含随机分布细胞的植物组织生物力学模型的均匀化
Homogenization of biomechanical models of plant tissues with randomly distributed cells
摘要：
本文研究了细胞随机分布的植物组织生物力学数学模型的均匀化问题。植物组织的力学性质是由一个强耦合系统来模拟的，该系统包括植物细胞和细胞壁中化学过程的反应-扩散-对流方程、植物细胞壁和中间层弹性变形的孔隙弹性方程以及细胞内流体流动的斯托克斯方程。力学和化学之间的非线性耦合由植物组织的弹性性质对化学物质密度的依赖性以及化学反应对组织中存在的机械应力的依赖性给出。利用随机均匀化技术，建立了细胞广义过程随机分布的植物组织生物力学的严格宏观模型。强随机两尺度收敛的非线性反应项的极限。引入边界项的适当含义，在微观尺度上定义具有通量边界条件和透射条件的宏观方程。
英文摘要：
In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells and cell walls, the equations of poroelasticity for elastic deformations of plant cell walls and middle lamella, and the Stokes equations for fluid flow inside the cells. The nonlinear coupling between the mechanics and chemistry is given by the dependence of elastic properties of plant tissue on densities of chemical substances as well as by the dependence of chemical reactions on mechanical stresses present in a tissue. Using techniques of stochastic homogenization we derive rigorously macroscopic model for plant tissue biomechanics with random distribution of cells. Strong stochastic two-scale convergence is shown to pass to the limit in the non-linear reaction terms. Appropriate meaning of the boundary terms is introduced to define the macroscopic equations with flux boundary conditions and transmission conditions on the microscopic scale.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
