Collaborative Research: GCR: Collective Behavior and Patterning of Topological Defects: From String Theory to Crystal Plasticity

该项目旨在开发一个统一的数学和概念框架，以描述拓扑缺陷并了解它们的相互作用和运动，利用工程，物理和数学的见解。拓扑缺陷出现在一系列令人震惊的现象中，从宇宙中的图案，到我们星球地壳中断层面上的破裂前沿，到汽车或喷气发动机或摩天大楼中金属的微观结构，到我们手机屏幕中的分子排列，并可能一直到物质本身的亚原子成分。潜在的，从这项研究中获得的新知识可以用来种子在地震预测，基础设施更新和节能运输的重大挑战相关的技术进步，研究小组将致力于建立一个收敛的定量语言的拓扑缺陷动力学的物理系统，解决看似无关的物理现象之间的共性。 他们将开发理论和计算工具，通过利用当前跨越工程，物理和数学的不同领域的见解来探测拓扑缺陷的结构，动力学和集体行为。主要焦点将是弦理论/量子引力如何与晶体固体中的缺陷力学相关的科学问题，使用全息对偶来研究反DeSitter空间中的弦理论，以了解强耦合凝聚态系统。了解塑性满足了社会对轻质、高强度、弹性金属材料的迫切需求，这些材料可用于节能运输、建筑基础设施和国防。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project seeks to develop a unifying mathematical and conceptual framework to describe topological defects and understand their interactions and motions, capitalizing on a convergence of insights from engineering, physics and mathematics. Topological defects show up throughout a stunningly wide range of phenomena, ranging from patterns in the cosmos, to rupture fronts on fault planes in our planet’s crust, to the microscopic structure of the metal in an automobile or a jet engine or a skyscraper, to the arrangements of molecules in our phone screens, and potentially all the way down to the subatomic constituents of matter itself. Potentially, new knowledge from this research can be leveraged to seed advances in technology relevant for grand challenges in seismic forecasting, infrastructure renewal, and energy-efficient transportation.The research team will work on establishing a convergent quantitative language of topological defect dynamics in physical systems that addresses commonalities between seemingly unrelated physical phenomena. They will develop theoretical and computational tools for probing the structure, dynamics, and collective behavior of topological defects by leveraging insights from currently disparate fields spanning engineering, physics, and mathematics. The primary focus will be the scientific question of how string theory/quantum gravity is related to the mechanics of defects in crystalline solids, using holographic dualities developed to study string theory in anti-DeSitter space to learn about strongly coupled condensed matter systems. Understanding plasticity serves the pressing societal need for light-weight, high-strength, resilient metallic materials for energy-efficient transportation, built infrastructure, and defense.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.