Energetic Phase Field Methods and Modeling in Biological Microstructures

王DMS-0807915 近年来，能量相场方法在研究微观组织演化方面具有许多优势，已成为一种成功的建模和模拟方法。 相场方法的思想是引入一组相场变量来隐式跟踪微结构的运动表面，这可能是非常复杂和非线性的。 在这个项目中，研究人员和他的合作者应用相场方法来研究生物微观结构，特别是细胞膜。 本项目主要是对相场方法进行进一步的分析，拓宽相场方法在生物微结构演化研究中的应用，使相场方法及其相关概念可以作为生物微结构演化研究的基础，从而更方便、更有效地处理生物微结构演化问题。 该项目包括建模，数值方法和理论分析。 本文研究了相场方法中至今尚未解决或部分尚未解决的一些理论和算法问题，如相场变量的渐近行为（与De Giorgi猜想有关）、流体耦合相场模型与sharpinterface模型的一致性、拓扑信息检索公式以及一些流行算法的收敛性和加速性。 他还将理论结果应用于一些复杂微结构系统的建模和仿真，特别是剪切流中的细胞粘附和滚动，这可用于血液流动的研究。 细胞运动是另一种复杂的生物现象，可以使用相场模型进行模拟。 也被认为是模拟acto-myosin驱动的细胞振荡，这可以应用于研究细胞分裂和迁移，两个最重要的功能活细胞。 除了模拟一些观察到的现象外，相场模型还可以用来预测一些尚不完全清楚的结构的细节，如高度折叠的膜。

WangDMS-0807915 During recent years, the energetic phase field approach hasemerged as a successful modeling and simulation method with manyadvantages in studying microstructure evolutions. The idea ofphase field methods is to introduce a set of phase fieldvariables to implicitly track the moving surfaces ofmicrostructures, which can be very complex and nonlinear. Inthis project, the investigator and his collaborators apply phasefield methods to study biological microstructures, especiallycell membranes. The project is mainly concerned with furtheranalysis on phase field methods, and the broadening ofapplications in studying the evolution of biologicalmicrostructures for which phase field methods and relatedconcepts can be used as a basis for more convenient or efficienttreatments. The project includes modeling, numerical methods,and theoretical analysis. The investigator studies some theoretic and algorithmicproblems in phase field methods that still remain unsolved orpartly unsolved today, such as asymptotic behavior of phase fieldvariables (which is related to the De Giorgi conjecture), theconsistency of the fluid coupled phase field model to the sharpinterface model, topological information retrieval formulations,and convergence and acceleration of some popular algorithms. Healso applies the theoretical results to the modeling andsimulation of some complex microstructure systems, especiallycellular adhesion and rolling in a shear flow, which can be usedin the study of blood flows. Cell motility is another complexbiological phenomenon that can be simulated using phase fieldmodels. Also considered is the simulation of acto-myosin drivencell oscillations, which can be applied to study cell divisionand migration, two of the most important functions of livingcells. Besides simulating some observed phenomenon, phase fieldmodels can also be applied to predict details of some structuresthat are not yet fully known, such as highly folded membranes.