Corrected mean-field models for spatially dependent advection-diffusion-reaction phenomena.
Corrected mean-field models for spatially dependent advection-diffusion-reaction phenomena.
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修正了空间相关的平流扩散反应现象的平均场模型。
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
R. Baker
中科院分区：
文献类型：
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作者：
M. Simpson;R. Baker
在排斥过程的文献中，平均场模型通常是通过假设晶格位置的占据状态是独立的来推导的。虽然这个假设是有问题的，但它是许多平均场模型的基础。在这项工作中，我们开发的方法来放松一系列离散的排斥过程为基础的机制，从细胞生物学的应用程序的独立性假设。以前的研究，侧重于放松独立性假设已限于研究最初的均匀种群，忽略了任何空间变化。由于晶格的平移不变性，忽略了空间变化，大大简化了以前的研究。这些以前的修正平均场模型不能应用于细胞生物学中的许多重要问题，如细胞的入侵波，其特征在于移动的前沿。在这里，我们提出了广义的方法，放松空间非齐次问题的独立性假设，导致校正的平均场描述的一系列排除过程为基础的模型，包括（i）无偏运动，（ii）有偏运动，（iii）无偏运动与代理出生和死亡过程。修正后的平均场模型适用于包括侵入波型问题在内的空间变化过程。我们表明，基于调用独立性假设，模拟数据与传统平均场模型之间可能存在很大偏差。此外，我们表明，校正后的平均场模型在所有情况下考虑的模拟数据得到了改进的匹配。
In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion-process-based mechanisms motivated by applications from cell biology. Previous investigations that focused on relaxing the independence assumption have been limited to studying initially uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterized by moving fronts. Here we propose generalized methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion-process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave-type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.