介观建模中的随机反应-扩散动力学在亚扩散 regime 中的研究
Mesoscopic modeling of stochastic reaction-diffusion kinetics in the subdiffusive regime
AI总结：
本文提出了一种适用于亚扩散过程的介观模型，揭示了两种化学反应模型，并推导了基本动态特性，通过分析和数值实验估计了亚扩散混合下的宏观效应。
摘要：
亚扩散已被提出作为解释细胞内各种动力学现象的可能解释。为了促进大规模亚扩散化学过程的计算研究，我们扩展了最近提出的一种亚扩散介观模型，使其成为一种准确且一致的反应-亚扩散计算框架。揭示了两种可能的化学反应模型，并推导了一些基本动态特性。在某些情况下，这些介观模型在宏观层面可以直接解释为在有限时间区间内的分数偏微分方程。通过分析和数值实验，我们估计了亚扩散混合下反应的宏观效应。这些模型表现出也出现在实验中的特性：在短时间区间内，扩散和反应的行为是普通的，在中间时间区间内行为是异常的，而在长时间区间内行为又变得普通。
英文摘要：
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model of subdiffusion into an accurate and consistent reaction-subdiffusion computational framework. Two different possible models of chemical reaction are revealed and some basic dynamic properties are derived. In certain cases those mesoscopic models have a direct interpretation at the macroscopic level as fractional partial differential equations in a bounded time interval. Through analysis and numerical experiments we estimate the macroscopic effects of reactions under subdiffusive mixing. The models display properties observed also in experiments: for a short time interval the behavior of the diffusion and the reaction is ordinary, in an intermediate interval the behavior is anomalous, and at long times the behavior is ordinary again.
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