CAREER: Geometry of Directed Folding and Soft Packing

职业：定向折叠和软包装的几何形状

• 批准号: 0846582
• 负责人: Christian Santangelo
• 金额: $ 41.1万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0846582&HistoricalAwards=false
• 关键词: CAREER; Geometry; Directed; Folding; Soft

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).TECHNICAL SUMMARYThis CAREER award supports an integrated theoretical research and education program to study the controlled formation of complex, three-dimensional structures. Analytical and numerical methods will be used for two related research topics. The first topic will involve a study of the folding of a thin membrane into three-dimensional shapes by controlling the differential in-plane swelling of the membrane. The second topic will focus on the development of a strong-segregation theory for the assembly of prototypical hard core/soft corona particles. This theory will relate the various structures observed in simulation phase diagrams to geometrical invariants and be used to predict the phase diagram in three dimensions of soft corona particles interacting through isotropic and anisotropic interactions.These projects study structure formation in two model systems in which geometry and frustration play a crucial role. The first project seeks to understand how to exploit membrane buckling as a design motif. New geometrical tools will be developed to understand how competition between bending and elastic strain results in three-dimensional shapes. The second project will develop a theory to predict structure in soft corona particle assemblies by relying on universal, geometrical quantities. These projects explore how the fundamental constraints imposed by differential geometry control and limit the packing of continuous two-dimensional objects and other soft materials in three-dimensional space.This CAREER award also supports educational activities, including the training of graduate students, the involvement of undergraduate students in theoretical research, and the development of a short workshop on soft materials that will be used as a recruitment tool during regular visits to predominantly-minority serving colleges and universities. This latter program will be coordinated with the larger efforts of the North Eastern Alliance for Graduate Education and the Professoriate.NONTECHNICAL SUMMARYThis CAREER award supports an integrated theoretical research and education program to study how to control the structure of soft materials. Soft materials are often composed of large molecules that may have many possible orientations leading to possibilities for materials and tiny structures to have complex shapes. The PI aims to study the interplay between the interactions among molecules and geometry to develop ways to control the shapes of soft materials. The research supported by this award will have an impact on materials design by introducing new theoretical techniques for the prediction of how three-dimensional structures can be constructed from soft materials. This CAREER award also supports a number of educational, including the training of graduate students, the involvement of undergraduates in theoretical research, and the development of a short workshop on soft materials that will be used as a recruitment tool during regular visits to predominantly-minority serving colleges and universities. This latter program will be coordinated with the larger efforts of the North Eastern Alliance for Graduate Education and the Professoriate (NEAGEP).

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。技术总结该职业生涯奖支持综合理论研究和教育计划，以研究复杂的三维结构的控制形成。 分析和数值方法将用于两个相关的研究课题。 第一个主题将涉及到一个薄膜的折叠成三维形状的研究，通过控制膜的差分面内溶胀。 第二个主题将集中在一个强偏析理论的原型硬核心/软电晕粒子的组装的发展。该理论将在模拟相图中观察到的各种结构与几何不变量联系起来，并用于预测软电晕粒子通过各向同性和各向异性相互作用相互作用的三维相图。这些项目研究两个模型系统中的结构形成，其中几何和挫折起着关键作用。第一个项目旨在了解如何利用膜屈曲作为一个设计主题。将开发新的几何工具来理解弯曲和弹性应变之间的竞争如何导致三维形状。第二个项目将发展一种理论，依靠普遍的几何量来预测软电晕粒子组件的结构。这些项目探索了微分几何所施加的基本约束如何控制和限制连续二维物体和其他软材料在三维空间中的包装。这个CAREER奖还支持教育活动，包括研究生的培训，本科生参与理论研究，以及举办一个关于软材料的短期讲习班，在定期访问以少数民族为主的学院和大学时将其用作招聘工具。后一个项目将与东北研究生教育联盟和教授会的更大努力相协调。非技术性总结这个职业奖支持一个综合的理论研究和教育项目，研究如何控制软材料的结构。软材料通常由大分子组成，这些大分子可能具有许多可能的取向，从而导致材料和微小结构具有复杂形状的可能性。PI旨在研究分子之间的相互作用和几何形状之间的相互作用，以开发控制软材料形状的方法。该奖项支持的研究将通过引入新的理论技术来预测如何从软材料构建三维结构，从而对材料设计产生影响。该职业奖还支持一些教育项目，包括研究生培训，本科生参与理论研究，以及开发一个关于软材料的短期讲习班，该讲习班将在定期访问以少数民族为主的学院和大学时用作招聘工具。后者计划将与东北研究生教育联盟和教授（NEAGEP）的更大努力协调。