论文标题
在具有部分渗透的部分吸收壁的系统中的细胞扩散
Subdiffusion in a system with a partially permeable partially absorbing wall
论文作者
论文摘要
我们考虑粒子在具有薄薄壁的一维系统中的细胞扩散。穿过墙壁，可以以一定概率吸收粒子。我们称这样的壁部分可渗透部分吸收壁（PPAW）。使用离散时间和空间变量的系统中的扩散模型，已经得出了描述系统中次扩散的概率密度（Green的功能）。知道绿色的功能，我们在墙壁处得出边界条件。边界条件采用特定形式，其中涉及由亚扩散参数控制的分数顺序的时间衍生物。我们假设只有当粒子跳过壁时，才能发生粒子的吸收。不可能将粒子暂时保留在薄壁内。墙壁可以代表薄膜。如果在其中考虑颗粒可以扩散的膜厚的系统，则可以将其视为三部分，厚度为厚的膜。对于PPAW，可以假定膜表面的边界条件。带有PPAW的系统可用于过滤扩散的颗粒。考虑尚未吸收扩散分子的概率的时间演变。此功能显示了过滤过程的效率。讨论了次扩散和壁参数对此功能的影响。
We consider subdiffusion of a particle in a one-dimensional system with a thin partially permeable wall. Passing through the wall, the particle can be absorbed with a certain probability. We call such a wall partially permeable partially absorbing wall (PPAW). Using the diffusion model in a system with discrete time and spatial variable, probability densities (Green's functions) describing subdiffusion in the system have been derived. Knowing the Green's functions we derive boundary conditions at the wall. The boundary conditions take a specific form in which time derivatives of the fractional order controlled by the subdiffusion parameter are involved. We assume that the absorption of a particle can occur only when the particle jumps through the wall. It is not possible to temporarily retain a particle inside a thin wall. The wall can represent a thin membrane. If a system with a thick membrane inside which particles may diffuse is considered, it can be treated as a three-part with a thick membrane as the middle part. The boundary conditions at membrane surfaces can be assumed as for PPAW. The system with PPAW can be used to filter diffusing particles. The temporal evolution of the probability that the diffusing molecule has not been absorbed is considered. This function shows the efficiency of the filtering process. The impact of subdiffusion and wall parameters on this function is discussed.
