Transport and Reactions in Complex Heterogeneous Multiphase Systems

该项目的目标是基于数学、物理和热力学原理，为复杂多相系统中的输运和反应建立一个可靠的理论和计算框架。该项目包括两个贯穿始终的主题：1.建模和分析的新的，有效的宏观运输配方的催化剂在燃料电池中，允许可靠的，有效的，和低维的计算方案相比，模型完全解决微观尺度。2.发展一个新的计算多尺度框架在复杂的非均相多相系统中的传输和反应。该项目采用严格的数学和物理建模，采用最先进的方法，如基于变分法，梯度流，统计力学和热力学的变分，物理和热力学分析，以及新颖的计算方法，允许复杂的多相系统的可靠和有效的离散化。最终目的是系统的和预测性的理论和计算分析，以及复杂的非均相多相系统的优化，以降低材料成本和增加寿命的一个新的和一般的计算多尺度框架的目标。因此，拟议工作的结果将指导实验，以获得对基本化学，物理和热力学过程的基本理解，但最终将推荐新的设计规则，材料，几何形状，工艺和操作策略，以及新的测量技术。最后，该项目为随后的随机复杂非均质多相系统的理论和计算研究奠定了基础，这些系统在许多应用中自然发生。

The goal of this project is to develop a reliable, theoretical, and computational framework for transport and reactions in complex heterogeneous multiphase systems based on mathematical, physical, and thermodynamic principles.The project consists of two main themes with cross-linking throughout: 1. Modelling and analysis of novel, effective macroscopic transport formulations for catalysts in fuel cells that allow for reliable, efficient, and low dimensional computational schemes in contrast to models fully resolving the microscale. 2. Developing a novel computational multiscale framework for transport and reactions in complex heterogeneous multiphase systems. The project applies rigorous, mathematical and physical modelling with state-of-the-art methodologies such as variational, physical, and thermodynamic analysis based on calculus of variations, gradient flows, statistical mechanics and thermodynamics as well as novel computational approaches allowing for the reliable and efficient discretisation of complex heterogeneous multiphase systems. The ultimate aim is the systematic and predictive theoretical and computational analysis as well as the optimization of complex heterogeneous multiphase systems with the goal of reducing material costs and of increasing longevity by a novel and general computational multiscale framework. As a consequence, the results from the proposed work shall guide experiments for gaining fundamental understanding of the underlying chemical, physical, and thermodynamic processes but shall ultimately recommend new design rules, materials, geometries, processes and operation strategies, as well as novel measurement techniques. Finally, this project builds the fundamental basis for the subsequent theoretical and computational investigation of random complex heterogeneous multiphase systems which naturally occur in many applications.