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.
