CAREER: Geometry of Directed Folding and Soft Packing

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。该职业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受控形成。分析和数值方法将用于两个相关的研究课题。第一个主题将涉及通过控制薄膜的平面内微分膨胀来将薄膜折叠成三维形状的研究。第二个主题将集中于原型硬核/软日冕粒子组装的强偏析理论的发展。该理论将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的三维相图。这些项目研究了两个模型系统中的结构形成，其中几何和挫折起着至关重要的作用。第一个项目旨在了解如何利用膜屈曲作为设计主题。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合的结构。这些项目探索微分几何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的基本约束。该奖项还支持教育活动，包括研究生培训，本科生参与理论研究，以及在定期访问以少数民族为主要服务对象的学院和大学期间，作为招聘工具的软材料短期研讨会的发展。后一项计划将与东北研究生教育和教授联盟的更大努力相协调。这个职业奖支持一个综合的理论研究和教育计划，研究如何控制软材料的结构。软材料通常由大分子组成，这些大分子可能有许多可能的方向，从而使材料和微小结构有可能具有复杂的形状。PI旨在研究分子之间的相互作用和几何之间的相互作用，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用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，以及在定期访问以少数民族为主要服务对象的学院和大学期间，作为招聘工具的软材料短期研讨会的发展。后一个方案将与东北研究生教育和教授联盟（NEAGEP）的更大努力相协调。

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).