带相互作用势的收敛反应-漂移-扩散主方程
A Convergent Reaction-Drift-Diffusion Master Equation with Interaction Potentials
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中文总结 AI 辅助
本文扩展收敛反应-扩散主方程至含两体相互作用势的系统，结合边平均有限元与质量集中求积，保留平衡与细致平衡性质，并验证二阶收敛。
中文摘要 AI 辅助
我们将非结构化网格上的收敛反应-扩散主方程（CRDME）框架扩展到包含粒子间的两体相互作用势。此类相互作用对于模拟粒子经历静电排斥、体积排斥或范德华吸引的系统至关重要。我们的方法对基于粒子的随机反应-漂移-扩散模型的前向方程的弱形式进行离散化，通过结合两种互补技术获得新的CRDME：一种是对包含势相互作用的空间输运项采用边平均有限元方法结合质量集中求积，另一种是对反应项采用有限体积与质量集中求积的混合近似。这为粒子在双网格体素之间跳跃并进行反应的空間跳跃过程提供了转移速率。所得的空間离散CRDME在封闭域内保留了连续系统的关键物理性质。它在无反应时保持吉布斯-玻尔兹曼平衡分布，并且对于具有可逆反应的系统，满足漂移-扩散通量和反应通量的细致平衡。与布朗动力学模拟的数值比较验证了我们的方法，并且我们展示了随着网格细化，经验二阶收敛性。
英文摘要
We extend the convergent reaction-diffusion master equation (CRDME) framework on unstructured grids to include two-body interaction potentials between particles. Such interactions are essential for modeling systems in which particles experience electrostatic repulsion, volume exclusion, or van der Waals attraction. Our approach discretizes the weak form of the forward equation for a particle-based stochastic reaction- drift-diffusion model to obtain a new CRDME by combining two complementary techniques: an edge- averaged finite element method with mass-lumping quadrature for spatial transport terms that include potential interactions, and a mix of finite volume and mass-lumping quadrature approximations for reaction terms. This yields transition rates for a spatial jump process of particles hopping between dual mesh voxels and undergoing reactions. The resulting spatially discrete CRDME retains key physical properties of the continuum system in closed domains. It preserves the Gibbs-Boltzmann equilibrium distribution in the absence of reactions, and satisfies detailed balance of both drift-diffusion and reactive fluxes for systems with reversible reactions. Numerical comparisons with Brownian dynamics simulations validate our method, and we demonstrate empirical second-order convergence as the mesh is refined.
发表机构
- Boston University（波士顿大学）
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