次优势指数的渐近优势

M. Berry
{"title":"次优势指数的渐近优势","authors":"M. Berry","doi":"10.1098/rspa.2004.1343","DOIUrl":null,"url":null,"abstract":"A prevalent though unexpected asymptotic phenomenon occurs near anti–Stokes lines, on which two exponentials contributing to a function have the same absolute value: the subdominant exponential contribution can be larger than that from the dominant exponential. The phenomenon arises because the factors multiplying the two exponentials have different asymptotic forms. The boundary of the region of dominance by the subdominant exponential (DSE) is a line, for which an explicit general form is given; this shows that the region of DSE is asymptotically infinitely wide. The DSE line contains the zeros of the function, resulting from complete destructive interference between the two exponential contributions. Several examples are given; two have a physical origin in diffraction physics, and illustrate the fact that DSE can explain observed optical phenomena.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2004-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Asymptotic dominance by subdominant exponentials\",\"authors\":\"M. Berry\",\"doi\":\"10.1098/rspa.2004.1343\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A prevalent though unexpected asymptotic phenomenon occurs near anti–Stokes lines, on which two exponentials contributing to a function have the same absolute value: the subdominant exponential contribution can be larger than that from the dominant exponential. The phenomenon arises because the factors multiplying the two exponentials have different asymptotic forms. The boundary of the region of dominance by the subdominant exponential (DSE) is a line, for which an explicit general form is given; this shows that the region of DSE is asymptotically infinitely wide. The DSE line contains the zeros of the function, resulting from complete destructive interference between the two exponential contributions. Several examples are given; two have a physical origin in diffraction physics, and illustrate the fact that DSE can explain observed optical phenomena.\",\"PeriodicalId\":20722,\"journal\":{\"name\":\"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rspa.2004.1343\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.2004.1343","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3

摘要

在反斯托克斯线附近出现了一种普遍但意想不到的渐近现象,在这种现象上,对一个函数有贡献的两个指数具有相同的绝对值:次优势指数的贡献可能大于优势指数的贡献。这一现象的产生是因为两个指数相乘的因子具有不同的渐近形式。次优势指数(DSE)优势区域的边界是一条直线,并给出了其一般形式;这表明DSE的区域是渐近无限宽的。DSE线包含函数的零点,这是由于两个指数贡献之间的完全相消干涉造成的。给出了几个例子;两个在衍射物理学中有物理起源,并说明了DSE可以解释观察到的光学现象的事实。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic dominance by subdominant exponentials
A prevalent though unexpected asymptotic phenomenon occurs near anti–Stokes lines, on which two exponentials contributing to a function have the same absolute value: the subdominant exponential contribution can be larger than that from the dominant exponential. The phenomenon arises because the factors multiplying the two exponentials have different asymptotic forms. The boundary of the region of dominance by the subdominant exponential (DSE) is a line, for which an explicit general form is given; this shows that the region of DSE is asymptotically infinitely wide. The DSE line contains the zeros of the function, resulting from complete destructive interference between the two exponential contributions. Several examples are given; two have a physical origin in diffraction physics, and illustrate the fact that DSE can explain observed optical phenomena.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊介绍: Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信