CAREER: Chiral Molecules, Structures and Materials

9732963 Kamien这是一个职业奖项，用于进行理论研究和发展相关的教育活动。特别是，首席研究员将研究手性分子体系，既包括通过研究单一手性聚合物(如DNA)在稀释极限下的研究，也包括在形成手性液晶的半稀释极限下的研究。在稀疏极限下，当n趋于零时，自回避随机游动与n分量Ising模型之间的精确映射的推广可以用来研究手征随机游动。正如单个自回避行走理论可以用来研究聚合物的半稀化熔体一样，这个推广也可以用来研究拓扑连接的聚合物的半稀化熔体。我们的计划是结合一些实验来追求这一点，并通过与数值相比较来增强分析理论。在浓度较高的区域，手性聚合物可以形成液晶相，如聚合物胆甾相和柱状六方相。通常，手性相互作用会因为分子的液晶堆积而受挫。最近对DNA的实验似乎发现了一个受挫阶段，在这个阶段没有手性，尽管理论表明没有受挫。对晶体或液晶有序对手性相互作用的影响进行广泛的分析，作为对观察到的相中手性弱于预期的可能解释。与研究计划相结合，将开发一门针对一年级学生的课程，主题是性质上的手性对称性。通过历史和科学的阐述，讲师将手性描述为引入对称概念的一种方式。由于手性是许多科学和工程中的中心概念，本课程将贯穿历史，涉及手性在不同背景下的使用和发现。这篇论文将包括巴斯德对手性的发现，蛋白质和DNA的结构，以及基本粒子物理学中宇称破坏的发现。课程将辅以简单的演示，例如玉米糖浆和石英中光的偏振旋转。最后，我们将讨论宇宙中的左右不对称，即重子不对称。这是一个集研究和教育于一体的职业奖项。在这种特殊情况下，将对手性分子体系进行理论研究。手性是自然界中区分左右对称性的系统的属性。手性聚合物，如DNA，以及形成手性液晶相的更浓缩的溶液将被研究。与研究计划相结合，将开发一门针对一年级学生的课程，主题是性质上的手性对称性。通过历史和科学的阐述，讲师将手性描述为引入对称概念的一种方式。由于手性是许多科学和工程中的中心概念，本课程将贯穿历史，涉及手性在不同背景下的使用和发现。这篇论文将包括巴斯德对手性的发现，蛋白质和DNA的结构，以及基本粒子物理学中宇称破坏的发现。课程将辅以简单的演示，例如玉米糖浆和石英中光的偏振旋转。最后，我们将讨论宇宙中的左右不对称，即重子不对称。***

9732963 Kamien This is a CAREER award to conduct theoretical research and to develop associated education activities. In particular, the principal investigator will study chiral molecular systems, both in the dilute limit by studying single chiral polymers, such as DNA, as well as in the semi-dilute limit where they form chiral liquid crystals. In the dilute limit a generalization of the exact mapping between self-avoiding random walks and the n-component Ising model, as n approaches zero, can be used to study chiral random walks. Just as the theory of a single self-avoiding walk can be used to study a semi-dilute melt of polymers, this extension can be used to study a semi-dilute melt of topologically linked polymers. The plan is to pursue this in connection with a number of experiments and to augment analytical theory with comparison to numerics. In the more concentrated regime, chiral polymers can form liquid crystalline phases such as the polymer cholesteric phase and the columnar hexagonal phase. Often, the chiral interactions are frustrated by the liquid crystalline packing of the molecules. Recent experiments on DNA appear to find a frustrated phase in which chirality is absent although theory suggests there is no frustration. An extensive analysis of the effect of the crystalline or liquid-crystalline order on the chiral interaction will be pursued as a possible explanation of the weaker than expected chirality in the observed phase. Integrated with the research program, a course will be developed aimed at first-year students on the subject of chiral symmetry in nature. Through both historic and scientific exposition the instructor will describe chirality as a way of introducing the idea of symmetry. Since chirality is a central notion in much of science and engineering, the course will thread through history touching on the use and discovery of chirality in different contexts. This discourse will include Pasteur's discovery of chirality, the structure of proteins and DNA as well as the discovery of parity violation in elementary particle physics. Lectures will be supplemented with simple demonstrations, such as rotation of the polarization of light in corn syrup and quartz. Finally, a discussion of left-right asymmetry in the Universe, i.e., baryon asymmetry, will be presented. %%% This is a CAREER award which integrates research and education. In this particular case, theoretical research will be conducted on the chiral molecular systems. Chirality is the property of systems in nature which distinguishes between left and right symmetry. Chiral polymers, such as DNA, will be studied as well as more concentrated solutions which form chiral liquid crystal phases. Integrated with the research program, a course will be developed aimed at first-year students on the subject of chiral symmetry in nature. Through both historic and scientific exposition the instructor will describe chirality as a way of introducing the idea of symmetry. Since chirality is a central notion in much of science and engineering, the course will thread through history touching on the use and discovery of chirality in different contexts. This discourse will include Pasteur's discovery of chirality, the structure of proteins and DNA as well as the discovery of parity violation in elementary particle physics. Lectures will be supplemented with simple demonstrations, such as rotation of the polarization of light in corn syrup and quartz. Finally, a discussion of left-right asymmetry in the Universe, i.e., baryon asymmetry, will be presented. ***