算法使用 RMPC 动力学来模拟反应和每个粒子的轨迹。RMPC 比其他基于分子的方法更快，并且在碰撞和自由流步骤中具有守恒质量、能量和动量的优点。新算法在三个反应扩散系统上进行了测试。在所研究的所有系统中，与相应微分方程的确定性解非常吻合。此外，还表明，与完整的 RMPC 算法相比，适当的计算域离散化可以显著提高速度。
