论文标题
扩散介导的表面反应的积累时间
Accumulation times for diffusion-mediated surface reactions
论文作者
论文摘要
在本文中，我们考虑了用于研究扩散介导的表面反应的最新概率框架的多片版。概率方法的基本思想是考虑粒子位置和所谓边界当地时间的关节概率密度或广义传播器。后者是布朗粒子在完全反射边界附近花费的时间的特征。然后，在当地时间通过适当的停止条件纳入表面反应的效果。传播器是通过解决罗宾边界值问题来确定的，其中恒定的反应性速率被确定为laplace变量$ z $ conjugate到当地时间，然后将解决方案反转相对于$ z $。在这里，我们将繁殖物重新解释为颗粒浓度，其中表面吸收由粒子源项平衡。我们研究了存在非平凡稳态溶液的条件，并通过计算相应的累积时间来分析稳态的弛豫。特别是，我们表明停止当地时间密度的前两个时刻必须是有限的。
In this paper we consider a multiparticle version of a recent probabilistic framework for studying diffusion-mediated surface reactions. The basic idea of the probabilistic approach is to consider the joint probability density or generalized propagator for particle position and the so-called boundary local time. The latter characterizes the amount of time that a Brownian particle spends in the neighborhood of a totally reflecting boundary; the effects of surface reactions are then incorporated via an appropriate stopping condition for the local time. The propagator is determined by solving a Robin boundary value problem, in which the constant rate of reactivity is identified as the Laplace variable $z$ conjugate to the local time, and then inverting the solution with respect to $z$. Here we reinterpret the propagator as a particle concentration in which surface absorption is counterbalanced by particle source terms. We investigate conditions under which there exists a non-trivial steady state solution, and analyze the relaxation to steady state by calculating the corresponding accumulation time. In particular, we show that the first two moments of the stopping local time density have to be finite.
