Sagués F, Shkilev V P, Sokolov I M
Departament de Química Física, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Mar;77(3 Pt 1):032102. doi: 10.1103/PhysRevE.77.032102. Epub 2008 Mar 17.
We consider a linear reversible isomerization reaction A <=> B under subdiffusion described by continuous time random walks (CTRW). The reactants' transformations take place independently on the motion and are described by constant rates. We show that the form of the ensuing system of mesoscopic reaction-subdiffusion equations is unusual: the equation for time derivative of say A(x,t) contains the terms depending not only on DeltaA , but also on DeltaB . This mirrors the fact that in subdiffusion the flux of particles at time t is defined by the distributions of the particles' concentrations at all previous times. Since the particles which jump as A at time t could previously be both A or B , this flux depends on both A and B concentrations.
我们考虑在连续时间随机游走（CTRW）描述的亚扩散情况下的线性可逆异构化反应A⇌B。反应物的转化在运动上独立发生，并由恒定速率描述。我们表明，由此产生的介观反应 - 亚扩散方程组的形式不同寻常：例如A(x,t)的时间导数方程不仅包含依赖于ΔA的项，还包含依赖于ΔB的项。这反映了一个事实，即在亚扩散中，时间t时粒子的通量由之前所有时间粒子浓度的分布定义。由于在时间t以A形式跳跃的粒子之前可能是A或B，所以这个通量取决于A和B的浓度。
