CAREER: Fundamental Research in Geometric Folding

摘要建议：0347776机构：麻省理工学院校长助理：Demaine，Erik D.职称：职业：几何折叠基础研究职业：几何折叠基础研究折叠和展开是计算几何学的一个新兴领域，研究几何对象的连续运动和重新配置，如连杆，纸张和多面体及其物理表现，如蛋白质，包装和金属板。 折叠问题出现在令人惊讶的许多情况下，从纯粹的计算几何到ad-hoc无线网络到蛋白质折叠。 本研究旨在建立几何折叠的基本理论，并随着该理论的发展，探索在科学和工程中的潜在应用。 潜在的应用包括安全气囊设计，空间部署和药物设计。 如何有效地计算运动，重新配置之间的任何两个所需的配置平面链联动？ 对于边长相等的三维链机构，是否总是存在这样的运动？ 核糖体可以生物合成哪些蛋白质构型（被视为3D链连接）？ 在疏水-亲水模型中，如何有效地设计蛋白质，使其稳定地折叠成所需的形状？无线信标在给定其邻居的局部信息的情况下如何有效地在全球几何中定位自己？如何有效地将纸张设计成所需的形状？ 一个多面体要切割成多少块才能不重叠地展开？ 除了解决诸如此类的问题，研究人员正在共同撰写一本关于折叠的书，并正在追求折叠本身作为一个有趣的领域和作为在其他领域呈现材料的工具的教育。

ABSTRACTPROPOSAL: 0347776INSTITUTION: MITPRINCIPAL INVESTIGATOR: Demaine, Erik D.TITLE: CAREER: Fundamental Research in Geometric FoldingCAREER: Fundamental Research in Geometric FoldingFolding and unfolding is an emerging field of computational geometry studying the continuous motion and reconfiguration of geometric objects such as linkages, paper, and polyhedra and their physical manifestations such as proteins, packaging, and sheet metal. Folding problems arise in surprisingly many contexts, ranging from pure computational geometry to ad-hoc wireless networks to protein folding. This research aims to build a basic theory of geometric folding and, as this theory develops, to explore potential applications throughout science and engineering. Potential applications include air-bag design, space deployment, and drug design.This research addresses several fundamental unsolved problems in geometric folding. How can one efficiently compute motions that reconfigure a planar chain linkage between any two desired configurations? Do such motions always exist for 3D chain linkages whose edge lengths are all equal? Which configurations of proteins (viewed as a 3D chain linkage) can be biosynthesized by a ribosome? How efficiently can one-design proteins in the hydrophobic-hydrophilic model that fold stably into a desired shape? How efficiently can wireless beacons locate themselves in a global geometry given just local information about their neighbors? How efficiently can be design optimal foldings of paper into desired shapes? How many pieces must a polyhedron be cut into to unfold without overlap? In addition to solving problems such as these, the investigator is coauthoring a book about folding and is pursuing education of folding both as an interesting area in its own right and as a vehicle for presenting material in other areas.