Patterns in Nature and in the Laboratory

自然界和实验室中的模式

• 批准号: 0906024
• 负责人: Alan Newell
• 金额: $ 28.8万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906024&HistoricalAwards=false
• 关键词: Patterns; Nature; Laboratory

The work will address two basic themes. First, we will attempt to understand more precisely why it is that the patterns seen near the shoot apical meristems of plants so often exhibit Fibonacci sequences, that is, leaves, bracts, and stickers lie on families of spirals enumerated by Fibonacci sequences. The study will explore both the mechanisms through which the biological structures are initiated and the nature of the patterns themselves. From work to date, it would seem that Fibonacci patterns are the preferred pattern in annular geometries in circumstances where the pattern gets laid down sequentially, annulus by annulus, so that the pattern forming region is quite narrow and the bias from the previously laid down structures is strong. Connections with optimal packing will be part of the study. Second, we will revisit the general description of patterns with the particular aim of understanding better the nature of the point and line singularities which occur when one moves from a microscopic description to a macroscopic description of the system by averaging over the pattern wavelength. What is intriguing is that the three dimensional line defects of such patterns have naturally defined indices of plus and minus one and two thirds and plus and minus one and that the masses of the former are much larger. Also, the defects have an additional natural index of one half. Possible connections with quarks and leptons will be explored. Patterns turn up all over the place. One sees them on desert dunes, on long sandy beaches, in cloud formations, on fingertips and animal coats, on the feathers of birds, and on fish skins. They are also ubiquitous in laboratory experiments on convection in fluids, on broad laser beams, and on flame fronts. Many of the patterns arising in different microscopic contexts have textures with much in common, so that by studying patterns in one context one can learn about their behaviors in other systems that share key symmetry properties. Besides being of interest for their intrinsic beauty, patterns are also worth studying for practical reasons. They have many potential uses from switches to information storage devices. They also tend to be the structures which, in certain special circumstances, can optimize such things as heat transfer in fluids and light gathering capacity in plants. This project will investigate fundamental questions underlying pattern formation, with the goal of providing deeper insight into this important phenomenon.

这项工作将涉及两个基本主题。 首先，我们将试图更准确地理解为什么在植物茎尖分生组织附近看到的图案经常表现出斐波那契序列，也就是说，叶，苞片和贴纸位于斐波那契序列所列举的螺旋家族上。 这项研究将探索生物结构启动的机制和模式本身的性质。 从迄今为止的工作来看，似乎斐波那契图案是环形几何形状中的优选图案，在这种情况下，图案依次被环形地铺设，使得图案形成区域相当窄，并且来自先前铺设的结构的偏差很强。 与最佳包装的连接将是研究的一部分。 第二，我们将重新审视模式的一般描述，特别是为了更好地理解点奇点和线奇点的性质，这些奇点是在通过对模式波长进行平均，从系统的微观描述转向宏观描述时发生的。 有趣的是，这种图案的三维线缺陷具有自然定义的正和负1和2/3以及正和负1的指数，并且前者的质量要大得多。 此外，缺陷具有二分之一的附加自然指数。 与夸克和轻子的可能联系将被探索。 到处都有作案模式 人们可以在沙丘上、长长的桑迪上、云层中、指尖和动物皮毛上、鸟类羽毛上和鱼皮上看到它们。 它们也普遍存在于流体对流、宽激光束和火焰前沿的实验室实验中。 在不同的微观环境中出现的许多模式都有许多共同的纹理，因此通过研究一种环境中的模式，人们可以了解它们在其他系统中的行为，这些系统具有关键的对称性。 除了因其内在的美而令人感兴趣之外，模式也因实用的原因而值得研究。 它们有许多潜在的用途，从交换机到信息存储设备。 它们也往往是在某些特殊情况下可以优化流体中的热传递和植物中的光收集能力等事情的结构。 本项目将研究模式形成的基本问题，目的是更深入地了解这一重要现象。