Modeling and Simulations of Complex Fluids and Atomistic Strain

该项目的主要目标是建立一个综合的数学和计算研究计划，其中包括相互连贯的数学学科，目标是但不限于复杂流体和原子应变的建模和模拟中的一些具有挑战性的应用。该项目的主要目标是了解蠕虫状胶束流体中的流动不稳定性，如振荡的下落球体和跳跃的气泡。利用考虑长短胶束和剪切诱导结构的三组分模型，研究了流动不稳定性与剪切诱导结构之间的猜想关系。该项目将在复杂流体模型中引入正则化技术，以实现稳健和稳定的模拟，并将它们与大规模并行计算技术框架中的快速多重网格求解器相结合。这种建模和计算相结合的方法有望开发出流变学建模软件。该项目还旨在开发新的纳米晶体材料的应变建模和模拟。应用连续体线弹性有限元方法建立了原子应变模型。与使用有限差分近似建立的传统应变模型不同，新提出的模型将反映并考虑真实的原子结构，如钻石和锌结构。在这个项目中开发的模型将被用来研究与应变相关的纳米结构的形成作为其应用。复杂流体在自然界和工业中普遍存在，它们被用于许多重要领域，包括制药、食品、军事、生物材料、印刷和石油工业，仅举几例。纳米晶体材料中的应变是材料科学研究的核心，了解这种应变对于指导发光二极管、注入激光器和太阳能电池等实际器件的设计应用至关重要。然而，对纳米晶体材料中复杂流体和应变的建模和模拟仍然是艰巨和艰巨的挑战，即使使用现代超级计算机也是如此。其中，现有数学模型的固有缺陷和传统数值技术的低效是阻碍科学家理解和设计材料的主要瓶颈。预计本研究中开发的建模和计算方法将弥补模型中的不足和计算中的低效，从而极大地消除数学和计算瓶颈，并最终为科学家提供宝贵的指导工具，以便更好地了解本项目范围内以及可以应用本项目开发的技术的其他邻近研究领域中感兴趣的材料。

The main objectives of the project is to build an integrated mathematical and computational research program that includes coherently interconnected mathematical disciplines, targeting, but not limited to, some challenge applications in modeling and simulation of complex fluids and atomic strain. The major goal in the project is to understand the flow instabilities in worm-like micellar fluids such as the oscillating falling sphere and jumping bubbles. Using the three species model that takes into account long and short micelles and the shear-induced structure, the conjectured relation between the flow instability and the shear-induced structures will be investigated. The project will introduce the regularization techniques in the complex-fluid models for robust and stable simulations and will integrate them with a fast multigrid solver in the framework of massively parallel computing techniques. Such integrated modeling and computational method is anticipated to make a rheological modeling software. The project is also aimed at developing the new strain modeling and simulation of nano-crystalline materials. The atomic strain model will be developed by applying the finite element methodology for the continuum linear elasticity. Unlike the conventional strain models developed by using the finite difference approximations, the newly proposed model will mirror and take into account the real atomic structures such as the diamond and zinc structures. The model developed in this project will then be used to investigate a sample strain-related nano-structure formation as its application. Complex fluids are ubiquitous in nature and industry and they are used in many important areas, including the pharmaceutical, food, military, bio-materials, printing, and oil industry, just to name a few. Strain in nano-crystalline materials is central in materials science research and understanding the strain is critical to provide guidance for the real-life device design applications such as light emitting diodes, injection lasers and solar cells. Yet, the modeling and simulation of complex fluids and strain in nano-crystalline materials remain formidable and grand challenges, even with modern supercomputers. Among others, the inherent deficiency of existing mathematical models and the inefficiency of conventional numerical techniques are the major bottlenecks, which defeat scientists' attempt to understand and design materials. It is anticipated that the modeling and computation methods developed in this research will remedy both the deficiency in the models and the inefficiency in the computation, thereby drastically eliminating the mathematical and computational bottlenecks and eventually providing valuable guiding tools for scientists to better understand the materials of interest within the scope of this project as well as in a number of other neighboring areas of research where the technologies developed in this project can be applied.