ITR/AP: Interactive Spatial Physics: Computational Foundations and Systems

该项目的目标是开发一种交互式几何方法来创建，编辑，转换和计算空间分布的物理现象的模型。资助的工作将涉及充实健全的理论基础，开发适当的数据结构和算法，以及实现交互式物理建模的原型系统。 该提案的核心是使用代数拓扑和几何代数工具来描述，分类和统一物理现象。 原型系统将允许用户通过根据熟悉和直观的控制元素设计的交互式几何界面创建物理现象模型。 所创建的模型可以被交互地变换、修改、组合、可视化和实例化。 拟议研究的成功结果应具有广泛的技术、经济、教育和社会影响。物理编辑器将允许用户快速轻松地创建，可视化，测试和实验物理现象的新模型。它可以大大提高有效创建和修改模块化、可重用和跨学科一致的科学软件的能力。工程师可能会发现一种实用的工具，使他们能够以直观的语言与计算机辅助设计系统进行交流，这种语言不需要深入的数学知识，并统一了大量的理论和特殊情况。也许最重要的是，拟议中的研究可以为大学和高中学生以及其他可能被数学物理和科学计算的传统方法所劝阻或恐吓的人打开计算科学的大门。

The goal of this project is to develop an interactive geometric approach to creating, editing, transforming, and computing with models of spatially distributed physical phenomena. The funded effort will involve fleshing out sound theoretical foundations, developing appropriate data structures and algorithms, as well as implementing a prototype system for interactive physical modeling. At the heart of the proposal is a novel use of tools from algebraic topology and geometric algebra to describe, classify, and unify physical phenomena. The prototype system will allow users to create models of physical phenomena through an interactive geometric interface designed in terms of familiar and intuitive control elements. The created models may be interactively transformed, modified, combined, visualized, and instantiated. The successful outcome of the proposed research should have broad technological, economic, educational, and social impact. The physics editor will allow users to create, visualize, test, and experiment with new models of physical phenomena quickly and effortlessly. It could greatly enhance the ability to efficiently create and modify scientific software that is modular, reusable, and consistent across the disciplinary boundaries. Engineers may discover a practical tool that will allow them to communicate with computer-aided design systems in a visual intuitive language that does not require deep mathematical knowledge and unifies a multitude of theories and special cases. And perhaps most importantly, the proposed research could open doors of computational sciences to college and high school students and others who may have been discouraged or intimidated by traditional methods of mathematical physics and scientific computing.