Emilie Blanc, Stefan Engblom, Andreas Hellander, Per Lötstedt
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引用次数: 9
Abstract
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.
期刊介绍:
Centered around multiscale phenomena, Multiscale Modeling and Simulation (MMS) is an interdisciplinary journal focusing on the fundamental modeling and computational principles underlying various multiscale methods.
By its nature, multiscale modeling is highly interdisciplinary, with developments occurring independently across fields. A broad range of scientific and engineering problems involve multiple scales. Traditional monoscale approaches have proven to be inadequate, even with the largest supercomputers, because of the range of scales and the prohibitively large number of variables involved. Thus, there is a growing need to develop systematic modeling and simulation approaches for multiscale problems. MMS will provide a single broad, authoritative source for results in this area.