Theoretical Problems in Soft Matter and Quantitative Biology

技术总结数学科学部和材料研究部为该奖项提供资金。它支持在材料研究和数学与生物的交界处进行软凝聚态和非平衡统计力学的理论研究和教育。这项研究包括花粉粒和多聚体的种群动态和性质的研究。这项研究以不同的方式促进了非平衡统计力学以及生物启发材料和纳米结构的发展。PI的目标是使用理论物理的方法来理解种群波动，这些种群波动在包括人类在内的许多物种的进化史中发挥了关键作用。中性遗传标记可用于推断有关生长、祖先种群大小和殖民路径的信息。通过在培养皿中跟踪剃须刀片接种产生的先锋微生物的遗传分解，可以实验地研究这种现象。在不断增长的前沿，由于种群规模较小而导致的波动加剧，可能会导致显著的影响，如“基因冲浪”。PI计划通过非平衡统计力学、概率论和种群遗传学的技术组合来研究这种现象，特别强调了解“通货膨胀”如何阻碍二维和三维径向扩张的混合。PI还计划构建一个关于种群移动边界的扇区数量、固定概率和遗传不稳定性的详细理论。使用解析和数值方法求解薄壳Foppl-von Karman方程，PI将探索花粉颗粒在脱水过程中从花迁移到花的折叠策略和形状。颗粒可模拟为具有弱扇形和非零自发曲率的加压高杨氏模数球体。在没有如此脆弱的部分的情况下，这些壳在压力下通过强烈的不稳定不可逆转地皱缩。一个扇形和三个扇形花粉粒的弱扇形部分消除了滞后现象，使授粉部位易于复水，有点像折叠椅的坍塌和随后的重新组装。PI旨在确定薄弱部分的最佳形状和位置，并看看大自然是否确实在特定情况下采取了此类策略。此外，PI还将研究热波动如何影响薄壳聚合体，这是一种由两嵌段共聚物制成的抗剪切的新型囊泡。该奖项还支持通过研究提供的机会对研究生进行跨学科培训。非技术总结：数学科学部和材料研究部为该奖项提供资金。它支持在材料研究和数学与生物的交界处进行软凝聚态和非平衡统计力学的理论研究和教育。这项研究包括花粉粒和多聚体的种群动态和性质的研究。这项研究以不同的方式促进了非平衡统计力学以及生物启发材料和纳米结构的发展。PI将使用非平衡统计力学和数学中的技术来理解生物有机体的迁移。潜在的应用包括阻止有害细菌，如铜绿假单胞菌，它可以沿着医疗管子或假肢设备的表面生长。在这种细菌感染以及更普遍的一些疾病中，在前沿攻击的基因组进化以逃避免疫系统的速度可以决定患者的生死。这项研究的第二个重点是利用材料和几何的基本原理来理解当花粉颗粒暴露在干燥的环境中时，它是如何折叠到自己身上的，以及聚合体是如何皱缩的。聚合体是由长链状分子组成的包围液体的囊泡。对聚合体的研究可能有助于更好地了解这些药物包埋装置的强度。更好地了解自然材料的功能有助于发现模仿生物的新材料并利用自然的设计思想。这项研究通过更好地了解自然的设计原则和力量，为发现新材料、新技术和疾病控制奠定了智力基础。该奖项还通过研究提供的机会支持研究生的跨学科培训。

TECHNICAL SUMMARYThe Division of Mathematical Sciences and the Division of Materials Research contribute funds to this award. It supports theoretical research and education on soft condensed matter and non-equilibrium statistical mechanics at the interface of materials research and mathematics with biology. The research includes the study of population dynamics and properties of pollen grains and polymersomes. In various ways, the research contributes to the advance of non-equilibrium statistical mechanics, and biologically inspired materials and nanostructures. The PI aims to use methods from theoretical physics to understand the population waves which have played a crucial role in the evolutionary history of many species, including humans. Neutral genetic markers can be used to infer information about growth, ancestral population size and colonization pathways. Such phenomena can be studied experimentally by tracking the genetic de-mixing of pioneer micro-organisms arising from razor blade inoculations in a Petri dish. Enhanced fluctuations due to small population sizes at a growing front can lead to remarkable effects, such as "gene surfing". The PI plans to study such phenomena through a combination of techniques from non-equilibrium statistical mechanics, probability theory, and population genetics, with particular emphasis understanding how "inflation" impedes de-mixing of radial expansions in two and three dimensions. The PI also plans to construct a detailed theory of sector numbers, fixation probabilities and genetic instabilities at moving population frontiers. Using analytical and numerical methods for solving the Foppl-von Karman equations for thin shells, the PI will explore folding strategies and shapes of pollen grains during dehydration as they migrate from flower to flower. The grain can be modeled as a pressurized high-Young-modulus sphere with a weak sector and a nonzero spontaneous curvature. In the absence of such a weak sector, these shells crumple irreversibly under pressure via a strong instability. The weak sectors of both one and three-sector pollen grains eliminate the hysteresis and allow easy rehydration at the pollination site, somewhat like the collapse and subsequent reassembly of a folding chair. The PI aims to determine the optimal shape and position of the weak sectors, and see if nature has indeed adopted such strategies in specific cases. In addition, the PI will study how thermal fluctuations affect thin-shelled polymersomes, a new kind of vesicle that resists shear and is made from diblock copolymers. This award also supports interdisciplinary training for graduate students through the opportunities provided by the research. NONTECHNICAL SUMMARY:The Division of Mathematical Sciences and the Division of Materials Research contribute funds to this award. It supports theoretical research and education on soft condensed matter and non-equilibrium statistical mechanics at the interface of materials research and mathematics with biology. The research includes the study of population dynamics and properties of pollen grains and polymersomes. In various ways, the research contributes to the advance of non-equilibrium statistical mechanics, and biologically inspired materials and nanostructures. The PI will use techniques from non-equilibrium statistical mechanics and mathematics to understand migrations of biological organisms. Potential applications include impeding harmful bacteria, such as Pseudomonas aeruginosa, which can grow along the surfaces of medical tubing or prosthetic devices. In such bacterial infections and more generally some diseases, the rate at which the attacking genome at the frontier evolves to evade the immune system, can determine whether patients live or die. A second thrust of the research is to understand how a pollen grain folds onto itself when it is exposed to a dry environment and polymersomes crumple using the fundamental principles of materials and geometry. Polymersomes are vesicles that are made of long chain-like molecules and surround liquid. The investigation of polymersomes could lead to a better understanding of the strength of these drug encapsulation devices. A better understanding of how natural materials function contributes to efforts to discover new materials that mimic biology and exploit nature's design ideas.This research contributes to the intellectual foundations of the discovery of new materials, new technologies, and disease control through a better understanding of the design principles and forces of nature.This award also supports interdisciplinary training for graduate students through the opportunities provided by the research.