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Global Description of Patterns Far from Onset

远未开始的模式的全球描述

基本信息

批准号：
0202440
负责人：
Alan Newell
金额：
$ 12.3万
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：
2002
资助国家：
美国
起止时间：
2002-07-01 至 2005-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0202440&HistoricalAwards=false
关键词：
Global Description Patterns Far Onset

项目摘要

NSF Award Abstract - DMS-0202440Mathematical Sciences: Global Description of Patterns Far from OnsetAbstract0202440 NewellNatural patterns turn up all over the place. One sees them on windswept sand dunes, as ripples on long sandy beaches, on plant skins and animal coats, as fingerprints, on optical beams, in cloud formations. The striking similarities between the textures of patterns and their defects which arise in diverse microscopic situations lead one to the conclusion that patterns are macroscopic objects whose behaviors are well described almost everywhere by universal equations that reflect overall symmetry properties shared by the individual systems. For example, the triradius defect on each human fingertip is also seen on optical beams and in magnetic materials. The reason is not that there is any fundamental connection between light and the fetal epidermis but rather that in both contexts the system under stress is two dimensional with translational and rotational invariance. The equations describing the overall pattern will be the same. The central goal of this research is to develop a global description of such stationary patterns far from onset. Up to now, certain individual parts of the textures were well understood, but there was no theory, for example, to say what the total convection pattern would be in an elliptical container whose side walls were heated.This research project will investigate the common mathematical structure that underlies the diverse occurrence of patterns in nature. The work will contribute to the understanding and prediction of important physical phenomena.

NSF奖摘要- DMS-0202440数学科学：远离开始的模式的全球描述摘要0202440 Newell自然模式出现在所有的地方。人们可以在被风吹的沙丘上看到它们，在长长的桑迪上看到它们的涟漪，在植物的皮肤和动物的皮毛上看到它们的指纹，在光束上看到它们，在云层中看到它们。图案的纹理和它们在不同微观情况下出现的缺陷之间的惊人相似性导致人们得出这样的结论：图案是宏观对象，其行为几乎在任何地方都可以通过反映单个系统共享的整体对称性的通用方程来很好地描述。例如，每个人指尖上的三角缺陷也可以在光束和磁性材料中看到。原因并不在于光和胎儿表皮之间有任何基本的联系，而是在这两种情况下，处于压力下的系统都是二维的，具有平移和旋转不变性。描述整体模式的方程将是相同的。这项研究的中心目标是开发一个全球性的描述这种静止的模式远离发病。到目前为止，人们对纹理的某些部分已经有了很好的了解，但还没有理论来说明，例如，在一个侧壁被加热的椭圆形容器中，总的对流模式会是什么。本研究项目将研究自然界中各种模式出现的共同数学结构。这项工作将有助于理解和预测重要的物理现象。