MESOSCOPIC MODELING OF STOCHASTIC REACTION-DIFFUSION KINETICS IN THE SUBDIFFUSIVE REGIME

作者：Blanc Emilie^*; Engblom Stefan; Hellander Andreas; Lotstedt Per

来源：Multiscale Modeling and Simulation, 2016, 14(2): 668-707.

DOI：10.1137/15M1013110

• continuous-time random walk
• subdiffusion
• fractional derivative
• anomalous kinetics
• multistate reaction-diffusion system

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 also observed 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.

• 出版日期2016