论文标题
在有限域中可逆反应的粒子模型的详细平衡
Detailed Balance for Particle Models of Reversible Reactions in Bounded Domains
论文作者
论文摘要
在基于粒子的随机反应扩散模型中，使用反应速率和放置内核来确定反应物颗粒之间可能发生反应的概率，并确定应放置产品颗粒的位置。当选择内核用于可逆反应时，关键的限制是确保空间反应 - 频率的详细平衡在平衡处的所有点都保持。在这项工作中，我们制定了一个一般的部分综合方程模型，该模型涵盖了几种常用的接触反应性（例如Smoluchowski-Collins-kimball）和体积反应性（例如DOI）粒子模型。从这些方程式中，我们得出了可逆的$ \ textrm {a} + \ textrm {b} \ leftrightArrows \ textrm {c} $反应的详细平衡条件。在具有无流量边界条件的有界域中，当选择与几个常用的结合内核一致的不闭合内核时，我们表明，在所有点上保持空间反应量的详细平衡需要在空间上以空间变化的范围速率函数在域边界附近。布朗动力学仿真算法可以通过在解开和拒绝未连接的事件期间忽略域边界来实现这种不同的速率，从而导致产品颗粒放置在域外。
In particle-based stochastic reaction-diffusion models, reaction rate and placement kernels are used to decide the probability per time a reaction can occur between reactant particles, and to decide where product particles should be placed. When choosing kernels to use in reversible reactions, a key constraint is to ensure that detailed balance of spatial reaction-fluxes holds at all points at equilibrium. In this work we formulate a general partial-integral differential equation model that encompasses several of the commonly used contact reactivity (e.g. Smoluchowski-Collins-Kimball) and volume reactivity (e.g. Doi) particle models. From these equations we derive a detailed balance condition for the reversible $\textrm{A} + \textrm{B} \leftrightarrows \textrm{C}$ reaction. In bounded domains with no-flux boundary conditions, when choosing unbinding kernels consistent with several commonly used binding kernels, we show that preserving detailed balance of spatial reaction-fluxes at all points requires spatially varying unbinding rate functions near the domain boundary. Brownian Dynamics simulation algorithms can realize such varying rates through ignoring domain boundaries during unbinding and rejecting unbinding events that result in product particles being placed outside the domain.
