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

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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.