生物细胞质中有效扩散系数的解析与数值逼近
Analytical And Numerical Approximation of Effective Diffusivities in The Cytoplasm of Biological Cells
AI总结：
针对细胞质复杂几何结构导致的标准离散化技术无法处理的问题，提出一种两步均匀化策略，通过解析均匀化与随机均匀化结合，计算有效扩散常数。
摘要：
如果必须考虑空间分布，哺乳动物细胞代谢的模拟就成为一个严重问题。特别是细胞质具有非常复杂的几何结构，标准离散化技术无法处理。在本文中，我们提出了一种用于计算有效扩散常数的均匀化技术。这是通过使用两步策略完成的。第一步包括从最小尺度到中间尺度的解析均匀化。通过将解析扩散常数与使用真实细胞几何获得的数值估计进行比较，来估计均匀化误差。第二步包括随机均匀化。由于该均匀化问题没有已知的解析解，因此提出了一种数值逼近算法。尽管相当昂贵，该算法提供了均匀化扩散常数的合理估计。
英文摘要：
The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard discretization techniques. In the present paper we propose a homogenization technique for computing effective diffusion constants. This is accomplished by using a two-step strategy. The first step consists of an analytic homogenization from the smallest to an intermediate scale. The homogenization error is estimated by comparing the analytic diffusion constant with a numerical estimate obtained by using real cell geometries. The second step consists of a random homogenization. Since no analytical solution is known to this homogenization problem, a numerical approximation algorithm is proposed. Although rather expensive this algorithm provides a reasonable estimate of the homogenized diffusion constant.
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