扩散介导的表面反应的累积时间
Accumulation times for diffusion-mediated surface reactions
摘要：
在本文中，我们考虑一个多粒子版本的最近的概率框架研究扩散介导的表面反应。概率方法的基本思想是考虑粒子位置的联合概率密度或广义传播子和所谓的边界局部时。后者表征了布朗粒子在全反射边界附近花费的时间量;然后通过适当的局部时间停止条件将表面反应的影响纳入其中。传播子是通过求解罗宾边值问题来确定的，其中反应性的恒定速率被识别为与本地时间共轭的拉普拉斯变量$z$，然后将解相对于$z$反转。在这里，我们重新解释的传播作为一个粒子的浓度，其中表面吸收是由粒子源项抵消。我们调查的条件下，存在一个非平凡的稳定状态的解决方案，并分析松弛到稳定状态，通过计算相应的积累时间。特别是，我们表明，停止本地时间密度的前两个时刻必须是有限的。
英文摘要：
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.
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