Theoretical Problems in Soft Matter and Quantitative Biology

技术摘要数学科学部和材料研究部为该奖项提供资金。它支持软凝聚态物质和非平衡统计力学的理论研究和教育，在材料研究和数学与生物学的界面。研究内容包括花粉粒和聚合体的种群动态和特性研究。在许多方面，这项研究对非平衡统计力学、生物启发材料和纳米结构的发展做出了贡献。该项目旨在利用理论物理学的方法来理解种群波动，种群波动在包括人类在内的许多物种的进化史上起着至关重要的作用。中性遗传标记可以用来推断有关生长、祖先种群大小和殖民化途径的信息。这种现象可以通过跟踪在培养皿中由剃须刀片接种产生的先锋微生物的遗传分离来实验研究。在生长前沿，由于种群规模小而导致的波动加剧可能导致显着的影响，例如“基因冲浪”。PI计划通过结合非平衡统计力学、概率论和种群遗传学等技术来研究这种现象，特别强调理解“膨胀”如何阻碍二维和三维径向膨胀的分离。PI还计划建立一个详细的理论，包括在人口流动边界的扇区数、固定概率和遗传不稳定性。利用解析和数值方法求解薄壳的Foppl-von Karman方程，PI将探索花粉粒在脱水过程中从一朵花迁移到另一朵花时的折叠策略和形状。晶粒可以被建模为一个具有弱扇区和非零自发曲率的高压高杨模量球体。在缺乏这样一个薄弱部门的情况下，这些壳在强大的不稳定性压力下不可逆转地坍塌。一扇区和三扇区花粉粒的弱扇区消除了滞后现象，使授粉部位容易再水化，有点像折叠椅的折叠和随后的重新组装。指数旨在确定弱势部门的最佳形态和位置，并看看大自然是否确实在特定情况下采用了这种策略。此外，PI将研究热波动如何影响薄壳聚合体，这是一种由双嵌段共聚物制成的抗剪切的新型囊泡。该奖项还通过研究提供的机会支持研究生的跨学科培训。非技术摘要：数学科学部和材料研究部为本奖项提供资金。它支持软凝聚态物质和非平衡统计力学的理论研究和教育，在材料研究和数学与生物学的界面。研究内容包括花粉粒和聚合体的种群动态和特性研究。在许多方面，这项研究对非平衡统计力学、生物启发材料和纳米结构的发展做出了贡献。PI将使用非平衡统计力学和数学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，它可以沿着医用管道或假体设备的表面生长。在这种细菌感染和更普遍的一些疾病中，前沿攻击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，了解花粉粒在干燥环境中是如何折叠的，以及聚合体是如何折叠的。聚合体是由长链状分子组成的囊泡，包裹在液体周围。对聚合体的研究可以更好地理解这些药物包封装置的强度。更好地了解天然材料的功能有助于发现模仿生物学和利用自然设计思想的新材料。这项研究通过更好地理解设计原则和自然力量，为发现新材料、新技术和疾病控制提供了知识基础。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.