Multi-constituent inhibitory systems with self-organizing properties

具有自组织特性的多成分抑制系统

• 批准号: 1311856
• 负责人: Xiaofeng Ren
• 金额: $ 14.97万
• 依托单位: George Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-15 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1311856&HistoricalAwards=false
• 关键词: Multi; constituent; inhibitory; systems; self

This project investigates several important binary and ternary systems with self-organizing properties, with an emphasis on ternary systems and the longer ranging confinement mechanism through nonlocal interaction or inhibitor variables. One intriguing feature that sets ternary systems apart from binary systems is the triple junction phenomenon. The three constituents of the system may meet at a point in the two dimensional case or at a curve in the three dimensional case. The PI proposes to show the existence of a double bubble assembly pattern, where the triple junction phenomenon occurs in each double bubble. Two novel techniques, restricted perturbation classes and internal variables, will be used in the proof. The second feature in ternary systems is the complexity of the long range interaction manifested in a two by two matrix of parameters. For instance it will be shown that the core-shell pattern appears only if the 2-2 entry is greater than the 1-2 entry of the matrix. When multi-constituent inhibitory systems appear in a curved space, such as a vesicle of lipid membranes, the role played by the Riemann curvature will also be investigated. Patterns and their possible defects will be shown as a balance and compromise of growth, inhibition, and curvature. Exquisitely structured patterns arise in many multi-constituent physical and biological systems as orderly outcomes of self-organization principles. Examples include morphological phases in block copolymers, animal coats, and skin pigmentation. Common in these pattern-forming systems is that a deviation from homogeneity has a strong positive feedback on its further increase. On its own, it would lead to an unlimited increase and spreading. Pattern formation requires in addition a longer ranging confinement of the locally self-enhancing process. This project derives geometrical patterns from self-organization principles in various binary and ternary physical and biological systems. Analysis of these geometric structures is a fundamental step in understanding the mechanical, optical, electrical, ionic, barrier and other properties of these systems. This project supports a culturally diverse environment that fosters critical and independent thinking both in classroom and research settings in the ethnically diverse metropolitan area of Washington, DC. It produces mathematics of depth and beauty, and offers profound insights into the natural world.

该项目研究了几个重要的二元和三元系统的自组织特性，重点是三元系统和更长范围的限制机制，通过非局部相互作用或抑制剂变量。三元体系与二元体系的一个有趣的区别是三元结现象。系统的三个组成部分可以在二维情况下在一点处相遇，或者在三维情况下在一条曲线处相遇。PI建议显示双气泡组装模式的存在，其中在每个双气泡中发生三重连接现象。两个新的技术，限制扰动类和内部变量，将用于证明。三元体系的第二个特征是长程相互作用的复杂性，表现在二乘二的参数矩阵中。例如，它将表明，只有当矩阵的2-2项大于1-2项时，核壳模式才会出现。当多组分抑制系统出现在一个弯曲的空间，如脂膜囊泡，黎曼曲率所发挥的作用也将被调查。模式及其可能的缺陷将显示为生长，抑制和曲率的平衡和妥协。在许多多成分的物理和生物系统中，作为自组织原理的有序结果，出现了结构精美的模式。实例包括嵌段共聚物中的形态相、动物皮毛和皮肤色素沉着。这些模式形成系统的共同点是，偏离均匀性会对进一步增加产生强烈的正反馈。它本身会导致无限的增长和蔓延。图案形成还需要局部自增强过程的更长范围的限制。这个项目从各种二元和三元物理和生物系统的自组织原理中推导出几何图案。分析这些几何结构是理解这些系统的机械、光学、电学、离子、势垒和其他性质的基本步骤。这个项目支持一个文化多样的环境，促进批判性和独立思考，无论是在课堂上和研究设置在种族多元化的大都会地区的华盛顿，DC。 它产生了深度和美丽的数学，并提供了对自然世界的深刻见解。